ACIDS AND BASES PDF

14: ACIDS AND BASES  CHAPTER OVERVIEW 14: Acids and Bases Acids and bases are common substances found in many every day items, from fruit juices and soft drinks to soap. In this chapter, we will examine the properties of acids and bases, and learn about the chemical nature of these important comp...

14: ACIDS AND BASES  CHAPTER OVERVIEW 14: Acids and Bases Acids and bases are common substances found in many every day items, from fruit juices and soft drinks to soap. In this chapter, we will examine the properties of acids and bases, and learn about the chemical nature of these important compounds. We will cover pH, and how to calculate the pH of a solution. 14.1: Sour Patch Kids and International Spy Movies 14.2: Acids- Properties and Examples 14.3: Bases- Properties and Examples 14.4: Molecular Definitions of Acids and Bases 14.5: Reactions of Acids and Bases 14.6: Acid–Base Titration 14.7: Strong and Weak Acids and Bases 14.8: Water - Acid and Base in One 14.9: The pH and pOH Scales - Ways to Express Acidity and Basicity 14.10: Buffers- Solutions that Resist pH Change 14.11: Prelude - Sour Patch Kids 14: Acids and Bases is shared under a CC BY-NC-SA 3.0 license and was authored, remixed, and/or curated by Marisa Alviar-Agnew & Henry Agnew. 1 14.1: Sour Patch Kids and International Spy Movies Sour Patch Kids are a soft candy with a coating of invert sugar and sour sugar. The candy's slogan, "Sour. Sweet. Gone.", refers to its sour-to-sweet taste. Figure 14.1.1 : Sour Patch Kids candies. Image courtesy of Evan-Amos (public domain). Sour sugar is a food ingredient that is used to impart a sour flavor, made from citric or tartaric acid and sugar. It is used to coat sour candies like Sour Patch Kids. Eating large amounts of sour sugar can cause irritation of the tongue because of the acid. It can also cause irreversible dental erosion. This page titled 14.1: Sour Patch Kids and International Spy Movies is shared under a CC BY-SA 4.0 license and was authored, remixed, and/or curated by Marisa Alviar-Agnew & Henry Agnew via source content that was edited to the style and standards of the LibreTexts platform. 14.1.1 https://chem.libretexts.org/@go/page/47552 14.2: Acids- Properties and Examples  Learning Objectives Examine properties of acids. Many people enjoy drinking coffee. A cup first thing in the morning helps start the day. But keeping the coffee maker clean can be a problem. Lime deposits build up after a while and slow down the brewing process. The best cure for this is to put vinegar (dilute acetic acid) in the pot and run it through the brewing cycle. The vinegar dissolves the deposits and cleans the maker, which will speed up the brewing process back to its original rate. Just be sure to run water through the brewing process after the vinegar, or you will get some really horrible coffee. Acids Acids are very common in some of the foods that we eat. Citrus fruits such as oranges and lemons contain citric acid and ascorbic acid, which is better known as vitamin C. Carbonated sodas contain phosphoric acid. Vinegar contains acetic acid. Your own stomach utilizes hydrochloric acid to digest food. Acids are a distinct class of compounds because of the properties of their aqueous solutions as outlined below: 1. Aqueous solutions of acids are electrolytes, meaning that they conduct electrical current. Some acids are strong electrolytes because they ionize completely in water, yielding a great many ions. Other acids are weak electrolytes that exist primarily in a non-ionized form when dissolved in water. 2. Acids have a sour taste. Lemons, vinegar, and sour candies all contain acids. 3. Acids change the color of certain acid-base indicates. Two common indicators are litmus and phenolphthalein. Blue litmus turns red in the presence of an acid, while phenolphthalein turns colorless. 4. Acids react with active metals to yield hydrogen gas. Recall that an activity series is a list of metals in descending order of reactivity. Metals that are above hydrogen in the activity series will replace the hydrogen from an acid in a single-replacement reaction, as shown below: Zn (s) + H SO (aq) → ZnSO (aq) + H (g) (14.2.1) 2 4 4 2 5. Acids react with bases to produce a salt compound and water. When equal moles of an acid and a base are combined, the acid is neutralized by the base. The products of this reaction are an ionic compound, which is labeled as a salt, and water. It should not be hard for you to name several common acids (but you might find that listing bases is a little more difficult). Below is a partial list of some common acids, along with some chemical formulas: Table 14.2.1 : Common Acids and Their Uses Chemist Name Common Name Uses Used in cleaning (refining) metals, in muriatic acid (used in pools) and stomach acid hydrochloric acid, HCl maintenance of swimming pools, and for is HCl household cleaning. Used in car batteries, and in the manufacture of sulfuric acid, H2SO4 fertilizers. Used in the manufacture of fertilizers, nitric acid, HNO3 explosives and in extraction of gold. acetic acid, HC2H3O2 vinegar Main ingredient in vinegar. carbonic acid, H2CO3 responsible for the "fizz" in carbonated drinks As an ingredient in carbonated drinks. Used in food and dietary supplements. Also citric acid, C6H8O7 added as an acidulant in creams, gels, liquids, and lotions. acetylsalicylic acid, C6H4(OCOCH3)CO2H aspirin The active ingredient in aspirin. 14.2.1 https://chem.libretexts.org/@go/page/47554 What exactly makes an acid an acid, and what makes a base act as a base? Take a look at the formulas given in the above table and take a guess. Hydrochloric Acid Hydrochloric acid is a corrosive, strong mineral acid with many industrial uses. A colorless, highly pungent solution of hydrogen chloride (HCl) in water. Hydrochloric acid is usually prepared by treating HCl with water. + − HCl(g) + H O(l) ⟶ H O (aq) + Cl (aq) 2 3 Hydrochloric acid can therefore be used to prepare chloride salts. Hydrochloric acid is a strong acid, since it is completely dissociated in water. Hydrochloric acid is the preferred acid in titration for determining the amount of bases. Sulfuric Acid Sulfuric acid is a highly corrosive strong mineral acid with the molecular formula H SO. Sulfuric acid is a diprotic acid and has a 2 4 wide range of applications including use in domestic acidic drain cleaners,[as an electrolyte in lead-acid batteries, and in various cleaning agents. It is also a central substance in the chemical industry. Figure 14.2.1 : Drops of concentrated sulfuric acid rapidly decompose a piece of cotton towel by dehydration. (CC BY-SA 3.0; Toxic Walker). Because the hydration of sulfuric acid is thermodynamically favorable (and is highly exothermic) and the affinity of it for water is sufficiently strong, sulfuric acid is an excellent dehydrating agent. Concentrated sulfuric acid has a very powerful dehydrating property, removing water (H O ) from other compounds including sugar and other carbohydrates and producing carbon, heat, 2 steam. Sulfuric acid behaves as a typical acid in its reaction with most metals by generating hydrogen gas (Equation 14.2.2). M + H SO → M(SO ) + H (14.2.2) 2 4 4 2 Nitric Acid Nitric acid (HNO ) is a highly corrosive mineral acid and is also commonly used as a strong oxidizing agent. Nitric acid is 3 normally considered to be a strong acid at ambient temperatures. Nitric acid can be made by reacting nitrogen dioxide (NO (g)) 2 with water. 3 NO (g) + H O(l) → 2 HNO (ag) + NO(g) 2 2 3 Nitric acid reacts with most metals, but the details depend on the concentration of the acid and the nature of the metal. Dilute nitric acid behaves as a typical acid in its reaction with most metals (e.g., nitric acid with magnesium, manganese or zinc will liberate H 2 gas): Mg + 2 HNO → Mg (NO ) +H 3 3 2 2 Mn + 2 HNO → Mn(NO ) +H 3 3 2 2 Zn + 2 HNO → Zn(NO ) +H 3 3 2 2 Nitric acid is a corrosive acid and a powerful oxidizing agent. The major hazard it poses is chemical burn, as it carries out acid hydrolysis with proteins (amide) and fats (ester) which consequently decomposes living tissue (Figure 14.2.2). Concentrated nitric acid stains human skin yellow due to its reaction with the keratin 14.2.2 https://chem.libretexts.org/@go/page/47554  Figure 14.2.2 : Second degree burn caused by nitric acid. (CC BY-SA 3.0; Alcamán). Carbonic Acid Carbonic acid is a chemical compound with the chemical formula H CO and is also a name sometimes given to solutions of 2 3 carbon dioxide in water (carbonated water), because such solutions contain small amounts of H CO (aq). Carbonic acid, which is 2 3 a weak acid, forms two kinds of salts: the carbonates and the bicarbonates. In geology, carbonic acid causes limestone to dissolve, producing calcium bicarbonate—which leads to many limestone features such as stalactites and stalagmites. Carbonic acid is a polyprotic acid, specifically it is diprotic, meaning that it has two protons which may dissociate from the parent molecule. When carbon dioxide dissolves in water, it exists in chemical equilibrium (discussed in Chapter 15), producing carbonic acid: CO +H O − ↽⇀ − H CO 2 2 2 3 The reaction can be pushed to favor the reactants to generate CO (g) 2 from solution, which is key to the bubbles observed in carbonated beverages (Figure 14.2.3). Figure 14.2.3 : A glass of sparkling water. (CC BY-SA 3.0; Nevit Dilmen). Formic Acid Formic acid (HCO H ) is the simplest carboxylic acid and is an important intermediate in chemical synthesis and occurs naturally, 2 most notably in some ants. The word "formic" comes from the Latin word for ant, formica, referring to its early isolation by the distillation of ant bodies. Formic acid occurs widely in nature as its conjugate base formate. Citric Acid Citric acid (C H O ) is a weak organic tricarboxylic acid that occurs naturally in citrus fruits. The citrate ion is an intermediate in 6 8 7 the TCA cycle (Krebs cycle), a central metabolic pathway for animals, plants and bacteria. Because it is one of the stronger edible acids, the dominant use of citric acid is used as a flavoring and preservative in food and beverages, especially soft drinks. Figure 14.2.4 : Lemons, oranges, limes, and other citrus fruits possess high concentrations of citric acid (CC BY-SA 2.5; André Karwath). Acetylsalicylic Acid Acetylsalicylic acid (also known as aspirin) is a medication used to treat pain, fever, and inflammation. Aspirin, in the form of leaves from the willow tree, has been used for its health effects for at least 2,400 years. 14.2.3 https://chem.libretexts.org/@go/page/47554  Figure 14.2.5 : Ball-and-stick model of the aspirin molecule. (Public Domain; Ben Mills). Aspirin is a white, crystalline, weakly acidic substance. Summary A brief summary of key aspects of several acids commonly encountered by students was given. Acids are a distinct class of compounds because of the properties of their aqueous solutions. Contributions & Attributions Peggy Lawson (Oxbow Prairie Heights School). Funded by Saskatchewan Educational Technology Consortium. 14.2: Acids- Properties and Examples is shared under a CK-12 license and was authored, remixed, and/or curated by Marisa Alviar-Agnew & Henry Agnew. 14.2.4 https://chem.libretexts.org/@go/page/47554 14.3: Bases- Properties and Examples  Learning Objectives Examine properties of bases. Perhaps you have eaten too much pizza and felt very uncomfortable hours later. This feeling is due to excess stomach acid being produced. The discomfort can be dealt with by taking an antacid. The base in the antacid will react with the HCl in the stomach and neutralize it, taking care of that unpleasant feeling. Bases Bases have properties that mostly contrast with those of acids. 1. Aqueous solutions of bases are also electrolytes. Bases can be either strong or weak, just as acids can. 2. Bases often have a bitter taste and are found in foods less frequently than acids. Many bases, like soaps, are slippery to the touch. 3. Bases also change the color of indicators. Litmus turns blue in the presence of a base, while phenolphthalein turns pink. 4. Bases do not react with metals in the way that acids do. 5. Bases react with acids to produce a salt and water. Figure 14.3.1 : Phenolphthalein indicator in presence of base.  Warning! Tasting chemicals and touching them are NOT good lab practices and should be avoided—in other words—don't do this at home. Bases are less common as foods, but they are nonetheless present in many household products. Many cleaners contain ammonia, a base. Sodium hydroxide is found in drain cleaner. Antacids, which combat excess stomach acid, are comprised of bases such as magnesium hydroxide or sodium hydrogen carbonate. Various common bases and corresponding uses are given in Table 14.3.2. Table 14.3.1 : Common Bases and Corresponding Uses Some Common Bases Uses sodium hydroxide, NaOH Used in the manufacture of soaps and detergents, and as the main (lye or caustic soda) ingredient in oven and drain cleaners. potassium hydroxide, KOH Used in the production of liquid soaps and soft soaps. Used in alkaline (lye or caustic potash) batteries. magnesium hydroxide, Mg(OH)2 Used as an ingredient in laxatives, antacids, and deodorants. Also used (milk of magnesia) in the neutralization of acidic wastewater. calcium hydroxide, Ca(OH)2 Used in the manufacture of cement and lime water. Also, added to (slaked lime) neutralize acidic soil. aluminum hydroxide Used in water purification and as an ingredient in antacids. Used as a building block for the synthesis of many pharmaceutical ammonia, NH3 products and in many commercial cleaning products. Used in the manufacture of fertilizers. 14.3.1 https://chem.libretexts.org/@go/page/47556 Sodium Hydroxide Sodium hydroxide, also known as lye and caustic soda, is an inorganic compound with formula NaOH. It is a white solid ionic compound consisting of sodium cations Na and hydroxide anions OH. + − Dissolution of solid sodium hydroxide in water is a highly exothermic reaction: + − NaOH(s) → Na (aq) + OH (aq) The resulting solution is usually colorless and odorless and feels slippery when it comes in contact with skin. Figure 14.3.1 : Sample of sodium hydroxide as pellets in a watch glass. (Public Domain; Walkerma.) Potassium Hydroxide Potassium hydroxide is an inorganic compound with the formula KOH , and is commonly called caustic potash. Along with sodium hydroxide (NaOH), this colorless solid is a prototypical strong base. It has many industrial and niche applications, most of which exploit its corrosive nature and its reactivity toward acids. Its dissolution in water is strongly exothermic. + − KOH(s) → K (aq) + OH (aq) Concentrated aqueous solutions are sometimes called potassium lyes. Magnesium Hydroxide Magnesium hydroxide is the inorganic compound with the chemical formula Mg(OH) 2. Magnesium hydroxide is a common component of antacids, such as milk of magnesia, as well as laxatives. Figure 14.3.1 : Bottle of Antacid tablets. (CC BY 2.,5; Midnightcomm). It is a white solid with low solubility in water. Combining a solution of many magnesium salts with basic water induces precipitation of solid Mg(OH). However, a weak concentration of dissociated ions can be found in solution: 2 2 + − Mg (OH) (s) − ↽⇀ − Mg (aq) + 2 OH (aq) 2 Calcium Hydroxide Calcium hydroxide (traditionally called slaked lime) is an inorganic compound with the chemical formula Ca(OH). It is a 2 colorless crystal or white powder. It has many names including hydrated lime, caustic lime, builders' lime, slaked lime, cal, or pickling lime. Calcium hydroxide is used in many applications, including food preparation. Limewater is the common name for a saturated solution of calcium hydroxide. 14.3.2 https://chem.libretexts.org/@go/page/47556 Calcium hydroxide is relatively insoluble in water, but is large enough that its solutions are basic according to the following reaction: 2 + − Ca (OH) (s) − ↽⇀ − Ca (aq) + 2 OH (aq) 2 Ammonia Ammonia is a compound of nitrogen and hydrogen with the formula NH and is a colorless gas with a characteristic pungent 3 smell. It is the active product of “smelling salts,” and can quickly revive the faint of heart and light of head. Although common in nature and in wide use, ammonia is both caustic and hazardous in its concentrated form. Figure 14.3.1 : Ball-and-stick model of the ammonia molecule. (Public Domain; Ben Mills). In aqueous solution, ammonia acts as a base, acquiring hydrogen ions from H 2 O to yield ammonium and hydroxide ions: + − NH (g) + H O(l) − ↽⇀ − NH (aq) + OH (aq) 3 2 4 Ammonia is also a building block for the synthesis of many pharmaceutical products and is used in many commercial cleaning products. Summary A brief summary of properties of bases was given. The properties of bases mostly contrast those of acids. Bases have many, varied uses. 14.3: Bases- Properties and Examples is shared under a CK-12 license and was authored, remixed, and/or curated by Marisa Alviar-Agnew & Henry Agnew. 14.3.3 https://chem.libretexts.org/@go/page/47556 14.4: Molecular Definitions of Acids and Bases  Learning Objectives Identify an Arrhenius acid and an Arrhenius base. Identify a Brønsted-Lowry acid and a Brønsted-Lowry base. Identify conjugate acid-base pairs in an acid-base reaction. There are three major classifications of substances known as acids or bases. The theory developed by Svante Arrhenius in 1883, the Arrhenius definition, states that an acid produces H+ in solution and a base produces OH-. Later, two more sophisticated and general theories were proposed. These theories are the Brønsted-Lowry and Lewis definitions of acids and bases. This section will cover the Arrhenius and Brønsted-Lowry theories; the Lewis theory is discussed elsewhere. The Arrhenius Theory of Acids and Bases In 1884, the Swedish chemist Svante Arrhenius proposed two specific classifications of compounds, termed acids and bases. When dissolved in an aqueous solution, certain ions were released into the solution. An Arrhenius acid is a compound that increases the concentration of H ions that are present when added to water. These H+ ions form the hydronium ion (H3O+) when they + combine with water molecules. This process is represented in a chemical equation by adding H2O to the reactants side. + − HCl(aq) → H (aq) + Cl (aq) In this reaction, hydrochloric acid (H C l) dissociates completely into hydrogen (H+) and chlorine (Cl-) ions when dissolved in water, thereby releasing H+ ions into solution. Formation of the hydronium ion equation: + − HCl(aq) + H O(l) → H O (aq) + Cl (aq) 2 3 An Arrhenius base is a compound that increases the concentration of OH − ions that are present when added to water. The dissociation is represented by the following equation: + − NaOH (aq) → Na (aq) + OH (aq) In this reaction, sodium hydroxide (NaOH) disassociates into sodium (Na ) and hydroxide (OH ) ions when dissolved in water, + − thereby releasing OH- ions into solution. Arrhenius acids are substances which produce hydrogen ions in solution and Arrhenius bases are substances which produce hydroxide ions in solution.  Limitations to the Arrhenius Theory The Arrhenius theory has many more limitations than the other two theories. The theory does not explain the weak base ammonia (NH3), which in the presence of water, releases hydroxide ions into solution, but does not contain OH- itself. The Arrhenius definition of acid and base is also limited to aqueous (i.e., water) solutions. The Brønsted-Lowry Theory of Acids and Bases In 1923, Danish chemist Johannes Brønsted and English chemist Thomas Lowry independently proposed new definitions for acids and bases, ones that focus on proton transfer. A Brønsted-Lowry acid is any species that can donate a proton (H+) to another molecule. A Brønsted-Lowry base is any species that can accept a proton from another molecule. In short, a Brønsted-Lowry acid is a proton donor (PD), while a Brønsted-Lowry base is a proton acceptor (PA). A Brønsted-Lowry acid is a proton donor, while a Brønsted-Lowry base is a proton acceptor. Let us use the reaction of ammonia in water to demonstrate the Brønsted-Lowry definitions of an acid and a base. Ammonia and water molecules are reactants, while the ammonium ion and the hydroxide ion are products: + − NH (aq) + H O(ℓ) − ↽⇀ − NH (aq) + OH (aq) (14.4.1) 3 2 4 14.4.1 https://chem.libretexts.org/@go/page/47558 What has happened in this reaction is that the original water molecule has donated a hydrogen ion to the original ammonia molecule, which in turn has accepted the hydrogen ion. We can illustrate this as follows: Because the water molecule donates a hydrogen ion to the ammonia, it is the Brønsted-Lowry acid, while the ammonia molecule— which accepts the hydrogen ion—is the Brønsted-Lowry base. Thus, ammonia acts as a base in both the Arrhenius sense and the Brønsted-Lowry sense. Is an Arrhenius acid like hydrochloric acid still an acid in the Brønsted-Lowry sense? Yes, but it requires us to understand what really happens when HCl is dissolved in water. Recall that the hydrogen atom is a single proton surrounded by a single electron. To make the hydrogen ion, we remove the electron, leaving a bare proton. Do we really have bare protons floating around in aqueous solution? No, we do not. What really happens is that the H+ ion attaches itself to H2O to make H3O+, which is called the hydronium ion. For most purposes, H+ and H3O+ represent the same species, but writing H3O+ instead of H+ shows that we understand that there are no bare protons floating around in solution. Rather, these protons are actually attached to solvent molecules.  The Hydronium Ion A proton in aqueous solution may be surrounded by more than one water molecule, leading to formulas like H 5 + O 2 or H O 9 + 4 rather than H O. It is simpler, however, to use H O to represent the hydronium ion. 3 + 3 + With this in mind, how do we define HCl as an acid in the Brønsted-Lowry sense? Consider what happens when HCl is dissolved in H2O: + − HCl(g) + H O(ℓ) → H O (aq) + Cl (aq) (14.4.2) 2 3 We can depict this process using Lewis electron dot diagrams: Now we see that a hydrogen ion is transferred from the HCl molecule to the H2O molecule to make chloride ions and hydronium ions. As the hydrogen ion donor, HCl acts as a Brønsted-Lowry acid; as a hydrogen ion acceptor, H2O is a Brønsted-Lowry base. So HCl is an acid not just in the Arrhenius sense, but also in the Brønsted-Lowry sense. Moreover, by the Brønsted-Lowry definitions, H2O is a base in the formation of aqueous HCl. So the Brønsted-Lowry definitions of an acid and a base classify the dissolving of HCl in water as a reaction between an acid and a base—although the Arrhenius definition would not have labeled H2O a base in this circumstance. A Brønsted-Lowry acid is a proton (hydrogen ion) donor. A Brønsted-Lowry base is a proton (hydrogen ion) acceptor. 14.4.2 https://chem.libretexts.org/@go/page/47558  All Arrhenius acids and bases are Brønsted-Lowry acids and bases as well. However, not all Brønsted-Lowry acids and bases are Arrhenius acids and bases.  Example 14.4.1 Aniline (C6H5NH2) is slightly soluble in water. It has a nitrogen atom that can accept a hydrogen ion from a water molecule, just like the nitrogen atom in ammonia does. Write the chemical equation for this reaction and identify the Brønsted-Lowry acid and base. Solution C6H5NH2 and H2O are the reactants. When C6H5NH2 accepts a proton from H2O, it gains an extra H and a positive charge and leaves an OH− ion behind. The reaction is as follows: + − C H NH (aq) + H O(ℓ) − ↽⇀ − C H NH (aq) + OH (aq) 6 5 2 2 6 5 3 Because C6H5NH2 accepts a proton, it is the Brønsted-Lowry base. The H2O molecule, because it donates a proton, is the Brønsted-Lowry acid.  Exercise 14.4.1 Identify the Brønsted-Lowry acid and the Brønsted-Lowry base in this chemical equation. − 2 − + H PO +H O − ↽⇀ − HPO +H O 2 4 2 4 3 Answer Brønsted-Lowry acid: H2PO4-; Brønsted-Lowry base: H2O  Exercise 14.4.2 Which of the following compounds is a Bronsted-Lowry base? a. HCl b. HPO42- c. H3PO4 d. NH4+ e. CH3NH3+ Answer A Brønsted-Lowry Base is a proton acceptor, which means it will take in an H+. This eliminates HCl, H 3 PO , NH and 4 + 4 CH NH 3 + 3 because they are Bronsted-Lowry acids. They all give away protons. In the case of HPO 2 − 4 , consider the following equation: 2 − 3 − + HPO (aq) + H O(l) → PO (aq) + H O (aq) 4 2 4 3 Here, it is clear that HPO42- is the acid since it donates a proton to water to make H3O+ and PO43-. Now consider the following equation: 2 − − − HPO (aq) + H O(l) → H PO + OH (aq) 4 2 2 4 In this case, HPO42- is the base since it accepts a proton from water to form H2PO4- and OH-. Thus, HPO42- is an acid and base together, making it amphoteric. Since HPO42- is the only compound from the options that can act as a base, the answer is (b) HPO42-. 14.4.3 https://chem.libretexts.org/@go/page/47558 Conjugate Acid-Base Pair In reality, all acid-base reactions involve the transfer of protons between acids and bases. For example, consider the acid-base reaction that takes place when ammonia is dissolved in water. A water molecule (functioning as an acid) transfers a proton to an ammonia molecule (functioning as a base), yielding the conjugate base of water, OH , and the conjugate acid of ammonia, NH : − + 4 This figure has three parts in two rows. In the first row, two diagrams of acid-base pairs are shown. On the left, a space filling model of H subscript 2 O is shown with a red O atom at the center and two smaller white H atoms attached in a bent shape. Above this model is the label “H subscript 2 O (acid)” in purple. An arrow points right, which is labeled “Remove H superscript plus.” To the right is another space filling model with a single red O atom to which a single smaller white H atom is attached. The label in purple above this model reads, “O H superscript negative (conjugate base).” Above both of these red and white models is an upward pointing bracket that is labeled “Conjugate acid-base pair.” To the right is a space filling model with a central blue N atom to which three smaller white H atoms are attached in a triangular pyramid arrangement. A label in green above reads “N H subscript 3 (base).” An arrow labeled “Add H superscript plus” points right. To the right of the arrow is another space filling model with a blue central N atom and four smaller white H atoms in a tetrahedral arrangement. The green label above reads “N H subscript 3 superscript plus (conjugate acid).” Above both of these blue and white models is an upward pointing bracket that is labeled “Conjugate acid-base pair.” The second row of the figure shows the chemical reaction, H subscript 2 O ( l ) is shown in purple, and is labeled below in purple as “acid,” plus N H subscript 3 (a q) in green, labeled below in green as “base,” followed by a double sided arrow arrow and O H superscript negative (a q) in purple, labeled in purple as “conjugate base,” plus N H subscript 4 superscript plus (a q)” in green, which is labeled in green as “conjugate acid.” The acid on the left side of the equation is connected to the conjugate base on the right with a purple line. Similarly, the base on the left is connected to the conjugate acid on the right side. In the reaction of ammonia with water to give ammonium ions and hydroxide ions, ammonia acts as a base by accepting a proton from a water molecule, which in this case means that water is acting as an acid. In the reverse reaction, an ammonium ion acts as an acid by donating a proton to a hydroxide ion, and the hydroxide ion acts as a base. The conjugate acid–base pairs for this reaction are N H /N H and H O/OH. + 4 3 2 − Figure 14.4.1. The pairing of parent acids and bases with conjugate acids and bases. 14.4.4 https://chem.libretexts.org/@go/page/47558  Figure 14.4.1 : The Relative Strengths of Some Common Conjugate Acid-Base Pairs. The strongest acids are at the bottom left, and the strongest bases are at the top right. The conjugate base of a strong acid is a very weak base, and, conversely, the conjugate acid of a strong base is a very weak acid.  Example 14.4.2 Identify the conjugate acid-base pairs in this equilibrium. + − CH CO H + H O − ↽⇀ − H O + CH CO2 3 2 2 3 3 Solution Similarly, in the reaction of acetic acid with water, acetic acid donates a proton to water, which acts as the base. In the reverse reaction, H O is the acid that donates a proton to the acetate ion, which acts as the base. 3 + Once again, we have two conjugate acid-base pairs: the parent acid and its conjugate base (C H C O H /C H 3 2 − 3 C O2 ) and the parent base and its conjugate acid (H O /H O). 3 + 2 14.4.5 https://chem.libretexts.org/@go/page/47558   Example 14.4.3 Identify the conjugate acid-base pairs in this equilibrium. + − (CH ) N + H O − ↽⇀ − (CH ) NH + OH 3 3 2 3 3 Solution One pair is H2O and OH−, where H2O has one more H+ and is the conjugate acid, while OH− has one less H+ and is the conjugate base. The other pair consists of (CH3)3N and (CH3)3NH+, where (CH3)3NH+ is the conjugate acid (it has an additional proton) and (CH3)3N is the conjugate base.  Exercise 14.4.3 Identify the conjugate acid-base pairs in this equilibrium. − − NH + H O ⇌ NH + OH 2 2 3 Answer H2O (acid) and OH− (base); NH2− (base) and NH3 (acid) 14.4: Molecular Definitions of Acids and Bases is shared under a CK-12 license and was authored, remixed, and/or curated by Marisa Alviar- Agnew & Henry Agnew. 14.4.6 https://chem.libretexts.org/@go/page/47558 14.5: Reactions of Acids and Bases  Learning Objectives Write acid-base neutralization reactions. Write reactions of acids with metals. Write reactions of bases with metals. Neutralization Reactions The reaction that happens when an acid, such as HCl, is mixed with a base, such as NaOH: HCl(aq) + NaOH(aq) → NaCl(aq) + H O(l) 2 When an acid and a base are combined, water and a salt are the products. Salts are ionic compounds containing a positive ion other than H and a negative ion other than the hydroxide ion, OH. Double displacement reactions of this type are called + − neutralization reactions. We can write an expanded version of this equation, with aqueous substances written in their longer form: + − + − + − H (aq) + Cl (aq) + Na (aq) + OH (aq) → Na (aq) + Cl (aq) + H O(l) 2 After removing the spectator ions, we get the net ionic equation: + − H (aq) + OH (aq) → H O(l) 2 When a strong acid and a strong base are combined in the proper amounts—when [H ] equals [OH ]\)—a neutral solution results + − in which pH = 7. The acid and base have neutralized each other, and the acidic and basic properties are no longer present. Salt solutions do not always have a pH of 7, however. Through a process known as hydrolysis, the ions produced when an acid and base combine may react with the water molecules to produce a solution that is slightly acidic or basic. As a general concept, if a strong acid is mixed with a weak base, the resulting solution will be slightly acidic. If a strong base is mixed with a weak acid, the solution will be slightly basic. acid-base reaction (HCl + NaOH) Video: Equimolar (~0.01 M) and equivolume solutions of HCl and NaOH are combined to make salt water. https://youtu.be/TS- I9KrUjB0  Example 14.5.1: Propionic Acid + Calcium Hydroxide Calcium propionate is used to inhibit the growth of molds in foods, tobacco, and some medicines. Write a balanced chemical equation for the reaction of aqueous propionic acid (CH3CH2CO2H) with aqueous calcium hydroxide [Ca(OH)2]. Solution Solutions to Example 14.5.1 Steps Reaction 14.5.1 https://chem.libretexts.org/@go/page/47560  Steps Reaction Write the unbalanced equation. This is a double displacement reaction, so the cations and anions CH3CH2CO2H(aq) + Ca(OH)2(aq)→(CH3CH2CO2)2Ca(aq) + H2O(l) swap to create the water and the salt. Balance the equation. 2CH3CH2CO2H(aq) + Ca(OH)2(aq)→(CH3CH2CO2)2Ca(aq) Because there are two OH− ions in the formula for Ca(OH)2, we need + +2H2O(l) two moles of propionic acid, CH3CH2CO2H, to provide H ions.  Exercise 14.5.1 Write a balanced chemical equation for the reaction of solid barium hydroxide with dilute acetic acid. Answer Ba (OH) (s) + 2 CH CO H(aq) → Ba (CH CO ) (aq) + 2 H O(l) 2 3 2 3 2 2 2 Acids and Bases React with Metals Acids react with most metals to form a salt and hydrogen gas. As discussed previously, metals that are more active than acids can undergo a single displacement reaction. For example, zinc metal reacts with hydrochloric acid, producing zinc chloride and hydrogen gas. Zn(s) + 2 HCl(aq) → ZnCl (aq) + H (g) 2 2 Bases also react with certain metals, like zinc or aluminum, to produce hydrogen gas. For example, sodium hydroxide reacts with zinc and water to form sodium zincate and hydrogen gas. Zn(s) + 2 NaOH(aq) + 2 H O(l) → Na Zn(OH) (aq) + H (g). 2 2 4 2 14.5: Reactions of Acids and Bases is shared under a Public Domain license and was authored, remixed, and/or curated by Marisa Alviar-Agnew, Henry Agnew, Peggy Lawson, & Peggy Lawson. 14.5.2 https://chem.libretexts.org/@go/page/47560 14.6: Acid–Base Titration  Learning Objectives Understand the basics of acid-base titrations. Understand the use of indicators. Perform a titration calculation correctly. The reaction of an acid with a base to make a salt and water is a common reaction in the laboratory, partly because so many compounds can act as acids or bases. Another reason that acid-base reactions are so prevalent is because they are often used to determine quantitative amounts of one or the other. Performing chemical reactions quantitatively to determine the exact amount of a reagent is called a titration. A titration can be performed with almost any chemical reaction for which the balanced chemical equation is known. Here, we will consider titrations that involve acid-base reactions. During an acid-base titration, an acid with a known concentration (a standard solution) is slowly added to a base with an unknown concentration (or vice versa). A few drops of indicator solution are added to the base. The indicator will signal, by color change, when the base has been neutralized (when [H+] = [OH-]). At that point—called the equivalence point, or end point—the titration is stopped. By knowing the volumes of acid and base used, and the concentration of the standard solution, calculations allow us to determine the concentration of the other solution. It is important to accurately measure volumes when doing titrations. The instrument you would use is called a burette (or buret). Figure 14.6.1 : Equipment for Titrations. A burette is a type of liquid dispensing system that can accurately indicate the volume of liquid dispensed. For example, suppose 25.66 mL (or 0.02566 L) of 0.1078 M HCl was used to titrate an unknown sample of NaOH. What mass of NaOH was in the sample? We can calculate the number of moles of HCl reacted: # mol HCl = (0.02566 L)(0.1078 M) = 0.002766 mol HCl We also have the balanced chemical reaction between HCl and NaOH: HCl + NaOH → NaCl + H O 2 So we can construct a conversion factor to convert to number of moles of NaOH reacted: 1 mol N aOH 0.002766 mol H C l × = 0.002766 mol N aOH 1 mol H C l Then we convert this amount to mass, using the molar mass of NaOH (40.00 g/mol): 40.00 g N aOH 0.002766 mol H C l × = 0.1106 g N aOH 1 mol H C l This type of calculation is performed as part of a titration.  Example 14.6.1: Equivalence Point What mass of Ca(OH)2 is present in a sample if it is titrated to its equivalence point with 44.02 mL of 0.0885 M HNO3? The balanced chemical equation is as follows: 2 HNO + Ca (OH) → Ca (NO ) +2 H O 3 2 3 2 2 Solution 14.6.1 https://chem.libretexts.org/@go/page/47562  In liters, the volume is 0.04402 L. We calculate the number of moles of titrant: # moles HNO3 = (0.04402 L)(0.0885 M) = 0.00390 mol HNO3 Using the balanced chemical equation, we can determine the number of moles of Ca(OH)2 present in the analyte: 1 mol C a(OH )2 0.00390 mol H N O3 × = 0.00195 mol C a(OH )2 2 mol H N O3 Then we convert this to a mass using the molar mass of Ca(OH)2: 74.1 g C a(OH )2 0.00195 mol C a(OH )2 × = 0.144 g C a(OH )2 mol C a(OH )2  Exercise 14.6.1 What mass of H2C2O4 is present in a sample if it is titrated to its equivalence point with 18.09 mL of 0.2235 M NaOH? The balanced chemical reaction is as follows: H C O + 2 NaOH → Na C O +2 H O 2 2 4 2 2 4 2 Answer 0.182 g  Exercise 14.6.2 If 25.00 mL of HCl solution with a concentration of 0.1234 M is neutralized by 23.45 mL of NaOH, what is the concentration of the base? Answer 0.1316 M NaOH  Exercise 14.6.3 A 20.0 mL solution of strontium hydroxide, Sr(OH)2, is placed in a flask and a drop of indicator is added. The solution turns color after 25.0 mL of a standard 0.0500 M HCl solution is added. What was the original concentration of the Sr(OH)2 solution? Answer 3.12 × 10 −2 M Sr(OH)2 Indicator Selection for Titrations The indicator used depends on the type of titration performed. The indicator of choice should change color when enough of one substance (acid or base) has been added to exactly use up the other substance. Only when a strong acid and a strong base are produced will the resulting solution be neutral. The three main types of acid-base titrations, and suggested indicators, are: The three main types of acid-base titrations, suggested indicators, and explanations Titration between... Indicator Explanation strong acid and strong base any strong acid and weak base methyl orange changes color in the acidic range (3.2 - 4.4) weak acid and strong base phenolphthalein changes color in the basic range (8.2 - 10.6) 14.6.2 https://chem.libretexts.org/@go/page/47562 Summary A titration is the quantitative reaction of an acid and a base. Indicators are used to show that all the analyte has reacted with the titrant. Contributions & Attributions Peggy Lawson (Oxbow Prairie Heights School). Funded by Saskatchewan Educational Technology Consortium. 14.6: Acid–Base Titration is shared under a CK-12 license and was authored, remixed, and/or curated by Marisa Alviar-Agnew & Henry Agnew. 14.6.3 https://chem.libretexts.org/@go/page/47562 14.7: Strong and Weak Acids and Bases  Learning Objectives Define a strong and a weak acid and base. Recognize an acid or a base as strong or weak. Determine if a salt produces an acidic or a basic solution. Strong and Weak Acids Except for their names and formulas, so far we have treated all acids as equals, especially in a chemical reaction. However, acids can be very different in a very important way. Consider HCl(aq). When HCl is dissolved in H2O, it completely dissociates into H+(aq) and Cl−(aq) ions; all the HCl molecules become ions: 100% + − HC l → H (aq) + C l (aq) Any acid that dissociates 100% into ions is called a strong acid. If it does not dissociate 100%, it is a weak acid. HC2H3O2 is an example of a weak acid: ∼5% + − H C2 H3 O2 ⟶ H (aq) + C2 H3 O (aq) 2 Because this reaction does not go 100% to completion, it is more appropriate to write it as a reversible reaction: + − H C2 H3 O2 ⇌ H (aq) + C2 H3 O (aq) 2 As it turns out, there are very few strong acids, which are given in Table 14.7.1. If an acid is not listed here, it is a weak acid. It may be 1% ionized or 99% ionized, but it is still classified as a weak acid. Any acid that dissociates 100% into ions is called a strong acid. If it does not dissociate 100%, it is a weak acid. Table 14.7.1 : Strong Acids and Bases Acids Bases HCl LiOH HBr NaOH HI KOH HNO3 RbOH H2SO4 CsOH HClO3 Mg(OH)2 HClO4 Ca(OH)2 Sr(OH)2 Ba(OH)2 Strong and Weak Bases The issue is similar with bases: a strong base is a base that is 100% ionized in solution. If it is less than 100% ionized in solution, it is a weak base. There are very few strong bases (Table 14.7.1); any base not listed is a weak base. All strong bases are OH– compounds. So a base based on some other mechanism, such as NH3 (which does not contain OH− ions as part of its formula), will be a weak base.  Example 14.7.1: Identifying Strong and Weak Acids and Bases Identify each acid or base as strong or weak. a. HCl b. Mg(OH)2 c. C5H5N Solution a. Because HCl is listed in Table 14.7.1, it is a strong acid. b. Because Mg(OH)2 is listed in Table 14.7.1, it is a strong base. c. The nitrogen in C5H5N would act as a proton acceptor and therefore can be considered a base, but because it does not contain an OH compound, it cannot be considered a strong base; it is a weak base.  Exercise 14.7.1 Identify each acid or base as strong or weak. a. RbOH b. HNO 2 Answer a strong base Answer b weak acid  Example 14.7.2: Characterizing Base Ionization Write the balanced chemical equation for the dissociation of Ca(OH)2 and indicate whether it proceeds 100% to products or not. Solution This is an ionic compound of Ca2+ ions and OH− ions. When an ionic compound dissolves, it separates into its constituent ions: 2 + − Ca (OH) → Ca (aq) + 2 OH (aq) 2 Because Ca(OH)2 is listed in Table 14.7.1, this reaction proceeds 100% to products. 14.7.1 https://chem.libretexts.org/@go/page/47564   Exercise 14.7.2 Write the balanced chemical equation for the dissociation of hydrazoic acid (HN3) and indicate whether it proceeds 100% to products or not. Answer a The reaction is as follows: + − HN → H (aq) + N (aq) 3 3 It does not proceed 100% to products because hydrazoic acid is not a strong acid. Key Takeaways Strong acids and bases are 100% ionized in aqueous solution. Weak acids and bases are less than 100% ionized in aqueous solution. Salts of weak acids or bases can affect the acidity or basicity of their aqueous solutions. Contributions & Attributions 14.7: Strong and Weak Acids and Bases is shared under a CK-12 license and was authored, remixed, and/or curated by Marisa Alviar-Agnew & Henry Agnew. 14.7.2 https://chem.libretexts.org/@go/page/47564 14.8: Water - Acid and Base in One  Learning Objectives Describe the autoionization of water. Calculate the concentrations of H O and OH in aqueous solutions, knowing the other concentration. 3 + − We have already seen that H 2 O can act as an acid or a base: + − NH +H O − ↽⇀ − NH + OH 3 2 4   base acid where H 2 O acts as an acid (in red). + − HCl + H O ⟶ H O + Cl 2 3   acid base where H 2 O acts as an base (in blue). It may not surprise you to learn, then, that within any given sample of water, some H O 2 molecules are acting as acids, and other H O molecules are acting as bases. The chemical equation is as follows: 2 + − H O+H O − ↽⇀ − H O + OH (14.8.1) 2 2 3   acid base This occurs only to a very small degree: only about 6 in 108 H 2 O molecules are participating in this process, which is called the autoionization of water. Figure 14.8.1 : Autoionization of water, resulting in hydroxide and hydronium ions. At this level, the concentration of both H O (aq) and OH (aq) in a sample of pure H O is about 1.0 × 10 M (at room 3 + − 2 −7 temperature). If we use square brackets—[ ]—around a dissolved species to imply the molar concentration of that species, we have + − −7 [H O ]=[ OH ] = 1.0 × 10 (14.8.2) 3 for any sample of pure water because H2O can act as both an acid and a base. The product of these two concentrations is 1.0 × 10 : −14 + − −7 −7 −14 [H O ]×[ OH ] = (1.0 × 10 )(1.0 × 10 ) = 1.0 × 10 3 For acids, the concentration of H O (aq) (i.e., [H O ]) is greater than 1.0 × 10 M. 3 + 3 + −7 For bases the concentration of OH (aq) (i.e., [OH ]) is greater than 1.0 × 10 M. − − −7 However, the product of the two concentrations—[H 3 O + ][ OH − ] —is always equal to 1.0 × 10 −14 , no matter whether the aqueous solution is an acid, a base, or neutral: + − −14 [H O ][ OH ] = 1.0 × 10 3 This value of the product of concentrations is so important for aqueous solutions that it is called the autoionization constant of water and is denoted K : w + − −14 Kw = [ H O ][ OH ] = 1.0 × 10 (14.8.3) 3 This means that if you know [H O ] for a solution, you can calculate what [OH ]) has to be for the product to equal 1.0 × 10 ; 3 + − −14 or if you know [OH ]), you can calculate [H O ]. This also implies that as one concentration goes up, the other must go down to − 3 + compensate so that their product always equals the value of K. w 14.8.1 https://chem.libretexts.org/@go/page/47566   Warning: Temperature Matters The degree of autoionization of water (Equation 14.8.1)—and hence the value of Kw —changes with temperature, so Equations 14.8.2 - 14.8.3 are accurate only at room temperature.  Example 14.8.1: Hydroxide Concentration What is [OH ]) of an aqueous solution if [H − 3 + O ] is 1.0 × 10 −4 M ? Solution Solutions to Example 14.7.1 Steps for Problem Solving Identify the "given" information and what the problem is asking you Given: [H O ] = 1.0 × 10 3 + −4 M to "find." Find: [OH−] = ? M List other known quantities. none Using the expression for K , (Equation w 14.8.3 ), rearrange the equation algebraically to solve for [OH−]. Plan the problem. −14 1.0 × 10 − [ OH ] = + [H3 O ] Now substitute the known quantities into the equation and solve. −14 − 1.0 × 10 −10 [ OH ] = = 1.0 × 10 M Calculate. 1.0 × 10 −4 It is assumed that the concentration unit is molarity, so [OH − ] is 1.0 × 10−10 M. The concentration of the acid is high (> 1 x 10-7 M), so [OH − ] Think about your result. should be low.  Exercise 14.8.1 What is [OH − ] in a 0.00032 M solution of H2SO4? Hint Assume both protons ionize from the molecule...although this is not the case. Answer −11 3.1 × 10 M When you have a solution of a particular acid or base, you need to look at the formula of the acid or base to determine the number of H3O+ or OH− ions in the formula unit because [H O ] or [OH ]) may not be the same as the concentration of the acid or base 3 + − itself.  Example 14.8.2: Hydronium Concentration What is [H 3 O + ] in a 0.0044 M solution of Ca(OH) ? 2 Solution Solutions to Example 14.7.2 Steps for Problem Solving Identify the "given" information and what the problem is asking you Given: [Ca(OH) ] = 0.0044 M 2 to "find." Find: [H O ] = ? M 3 + 14.8.2 https://chem.libretexts.org/@go/page/47566  Steps for Problem Solving We begin by determining [OH ]. The concentration of the solute is − 0.0044 M, but because Ca(OH) is a strong base, there are two OH− 2 ions in solution for every formula unit dissolved, so the actual [OH ] − List other known quantities. is two times this: − [OH ]=2 × 0 ⋅ 0044 M=0 ⋅ 0088 M⋅ Use the expression for K (Equation 14.8.3 ) and rearrange the w equation algebraically to solve for [H O ]. 3 + Plan the problem. −14 1.0 × 10 + [ H3 O ] = − [O H ] Now substitute the known quantities into the equation and solve. −14 1.0 × 10 Calculate. [ H3 O + ] = = 1.1 × 10 −12 M (0.0088) [H O 3 + ] has decreased significantly in this basic solution. The concentration of the base is high (> 1 x 10-7 M) so [H + O ] Think about your result. 3 should be low.  Exercise 14.8.2 What is [H 3 + O ] of an aqueous solution if [OH − ] is 1.0 × 10 −9 M ? Answer 1.0 × 10−5 M In any aqueous solution, the product of [H 3 + O ] and [OH − ] equals 1.0 × 10 −14 (at room temperature). Contributions & Attributions 14.8: Water - Acid and Base in One is shared under a CK-12 license and was authored, remixed, and/or curated by Marisa Alviar-Agnew & Henry Agnew. 14.8.3 https://chem.libretexts.org/@go/page/47566 14.9: The pH and pOH Scales - Ways to Express Acidity and Basicity  Learning Objectives Define pH and pOH. Determine the pH of acidic and basic solutions. Determine the hydronium ion concentration and pOH from pH. As we have seen, [H O ] and [OH ] values can be markedly different from one aqueous solution to another. So chemists defined 3 + − a new scale that succinctly indicates the concentrations of either of these two ions. pH is a logarithmic function of [H 3O + : ] + pH = − log[ H3 O ] (14.9.1) pH is usually (but not always) between 0 and 14. Knowing the dependence of pH on [H 3O + , we can summarize as follows: ] If pH < 7, then the solution is acidic. If pH = 7, then the solution is neutral. If pH > 7, then the solution is basic. This is known as the pH scale. The pH scale is the range of values from 0 to 14 that describes the acidity or basicity of a solution. You can use pH to make a quick determination whether a given aqueous solution is acidic, basic, or neutral. Figure 14.9.1 illustrates this relationship, along with some examples of various solutions. Because hydrogen ion concentrations are generally less than one (for example 1.3 × 10 M ), the log of the number will be a negative number. To make pH even easier to work with, pH −3 is defined as the negative log of [H O ], which will give a positive value for pH. 3 + Figure 14.9.1 : The pH values for several common materials.  Example 14.9.1 Label each solution as acidic, basic, or neutral based only on the stated pH. a. milk of magnesia, pH = 10.5 b. pure water, pH = 7 c. wine, pH = 3.0 Answer a. With a pH greater than 7, milk of magnesia is basic. (Milk of magnesia is largely Mg(OH)2.) b. Pure water, with a pH of 7, is neutral. 14.9.1 https://chem.libretexts.org/@go/page/47568  c. With a pH of less than 7, wine is acidic.  Exercise 14.9.1 Identify each substance as acidic, basic, or neutral based only on the stated pH. a. human blood with pH = 7.4 b. household ammonia with pH = 11.0 c. cherries with pH = 3.6 Answer a basic Answer b basic Answer c acidic Calculating pH from Hydronium Concentration The pH of solutions can be determined by using logarithms as illustrated in the next example for stomach acid. Stomach acid is a solution of H C l with a hydronium ion concentration of 1.2 × 10 M , what is the pH of the solution? −3 + pH = − log[ H3 O ] −3 = − log(1.2 × 10 ) = −(−2.92) = 2.92  Logarithms To get the log value on your calculator, enter the number (in this case, the hydronium ion concentration) first, then press the LOG key. If the number is 1.0 x 10-5 (for [H3O+] = 1.0 x 10-5 M) you should get an answer of "-5". If you get a different answer, or an error, try pressing the LOG key before you enter the number.  Example 14.9.2: Converting Ph to Hydronium Concentration Find the pH, given the [H 3O + ] of the following: a. 1 ×10-3 M b. 2.5 ×10-11 M c. 4.7 ×10-9 M Solution Solutions to Example 14.9.2 Steps for Problem Solving Given: a. [H3O+] =1 × 10−3 M Identify the "given" information and what the problem is asking you b. [H3O+] =2.5 ×10-11 M to "find." c. [H3O+] = 4.7 ×10-9 M Find: ? pH Need to use the expression for pH (Equation 14.9.1 ). Plan the problem. pH = - log [H3O+] 14.9.2 https://chem.libretexts.org/@go/page/47568  Steps for Problem Solving Now substitute the known quantity into the equation and solve. a. pH = - log [1 × 10−3 ] = 3.0 (1 decimal places since 1 has 1 significant figure) b. pH = - log [2.5 ×10-11] = 10.60 (2 decimal places since 2.5 has 2 significant figures) c. pH = - log [4.7 ×10-9] = 8.30 (2 decimal places since 4.7 has 2 significant figures) Calculate. The other issue that concerns us here is significant figures. Because the number(s) before the decimal point in a logarithm relate to the power on 10, the number of digits after the decimal point is what determines the number of significant figures in the final answer:  Exercise 14.9.2 Find the pH, given [H3O+] of the following: a. 5.8 ×10-4 M b. 1.0×10-7 Answer a 3.22 Answer b 7.00 Calculating Hydronium Concentration from pH Sometimes you need to work "backwards"—you know the pH of a solution and need to find [H O ], or even the concentration of 3 + the acid solution. How do you do that? To convert pH into [H O ] we solve Equation 14.9.1 for [H O ]. This involves taking the 3 + 3 + antilog (or inverse log) of the negative value of pH. + [H O ] = antilog(−pH ) 3 or + −pH [H O ] = 10 (14.9.2) 3 As mentioned above, different calculators work slightly differently—make sure you can do the following calculations using your calculator.  Calculator Skills We have a solution with a pH = 8.3. What is [H3O+] ? With some calculators you will do things in the following order: 1. Enter 8.3 as a negative number (use the key with both the +/- signs, not the subtraction key). 2. Use your calculator's 2nd or Shift or INV (inverse) key to type in the symbol found above the LOG key. The shifted function should be 10x. 3. You should get the answer 5.0 × 10-9. Other calculators require you to enter keys in the order they appear in the equation. 1. Use the Shift or second function to key in the 10x function. 14.9.3 https://chem.libretexts.org/@go/page/47568  2. Use the +/- key to type in a negative number, then type in 8.3. 3. You should get the answer 5.0 × 10-9. If neither of these methods work, try rearranging the order in which you type in the keys. Don't give up—you must master your calculator!  Example 14.9.3: Calculating Hydronium Concentration from pH Find the hydronium ion concentration in a solution with a pH of 12.6. Is this solution an acid or a base? How do you know? Solution Solutions to Example 14.9.3 Steps for Problem Solving Identify the "given" information and what the problem is asking you Given: pH = 12.6 to "find." Find: [H3O+] = ? M Need to use the expression for [H3O+] (Equation 14.9.2 ). Plan the problem. [H3O+] = antilog (-pH) or [H3O+] = 10-pH Now substitute the known quantity into the equation and solve. [H3O+] = antilog (12.60) = 2.5 x 10-13 M (2 significant figures since 4.7 has 12.60 2 decimal places) or [H3O+] = 10-12.60 = 2.5 x 10-13 M (2 significant figures since 4.7 has 12.60 2 decimal places) Calculate. The other issue that concerns us here is significant figures. Because the number(s) before the decimal point in a logarithm relate to the power on 10, the number of digits after the decimal point is what determines the number of significant figures in the final answer:  Exercise 14.9.3 If moist soil has a pH of 7.84, what is [H3O+] of the soil solution? Answer 1.5 x 10-8 M The pOH scale As with the hydrogen-ion concentration, the concentration of the hydroxide ion can be expressed logarithmically by the pOH. The pOH of a solution is the negative logarithm of the hydroxide-ion concentration. − pOH = −log [ OH ] T