Final Exam Unit 1 PDF

UNIT 1 Chapter 11 CHEM 0120  Chapter 11: Solutions Solution: a homogeneous mixture of two or more substances What are the components of a solution? Solute Solvent Solutions can exist as any of the 3 states of matter: Gases Liquids Solids...

UNIT 1 Chapter 11 CHEM 0120  Chapter 11: Solutions Solution: a homogeneous mixture of two or more substances What are the components of a solution? Solute Solvent Solutions can exist as any of the 3 states of matter: Gases Liquids Solids 2  Components of a Solution Solute When the solution is a gas or a solid dissolved in a liquid, the solute is the gas or solid In remaining cases, the solute is the component in the smaller amount Solvent When the solution is a gas or solid dissolved in a liquid, the solvent is the liquid In the remaining cases, the solvent is the component in the greater amount 3  Dissolving a Solute in a Solution Let’s start with a solid in water. Go from (s) (aq) Is there a difference between dissolving a molecular and an ionic compound? 4  Dissolving a Solute in a Solution Let’s start with a solid in water. Go from (s) (aq) Is there a difference between dissolving a molecular and an ionic compound? C12H22O11(s) K2Cr2O7(s) 5 Common Types of Solutions 6  What favors the spontaneous formation of a solution? Spontaneous process: a process that occurs under specified conditions without the requirement of energy from some external source Two criteria that favor the spontaneous formation: Decrease in the internal energy of the system Increased dispersal of matter in the system 7  Solubility Solubility: the amount that dissolves in a given quantity of solvent at a given temperature to give a saturated solution The maximum amount of solute that can be dissolved in a given amount of solvent. When one substance does not dissolve in another, it is said to be insoluble. Oil is insoluble in water. The solubility of one substance in another depends on the following: Nature’s tendency toward mixing The types of intermolecular attractive forces 8  Solubility A solution that has the solute and solvent in dynamic equilibrium is said to be saturated. If you add more solute, it will not dissolve. The saturation concentration depends on the temperature and pressure of gases. A solution that has less solute than saturation is said to be unsaturated. More solute will dissolve at this temperature. A solution that has more solute than saturation is said to be supersaturated. 10 Solubility 11 Solubility: Supersaturated 12  Solubility Limit There is typically a limit to the solubility. Gases are always soluble in each other. Two liquids that are mutually soluble are miscible. Ethanol and water are miscible. Oil and gasoline are miscible. Oil and water are immiscible. Miscible Fluids: fluids that mix with or dissolve in each other in all proportions 13  Solubility: Will it Dissolve? (Already answered.) Why or why not? Ethanol and water are miscible. (CH3CH2OH & H2O) Both are polar substances. Both have –OH groups which have strong hydrogen bonding attractions. Oil and gasoline are miscible. Both are mixtures of hydrocarbons and are nonpolar. Oil and water are immiscible. Water is polar and oil is nonpolar. Mixing will not take place because the hydrogen bonding between the water molecules will not break and be replaced with London forces. “Like dissolves Like”. 14  “Like dissolves Like” Summary A chemical will dissolve in a solvent if it has a structure similar to that of the solvent. Compatible intermolecular forces Polar molecules and ionic compounds will be more soluble in polar solvents. Nonpolar molecules will be more soluble in nonpolar solvents. 15  Solubilities of Alcohols in Water: Why the Change? Although water and alcohols both have –OH groups, as the hydrocarbon end (–R) increases in size, the alcohol becomes less like water and the solubilities decrease. 16  Solubility of Ionic Substances in Water Ionic substances can have largely different solubilities in water. NaCl: 36 g / 100 mL (at RT) Ca3(PO4)2: 0.002 g / 100 mL Differences in solubility due to: Hydration energy Lattice energy 17  Ion-dipole interactions Ion-dipole force is responsible for the energy of attraction between an ion and a water molecule. When ions dissolve in water, they become hydrated. Hydration: the attraction of ions for water molecules. Each ion is surrounded by water molecules. 18 Hydration Example of polar water molecules orienting with respect to nearby ions. The O atom in water orients toward the cation (Li+). Each H atom in water orients toward the anion (F-). 19  Dissolving of LiF in H2O Ions on the surface initially hydrate. The ions at the corners are easier to remove due to fewer lattice forces. Upon hydration, ions are removed away from the crystal and move into the body of the liquid. 20  Lattice Energy Lattice Energy: the energy holding ions together in the crystal lattice Works against the solution process. Dependent on the charges of the ions. Alkali metal ions (Na+ and K+) are generally soluble, but phosphate ions (PO43-) are generally insoluble. It is inversely proportional to the distance between neighboring ions (the distance depends on the sum of the radii of the ions). Example: Alkaline earth hydroxides. The solubility ranking is: Mg(OH)2 < Ca(OH)2 < Sr(OH)2 < Ba(OH)2 21  Solution Process of Ionic Solids Hydration energy pulls ions apart. Lattice energy keeps the ions Hydration energy together. If a solid has a large lattice + – energy, it is typically insoluble. Lattice energy 22  Effects of Temperature on Solubility The solubility of one substance in another varies with temperature and pressure. Solubility is generally given in grams of solute that will dissolve in 100 g of water. For most solids, the solubility of the solid increases as the temperature increases. Solubility curves can be used to predict whether a solution with a particular amount of solute dissolved in water is saturated (on the line), unsaturated (below the line), or supersaturated (above the line). 23  Effects of Pressure Cylinder containing carbon Change on Solubility dioxide gas and water saturated with carbon dioxide. Pressure change: Little to no effect on the solubility of liquids or solids in water. Has a large Piston effect on the solubility of a gas. Gaseous CO2 Aqueous solution CO2 is more soluble at higher of CO2 pressures since the partial pressure is increased. When the piston is pushed down, increasing the partial pressure of carbon dioxide, Once the partial pressure is more gas dissolves (which tends to reduce thecarbon reduced, the solubility decreases. dioxide partial pressure). 24  Henry’s Law It is possible to predict the effect of pressure on the solubility of a gas in a liquid using Henry’s Law. The solubility of a gas (Cgas) is directly proportional to its partial pressure, (Pgas). Cgas = kHPgas kH is called the Henry’s law constant. 25  Colligative Properties Colligative properties are properties whose value depends only on the number of solute particles and not on what they are. Value of the property depends on the concentration of the solution. Ways to express concentrations: Molarity Mass Percentage of Solute Molality Mole Fraction 26  Solutions and Concentrations Molarity is used to quantitatively discuss the concentration. It is the ratio of the number of moles of solute to the number of liters of solution moles of solute Molarity M = liters of solution Molarity becomes a way of expressing concentration as well as a conversion factor between volume and moles Can then further convert between moles and grams 27  Example 0.42 g NaNO3 is dissolved to make 50.0 mL of solution. What is the solution’s concentration (in M)? 28  Example How many mL of 1.75 M NaCl are needed to get 100.0 g of NaCl? 29  Molality Molality of a solution is the moles of solute per kilogram of solvent moles of solute molality = kilograms of solvent What are the differences between molarity and molality? 30  Example An aqueous solution is 0.273 m KCl. What is the molar concentration of KCl? The density of the solution is 1.011 x 103 g/L. (Molar mass of KCl = 74.6 g/mol) 31  Mass Percentage of Solute Mass percentage: the percentage by mass of solute contained in a solution. mass of solute Mass percentage of solute = × 100% mass of solution 32  Mole Fraction Mole fraction: the fraction of the moles of component substance in the total moles of solution moles of substance A = total moles of solution The total of all the mole fractions in a solution is 1. The mole fraction has no units. 33  Chapter 11 Part 2... Vapor Pressure of Solutions Raoult’s Law Freezing Point Depression and Boiling Point Elevation Review of Phase Diagrams 34 Chapter 11: Part 2 CHEM 0120  Vapor Pressure of Solutions The vapor pressure of a solvent above a solution is lower than the vapor pressure of the pure solvent. The solute particles replace some of the solvent molecules at the surface. 2 Chapter 13: Part 1 CHEM 0120 2  Arrow Conventions Chemists commonly use two kinds of arrows in reactions to indicate the degree of completion of the reactions. A single arrow indicates that all the reactant molecules are converted to product molecules at the end. A double arrow indicates that the reaction reaches equilibrium with reactant and products present. 3  Reaction Dynamics When a reaction starts, the reactants are consumed and products are made. The reactant concentrations decrease and the product concentrations increase. Eventually, the products can react to re-form some of the reactants, assuming that the products are not allowed to escape. Processes that proceed in both the forward and reverse directions are said to be reversible. Reactants ⇌ Products 4  Example Catalytic methanation: CO(g) + 3H2(g) → CH4(g) + H2O(g) Steam reforming: CH4(g) + H2O(g) → CO(g) + 3H2(g) Consists of a forward and reverse reaction; therefore we can write it as: CO g + 3H g ⇌ CH g + H O(g) The favorability of products or reactants depends upon the conditions of the reaction. 5  Chemical Equilibrium Chemical equilibrium: the state reached by a reaction mixture when the rates of forward and reverse reactions have become equal 6  Equilibrium notes At equilibrium, the rates of the forward and reverse reactions are equal. This does not mean the concentrations of reactants and products are equal. Some reactions reach equilibrium after almost all of the reactant molecules are consumed The position of equilibrium favors the products. Other reactions reach equilibrium when only a small amount of the reactant molecules are consumed The position of equilibrium favors the reactants. 7  Equilibrium Constant, Kc 𝑎A + 𝑏B ⇌ 𝑐C + 𝑑D [C] [D] 𝐾 = [A] [B] Kc is the value obtained for the equilibrium-constant expression when equilibrium concentrations are substituted Law of mass action: a relation that states that the values of the equilibrium-constant expression Kc are constant for a particular reaction at a given temperature, whatever equilibrium concentrations are substituted 8  Writing Equilibrium Constant Expressions So, for the reaction 2 N2O5(g) ⇌ 4 NO2(g) + O2(g) Write the expression for the equilibrium constant, Kc 9  Kinetics of Equilibrium Dynamic equilibrium: consists of a forward reaction and a reverse reaction occurring at the same speed. Once at equilibrium, the forward and reverse reactions continue. 𝑎A ⇌ 𝑏B At equilibrium, kf[A]a = kr[B]b (rate of forward reaction = rate of reverse reaction) Kc can be identified as the ratio of rate constants for the forward and reverse reactions 𝑘 𝐾 = 𝑘 This ratio is just a comparison of the rate constants. The rate is dependent on the concentrations, coefficients and rate constants. 10  K for Reactions involving Gases The concentration of a gas in a mixture is proportional to its partial pressure. Kp: an equilibrium constant for a gaseous reaction in terms of partial pressures For 𝑎A(𝑔) + 𝑏B(𝑔) ⇌ 𝑐C(𝑔) + 𝑑D(𝑔), 𝑃 𝑃 𝐾 = 𝑃 𝑃 11  Relationship between Kc and Kp The relationship between Kc and Kp is: Kp = Kc(RT)Δn Δn is the sum of the coefficients of gaseous products minus the sum of the coefficients of gaseous reactants in the chemical equation 12  Example Nitrogen monoxide, a pollutant in automobile exhaust, is oxidized to nitrogen dioxide in the atmosphere. 2NO g + O g ⇌ 2NO (g) Kp = 2.2 x 1012 at 298 K Solve Kc for this reaction. 13  Equilibrium Constant for the Sum of Reactions Useful rule: If a given chemical equation can be obtained by taking the sum of other equations, the equilibrium constant for the given equation equals the product of the equilibrium constants of the added equations. For the reactions (1) 𝒂𝐀 ⇌ 𝒃𝐁 and (2) 𝒃𝐁 ⇌ 𝒄𝐂, the equilibrium constant expressions are as follows: [ ] [ ] 𝐾 = 𝐾 = [ ] [ ] For the reaction 𝒂𝐀 ⇌ 𝒄𝐂, the equilibrium constant expression is as follows: [𝐶] 𝐾 𝐾 =𝐾 = [𝐴] 14  Heterogeneous Equilibria Heterogeneous equilibrium: an equilibrium involving reactants and products in more than one phase. The concentrations of pure solids and pure liquids do not change during the course of a reaction. Because their concentration doesn’t change, solids and liquids are not included in the equilibrium constant expression. 15  Example for Heterogeneous Equilibria Write the expression for Kc for the following reactions: CaCO3(s) ⇌ CaO(s) + CO2(g) H2O(l) ⇌ H2O(g) 16  Using the Equilibrium Constant Ways to use the equilibrium constant: Qualitatively interpret the equilibrium constant. Does the equilibrium favor reactants or products? To predict the direction of the reaction. To calculate the equilibrium concentrations. 17  Qualitatively Interpreting Kc 𝑎A + 𝑏B ⇌ 𝑐C + 𝑑D [C] [D] 𝐾 = [A] [B] When Kc >> 1, the equilibrium mixture is mostly products. When Kc Kc, the reaction will go to the left. Indicates that the reaction mixture has more products. If Qc < Kc, the reaction will go to the right. Indicates that the reaction mixture has more reactants. If Qc = Kc, the reaction mixture is at equilibrium. 20  Reaction Quotient, Qc If Qc > Kc, the reaction will go to the left. If Qc < Kc, the reaction will go to the right. If Qc = Kc, the reaction mixture is at equilibrium. 21 Chapter 13 Part 2 CHEM 0120  Calculating Equilibrium Concentrations Steps to follow when solving for equilibrium concentrations: 1) Set up an ICE table with expressions in x Initial concentration or Starting concentration Change in concentration to reach equilibrium Equilibrium concentration 2) Substitute the expressions in x for equilibrium concentrations into the equilibrium-constant equation. 3) Solve the equilibrium-constant equation for the values of the equilibrium concentrations. 2  Change in Reaction Conditions Ways to alter the equilibrium composition of a gaseous reaction mixture: 1) Change the concentrations by adding reactants to the reaction vessel or by removing products from the reaction vessel. 2) Change the partial pressure of gaseous substances by changing the volume. 3) Change the temperature. 3 Removing Products or Adding Reactants Apply Le Chatelier’s principle When a system in chemical equilibrium is disturbed by a change of temperature, pressure, or a concentration, the system shifts in equilibrium composition in a way that tends to counteract this change of variable. Example: CO g + 3H g CH g + H O(g) At the new equilibrium position, the concentrations of reactants and products will be such that the value of the equilibrium constant is the same. 4  Effect of Concentration Changes on Equilibria The net reaction occurs left to right (the reaction occurs in the forward direction) to give a new equilibrium when reactant is added or product is removed from an equilibrium mixture. More products are produced. The net reaction occurs right to left (reverse direction) to give a new equilibrium when more product is added or reactant is removed from an equilibrium mixture. More reactants are produced. 5  Effect of Pressure Change If the volume of the container is decreased, the concentration of the gases increases. Partial pressure of the gases increases, which causes an increase of the total pressure in the container. According to Le Chatelier’s principle, the equilibrium will shift to remove that pressure. If the pressure is increased by decreasing the volume of a reaction mixture, the equilibrium shifts to the side with fewer gas molecules. 6 Chemical equilibrium change with pressure change CO g + 3H g CH g + H O(g) Comparison of gases: 1) At equilibrium (consider the amounts in the earlier example) 2) After compression 3) Compressed and at equilibrium (shifts equilibrium to the right) 7  Effect of Temperature: Endothermic Endothermic reactions absorb energy. Heat is “behaving” as a reactant. In an endothermic chemical reaction, heat is a reactant. Increasing the temperature causes an endothermic reaction to shift right (in the direction of the products); the equilibrium constant increases. Decreasing the temperature causes an endothermic reaction to shift left (in the direction of the reactants); the equilibrium constant decreases. 8  Effect of Temperature: Exothermic Exothermic reactions release energy. Heat is “acting” as a product. In an exothermic chemical reaction, heat is a product. Increasing the temperature causes an exothermic reaction to shift left (in the direction of the reactants); the value of the equilibrium constant decreases. Decreasing the temperature causes an exothermic reaction to shift right (in the direction of the products); the value of the equilibrium constant increases. 9 Chapter 16 CHEM 0120  Thermodynamics Thermodynamics: the study of the relationship between heat and other forms of energy involved in a chemical or physical process Used to predict whether a process will occur under the specified conditions. Processes that will occur are spontaneous. Nonspontaneous processes require the application of an external force. 2  First Law of Thermodynamics The change in internal energy of a system, U, equals heat plus work (q + w). Total energy must be conserved. Energy is neither created nor destroyed, only transferred and transformed. = + Internal energy: Sum of potential and kinetic energy of all particles that compose the system. It is a state function (it is not affected by the path). 3  Pressure-Volume Work Pressure is a force that acts against the sides of a container. If a part of that container can move, then work can be done w = -P V Pressure-volume work – volume change against an external pressure  Enthalpy Enthalpy – the heat exchanged in a reaction under constant pressure Constant pressure generally means an open system It is a state function Enthalpy can also be defined as the internal energy plus the product of pressure and volume H = U + PV If we want to look at the change in enthalpy: H= U+P V  Enthalpy The value of H is the amount of heat absorbed or released by a reaction under constant pressure If the value of H is positive, then the system has absorbed energy from the surroundings, and the reaction is endothermic If the value of H is negative, then the system has given off energy to the surroundings (heat has evolved), and the reaction is exothermic  Spontaneity Determined by comparing the chemical potential energy of the system before the reaction with the free energy of the system after the reaction. If the system after the reaction has less potential energy than the system before the reaction, the reaction is thermodynamically favorable. 7  Spontaneous vs Reversible Processes A spontaneous process is irreversible because there is a net release of energy when it proceeds in that direction. Proceeds in one direction. If one direction is spontaneous, the opposite direction must be nonspontaneous. A reversible process will proceed back and forth between the two end conditions. The result is no change in free energy. 8  Spontaneous Processes Spontaneous processes occur because they release energy from the system. Most spontaneous processes proceed from a system of higher potential energy to a system at lower potential energy. Exothermic But there are some spontaneous processes that proceed from a system of lower potential energy to a system at higher potential energy. Endothermic 9  Determining Whether a Reaction is Spontaneous. Two factors determine whether a reaction is spontaneous: Enthalpy change and Entropy change of the system. The H, is the difference between the sum of the internal energy and PV work energy of the reactants and that of the products. The entropy change, S, is the difference between the randomness of the reactants and that of the products. 10  Entropy Entropy (S): a thermodynamic quantity that is a measure of how dispersed the energy of a system is among the different possible ways that a system can contain energy It is a state function. In spontaneous processes, the entropy of the system plus its surroundings increases. *Entropy change entirely in the system for the flasks. 11  Entropy A state function that is a measure of the matter and/or energy dispersal within a system, determined by the number of system microstates; often described as a measure of the disorder of the system 12  Changes in Entropy ( S) S = Sfinal Sinitial Entropy change is favorable when the result is a more random system. S is positive. Changes that increase the entropy are as follows: Reactions whose products are in a more random state Solid more ordered than liquid; liquid more ordered than gas Reactions that have larger numbers of product molecules than reactant molecules Increase in temperature Solids dissociating into ions upon dissolving 13  Example of the Change in Entropy Ssolid < Sliquid < Sgas Calculate S for the melting of ice. Entropy of 1 mol of ice = 41 J/K Entropy of 1 mol of liquid water = 63 J/K H2O(s 2O(l) 14  Second Law of Thermodynamics The total entropy of a system and its surroundings always increases for a spontaneous process. Energy can be neither created nor destroyed during a spontaneous process, but the energy is dispersed, so entropy is produced. = entropy created + Second Law restated: For a spontaneous process at a given temperature (T), the change in entropy of the system is greater than the heat divided by the absolute temperature, q/T > 15  Entropy Change for a Phase Transition At equilibrium, entropy change results from the absorption of heat. = Repeat the calculation for change in entropy for the melting of ice. fus = 6.0 kJ / 1 mol of ice 16  Example #1 The enthalpy change when liquid methanol, CH3OH, vaporizes at 25 is 38.0 kJ/mol. What is the entropy change when 1.00 mol of vapor in equilibrium with liquid condenses to liquid at 25 ? 17  Standard States The state of a material at a defined set of conditions. Represented by a superscript degree sign on the symbol of the quantity For gases: pure gas at exactly 1 atm pressure For pure liquids and solids: 1 atm pressure Temperature is usually 298 K For solutions: 1 M concentration 18  Third Law of Thermodynamics A substance that is perfectly crystalline at 0 K has an entropy of zero. Therefore, every substance that is not a perfect crystal at absolute zero has some energy from entropy. Therefore, the absolute entropy of substances is always positive. 19  Standard Absolute Entropies, S° S° designates standard state conditions. Entropy is an extensive physical property of matter. Entropies are for 1 mol of a substance at 298 K for a particular state, a particular allotrope, a particular molecular complexity, a particular molar mass, and a particular degree of dissolution. 20  Relative Standard Entropies: States The gas state has a larger entropy than the liquid state at a particular temperature. The liquid state has a larger entropy than the solid state at a particular temperature. 21 Standard Molar Entropy Values 22  Relative Standard Entropies: Molar Mass The larger the molar mass, the larger the entropy. Available energy states are more closely spaced, allowing more dispersal of energy through the states. 23  Relative Standard Entropies: Allotropes The less constrained the structure of an allotrope is, the larger its entropy. The fact that the layers in graphite are not bonded together makes graphite less constrained. 24  Relative Standard Entropies: Dissolution Dissolved solids generally have larger entropy, distributing particles throughout the mixture. 25  Relative Standard Entropies: Molecular Complexity Larger, more complex molecules generally have larger entropy. More energy states are available, allowing more dispersal of energy through the states. 26  Free Energy (G) Free energy: a thermodynamic quantity defined by the equation G = H – TS Gives a direct relationship to the spontaneity of a reaction. = S is positive when spontaneous, so G must be negative. Standard free-energy change = 27  Standard Free Energy of Formation, Gf° Gf°: the free-energy change that occurs when 1 mole of substance is formed from its elements in their reference forms at 1 atmosphere and at a specified temperature For elements in their most stable states, the value is zero. = 28  Spontaneity of a Reaction using G° Useful rules in judging the spontaneity of a reaction: If G°is a large negative number, the reaction is spontaneous Reactants transform almost entirely to products at equilibrium. If G°is a large positive number, the reaction is nonspontaneous Reactants do not give significant amounts of products at equilibrium. When G°has a small negative or positive value, the reaction gives an equilibrium mixture with significant amounts of both reactants and products. 29  Why is it “free” energy? The free energy is the maximum amount of energy released from a system that is available to do work on the surroundings. For many exothermic reactions, some of the heat released as a result of the enthalpy change goes into increasing the entropy of the surroundings, so it is not available to do work. And even some of this free energy is generally lost to heating up the surroundings. 30  Free Energy Change During a Reaction A decrease in free energy can show up as work done (to give maximum work), but also appears as an increase in entropy. 31  Gibbs Free Energy, G A process will be spontaneous when G is negative. G will be negative under the following conditions: H is negative and S is positive. Exothermic and more random H is negative and large and S is negative but small. H is positive but small and S is positive and large. Or high temperature G will be positive under the following conditions: H is positive and S is negative. Never spontaneous at any temperature When G = 0, the reaction is at equilibrium. 32  Relating G° to the equilibrium constant, K G = G° only when the reactants and products are in their standard states. Their normal state at that temperature Partial pressure of gas = 1 atm Concentration = 1 M Under nonstandard conditions, G = G° + RT ln Q. Q is the reaction quotient. At equilibrium, G = 0. G° RT ln K 33  Thermodynamic Equilibrium Constant, K K is the equilibrium constant in which: The concentrations of gases are expressed in partial pressures in atmospheres; The concentrations of solutes in liquid solutions are expressed in molarities. 34  Spontaneity using G° and K Since G = 0 at equilibrium, = ln When K > 1, G° is negative and the reaction is spontaneous in the forward direction under standard conditions. When K < 1, G° is positive and the reaction is nonspontaneous as written. 35  Example #2 What is the standard free-energy change G°at 25 for the following reaction? (What information is required?) H2(g) + Br2(l HBr(g) What is the value of the thermodynamic equilibrium constant K? 36  Why is K temperature dependent? Combining these two equations, G° = H° – T S° and G° = – RT ln(K) it can be shown that – H°rxn 1 S°rxn ln(K) = + R T R This equation is in the form y = mx + b. The graph of ln(K) versus inverse T is a straight line. 37  Changes of Free Energy with Temperature Assume H°and S°are constant with respect to temperature; = 38  Example #3 Sodium carbonate can be prepared by heating sodium hydrogen carbonate. 2 NaHCO3(s 2CO3(s) + H2O(g) + CO2(g) Estimate the temperature at which NaHCO3 decomposes to products at 1 atm. (What info is required?) 39