Angola Chemistry Grade 9 Mole Concept PDF

 INTRODUCTION In daily life, the use of suitable measurement units enables us to evaluate quantities more precisely. Instead of requesting 123 cherries from your grocer,...

 INTRODUCTION In daily life, the use of suitable measurement units enables us to evaluate quantities more precisely. Instead of requesting 123 cherries from your grocer, isn’t it easier to ask him for a desired quantity in kilograms? Or, instead of packets of sugar, would you rather ask for 240 lumps in a supermarket (Figure 1)? 123 or 1 kg 240 or a packet Figure 1: The use of suitable measurement units enables us to better express quantities The “mole” is abbreviated as mol. Similarly, when we study small particles in chemistry we use a special unit known as the mole (mol). 1. MOLE One of the most important unit in chemistry is the mole. One mole is accepted as 6.02 ⋅ 1023 particles. Here, the particles may be any atom, molecule, pencils etc... Fe Fe Fe Fe Fe Fe Fe Fe Fe Fe Fe Fe Fe Fe Fe Fe Fe Fe Fe Fe Fe Fe Fe Fe Fe Fe Fe Fe Fe Fe Fe Fe Fe Fe Fe Fe Fe Fe Fe Fe Fe Fe Fe Fe Fe Fe Fe Fe Fe Fe Fe Fe Fe Fe = 1 mol of iron atoms 602,000,000,000,000,000,000,000 iron atoms = 1 mol of people 602,000,000,000,000,000,000,000 people = 1 mol of apples 602,000,000,000,000,000,000,000 apples 8 Chemistry Grade 9 2. AVOGADRO’S NUMBER 602,000,000,000,000,000,000,000 is a very large number, known as Avogadro’s number is also known as Avogadro’s number. It is abbreviated as NA. Avogadro’s constant, which refers to 6.02 ⋅ 1023 particles / mole. Why do we use such huge numbers in chemistry? The answer is quite easy: Because quantities in chemistry can sometimes be very, very small. For example, 1 hydrogen atom weighs about, 1 amu = 0.00000000000000000000000166 g How is it possible to weigh this amount in a laboratory? 1 amu. 6.02. 1023 = 1 g Avogadro’s number, 6.02. 1023, has proved to be a very good conversion factor. It makes our calculations easier. 1 gram = 6.02 ⋅ 1023 ⋅ amu or 1 g = 1 mol ⋅ amu Let’s remember again the example of the hydrogen atom: 1 hydrogen atom is 1 amu. 6.02 ⋅ 1023 of hydrogen atoms is 1 gram. Amadeo Avogadro (1776–1856) 1 mol Avogadro was an Italian lawyer and or 1 mol of hydrogen atoms is 1 gram, it’s that simple. scientist, who studied physics and mathematics. Similar to hydrogen, this conversion can be used for all atoms or molecules. He found that equal volumes of Let’s look at the following examples, gases contain equal numbers of I. The atomic mass of a carbon atom is 12 amu, or particles under the same conditions. 1 mol of carbon atoms is 12 g. II. The atomic mass of a calcium atom is 40 amu, or The atomic mass of each atom is given 1 mol of calcium atoms is 40 g. in the periodic table. III. The atomic mass of a platinum atom is 195 amu, or 1 mol of platinum atoms is 195 g. Mole Concept 9  3. MOLAR MASS (M) A formula The mass of 1 mol (6.02 ⋅ 1023) of substance in grams is defined as its molar mass. Na - CI - Na 1 mol of sodium atoms (Na) = 6.02 ⋅ 1023 Na atoms = 23 g CI - Na - CI Na - CI - Na 1 mol of zinc atoms (Zn) = 6.02 ⋅ 1023 O atoms = 65.4 g Because of its crystalline structure, an 1 mol of oxygen molecules (O2) = 6.02 ⋅ 1023 O2 molecules = 32 g ionic compound is expressed as a formula, not in molecules like molecular 1 mol of carbon dioxide molecules (CO2) = 6.02 ⋅ 1023 CO2 molecules = 44 g compounds. 1 mol of sodium chloride (NaCl) = 6.02 ⋅ 1023 NaCl formula = 58.5 g 1 mol of hydrogen ions (H+) = 6.02 ⋅ 1023 H+ ions =1g 1 mol Zn (metal pieces) 1 mol NaCl (granules) 1 Calculate the molar mass of water, H2O. The formula for water, H2O, is composed of 2 hydrogen atoms and 1 oxygen atom. By looking at the periodic table (Appendix D); you can find the mass of a hydrogen atom as 1 amu, and the mass of an oxygen atom as 16 amu. Molar Mass of H2O = 2 ⋅ (mass of the H atom) + 1 ⋅ (mass of O atom) Molar Mass of H2O = (2 ⋅ 1) + (1 ⋅ 16) Remember Molar Mass of H2O = 18 amu 1 amu. 1 mol = 1g If a water molecule is 18 amu, then 1 mole of water molecule becomes 18 g. 10 Chemistry Grade 9 Exercise 1: What is the molar mass of Al2(SO4)3? 4. MOLAR VOLUME OF GASES The volume of 1 mol of gas is called the molar volume of that gas. At a standard temperature and pressure (STP), one mole of any gas occupies 22.4 L volume. STP = 0 ºC and 1 atm pressure For example: 1 mole of O2 has 22.4 L volume at STP 1 mole of He has 22.4 L volume at STP 1 mole of CO2 has 22.4 L volume at STP He O2 CO O2 22.4 L 22.4 L 2 22.4 L 4g He 32 g O2 44 g CO2 1 mol He 1 mol O2 1 mol CO2 2 What is the volume of 0.1 mol of hydrogen (H2) gas at STP? If 1 mol of H2 22.4 L at STP then 0.1 mol of H 2 x L 0.1. 22.4 x= =2.24 L 1 Exercise 2: What are the masses of 5.6 L of SO3 and 5.6 L of CO gases at STP? Mole Concept 11  5. THE MOLE CONCEPT CALCULATIONS The number of moles, which is represented by n, is used for various calculations Did you know? in chemistry. The number of moles is related to the number of particles, mass or In some countries, Mole Day is volume of substances. celebrated annually on October 23 from 6:02 am to 6:02 pm. (To commemorate Avogadro’s number 6.02 ⋅ 1023.) Number of On this day, schools have particles different activities related to the (6.0 mole concept or chemistry. 2 ×1 0 23 n= ) N NA Number of (Molar Mass) Mass moles m n= M es TP as t S ) rg a fo 2.4 In chemical calculations, use the (2 V.4 Periodic Table in Appendix D to find the 22 n= molar mass of any substance. Volume 5.1. MOLE - NUMBER OF PARTICLES RELATIONSHIP If the number of particles (atoms, molecules, ions....) for a substance is known, the mole number of that substance can easily be calculated, using the following: Number of particles Number of moles= 6.02 ⋅10 23 N Number of particles n= NA mol Avogadro’s number 12 Chemistry Grade 9  3 What is the number of moles of 3.01. 1022 atoms of helium (He)? N By using the formula, n He = NA 3.01 ⋅10 22 helium atom nHe = = 0.05 mol 6.02 ⋅10 23 4 What is the total number of atoms found in two moles of a H2SO4 molecule? N By using the formula, n (H = 2 SO4 ) NA N 2= ⇒ N=1.204 ⋅10 24 H 2SO 4 molecules 6.02 ⋅10 23 A H2SO4 molecule is composed of 7 atoms (2 Hydrogen, 1 Sulfur and 4 Oxygen) If a H2SO4 molecule contains 7 atoms 1.204. 1024 H2SO4 molecules contain x 1.204 ⋅10 24 ⋅ 7 x= = 8.428 ⋅10 24 atoms 1 Exercise 3: If 10 moles of oxygen (O2) molecules are given: a) Calculate the number of oxygen molecules present. b) Calculate the number of oxygen atoms present. c) Calculate the volume of the oxygen molecules at STP. Oxygen gas Mole Concept 13  5.2. MOLE - MASS RELATIONSHIP The number of moles in a substance can be calculated with the help of its molar mass and mass. The following formula shows the relationship between the number of moles and mass. Molar mass, MM or M, can be used for the atom, molecule or ion, etc... Mass Number of moles = Molar Mass m g m n= n= here M mol M g/mol 5 What is the mole number of 11 g of carbon dioxide (CO2) gas? First, the molar mass of CO2 is calculated. M(CO )=1 ⋅ 12 + 2 ⋅ 16 = 44 g/mol. 2 m Then, the number of moles can be calculated by using the n = formula. M 11g n= = 0.25 mol 44g/mol 6 What is the mass of 2.5 moles of sodium hydroxide (NaOH)? M(NaOH) = (1 ⋅ 23) + (1 ⋅ 16) + (1 ⋅ 1) = 40 g/mol m Then, the formula mass of NaOH can be calculated by using n = M Exercise 4: How many moles of sulfur (S) and oxygen (O) exist in 32 g SO2? 14 Chemistry Grade 9 5.3. MOLE - VOLUME RELATIONSHIP For gases at STP (0 ºC and 1 atm), 1 mole of any gas occupies 22.4 L. Therefore, the number of moles of a gas can be calculated, if the volume of a gas is known at STP. Volume Number of moles = 22.4 V V L n= here n= 22.4 mol 22.4 L / mol 7 What is the number of moles of 112 L chlorine (Cl2) gas at STP? 112 L CI2 V By using the formula of n = , the number of moles of Cl 2 can be calculated. 22.4 112L n=? n= 22.4L / mol n = 5 mol 8 How many liters does two moles of oxygen gas (O2) occupy at STP? 2m mol O2 V V n= ⇒ 2= ⇒ V = 44.8 L 22.4 22.4 V=? Exercise 5: Answer the following questions for 3.01. 1023 carbon dioxide molecules (CO2) at STP: a) What is the volume of CO2? b) What is the total number of atoms in CO2? Mole Concept 15  6. SEVERAL TYPES OF PROBLEMS 6.1. FINDING DENSITY OF A GAS AT STP The density of gas at STP can be calculated if its molar mass is known. 9 In general, the unit of density of a gas is Find the density of 2 moles of carbon dioxide (CO2) at STP. given in g / L instead of g / mL or g / cm3. 1 mole of CO2 occupies 22.4 L at STP 2 mole of CO2 occupies x _______________________________________ x = 44.8 L M (CO2) = 12 + (16. 2) = 44 g/mol. Then the density of CO2 is, m 44 g ρ= ⇒ =1.96 g/L V 22.4 L Exercise 6: What is the density of oxygen (O2) gas at STP? 6.2. MASS PERCENTAGE OF ELEMENTS IN A COMPOUND The percentage of mass in an element in a compound can easily be found when the molecular formula and molar mass (or atomic mass) of elements are known. 10 Sodium hydroxide (NaOH) is known to Find the mass percentages of each element in sodium hydroxide (NaOH). be caustic. M(NaOH) = 23 + 16 +1 = 40 g/mol molar mass 16 % Na in NaOH = ratio = , % O in NaOH = ⋅100= 40% and molar mass 40 1 % H in NaOH = ⋅100= 2.5% 40 Sucrose (C12 H22 O11) is better known as Exercise 7: table sugar. What is the mass percentage of carbon (C) in sugar (C12 H22 O11)? 16 Chemistry Grade 9 6.3. CALCULATION OF EMPIRICAL FORMULA BY MASS PERCENTAGES The mass of elements in a compound is crucial when solving problems with the Empirical Formula = Simplest Formula empirical formula. First, the number of moles in atoms are found by dividing their masses by their molar masses. Next, the number of moles are either divided by the smallest mole number or, if necessary to calculate mole ratio of elements, Whole number = Integers (positive) n = 0, 1, 2, 3..... multiplied with certain multipliers to get whole numbers for each element. These numbers for different elements provide the empirical formula. 11 What is the empirical formula of 26.6 g nitrogen oxide (NO) that contains 9.8 Nx Oy grams of nitrogen? Total mass = m(N) + m(O) = 26.6 26.6 = 9.8 + m(O) m(O) = 16.8 g Step 1: Find the number of moles of atoms. 16.8 Number of moles of O : n= =1.05 mol, 16 9.8 Number of moles of N : n = = 0.7 mol. 14 Step 2: Divide the number of moles by the smallest number, which is 0.7, to get the mole ratio between elements. 0.7 1.05 For N : =1, for O : =1.5 0.7 0.7 Step 3: The number of atoms must be expressed as positive integers. Thus, the numbers should be multiplied by 2. For N : 2. 1 = 2, for O : 2. 1.5 = 3 The empirical formula of the compound is N2O3. Exercise 8: A compound of C, H, and O is composed of 40 % of carbon, 6.66 % of hydrogen Cx HyOz and 53.34 % of oxygen by mass. What is the empirical formula for this compound? Mole Concept 17  6.4. DETERMINING MOLECULAR FORMULA The molecular formula of a compound can be calculated after its empirical formula has been found. First, the relation between the molar masses of molecular formula and the empirical formula is found by using the relation below. molar mass of molecular formula ratio = molar mass of empirical formula The number of atoms in an empirical formula is multiplied by the obtained value in ratio calculations. 12 Lactic acid is a compound (containing C, H and O), with a molar mass of 90 g/mol. 25.2 g of lactic acid contains 10.08 g of carbon and 13.44 g of oxygen. What is the molecular formula of lactic acid? First, the mass of hydrogen in the compound is calculated. 25.2 – (10.08 + 13.44) = 1.68 g. Then, we find the number of moles of C, H and O atoms. 10.08 Number of moles of C atoms, n = = 0.84 mol. 12 1.68 Number of moles of H atoms, n = =1.68 mol. Lactic acid is the acid found in milk. 1 13.44 Number of moles of O atoms, n = = 0.84 mol. 16 Then, we divide these numbers by 0.84, C 0.84 H1.68 O0.84 ⇒ C1H 2O1 =1 =2 =1 0.84 0.84 0.84 The empirical formula for the compound is C1H2O1 or CnH2nOn. The molar mass of CH2O = 12 + (2. 1) + 16 = 30 g/mol. molar mass of lactic acid 90 ratio = = = 3 then molar mass of empirical formula 30 The molecular formula of lactic acid is C1.3 H2.3 O1.3 ⇒ C3H6O3 Exercise 9: What is the molecular formula, and the name, of 2 g of a compound that is composed of 0.5306 g K (potassium), 0.7076 g Cr (chromium) and 0.7618 g O A sample of potassium dichromate (oxygen)? 18 Chemistry Grade 9 6.5. MIXTURE PROBLEMS In these types of problems, the components of a mixture can be calculated by using basic mathematical operations, as shown in the following example. 13 The mixture of oxygen and helium is 9.8 gram, and has a volume of 31.36 liters, at STP. What is the number of moles of each gas in the given mixture? He a H and d O2 First, find the number of moles in the mixture. V = 31.36 L 31.36 L n(mixture) = =1.4 mol mixture 22.4 L/mol If the number of oxygen in the mixture is accepted as x mole, then the number of moles of helium in the mixture becomes 1.4 – x. Remember the formula, m n= ⇒ m=n. M M Since the molar mass of O2 is 32, and the molar mass of the He is 4; the masses of oxygen and helium gases are: m(O2) = 32. x m(He) = 4. (1.4 – x) and the value of x will be, m(O ) + m(He) = m(total) 2 32. x + 4. (1.4 – x) = 9.8 x = 0.15 mol So, the number of moles of O2(g) is 0.15. The number of moles of helium can be determined as such, n(He) = 1.4 – x = 1.4 – 0.15 ⇒ n(He) = 1.25 mol Exercise 10: What is the total mass of the mixture of C3H4, C2H2 and CH4 gases, if each gas contains 2 moles of hydrogen atoms? Mole Concept 19