Quantitative aspects of chemical change: Moles and molar mass
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1 OpenStax-CNX module: m Quantitative aspects of chemical change: Moles and molar mass Free High School Science Texts Project This work is produced by OpenStax-CNX and licensed under the Creative Commons Attribution License Quantitative Aspects of Chemical Change An equation for a chemical reaction can provide us with a lot of useful information. It tells us what the reactants and the products are in the reaction, and it also tells us the ratio in which the reactants combine to form products. Look at the equation below: F e + S FeS In this reaction, every atom of iron (F e) will react with a single atom of sulphur (S) to form one molecule of iron sulphide (FeS). However, what the equation doesn't tell us, is the quantities or the amount of each substance that is involved. You may for example be given a small sample of iron for the reaction. How will you know how many atoms of iron are in this sample? And how many atoms of sulphur will you need for the reaction to use up all the iron you have? Is there a way of knowing what mass of iron sulphide will be produced at the end of the reaction? These are all very important questions, especially when the reaction is an industrial one, where it is important to know the quantities of reactants that are needed, and the quantity of product that will be formed. This chapter will look at how to quantify the changes that take place in chemical reactions. 2 The Mole Sometimes it is important to know exactly how many particles (e.g. atoms or molecules) are in a sample of a substance, or what quantity of a substance is needed for a chemical reaction to take place. The amount of substance is so important in chemistry that it is given it's own name, which is the mole. Denition 1: Mole The mole (abbreviation 'n') is the SI (Standard International) unit for 'amount of substance'. Now that we know what a mole is, we can relate it to something that we know already. This is the relative atomic mass. For example, if we have a sample containing 1g of hydrogen then we have 1 mole of hydrogen, since the relative atomic mass of hydrogen is 1u. We can build up to the idea of Avogadro's number. For example, if you have 12 eggs then you have a dozen eggs. After this number we get a gross of eggs, which is 144 eggs. Finally if we wanted one mole of eggs this would be 6, That is a lot of eggs! In one mole of any substance, there are 6, particles. When we talk about the mole, we should always say what the particles are. The particles can be atoms, molecules, electrons, or almost anything else. Version 1.2: Sep 29, :08 am
2 OpenStax-CNX module: m Denition 2: Avogadro's number The number of particles in a mole, equal to 6, If we were to write out Avogadro's number then it would look like: This is a very large number. If we had this number of cold drink cans, then we could cover the surface of the earth to a depth of over 300 km! If you could count atoms at a rate of 10 million per second, then it would take you 2 billion years to count the atoms in one mole! note: The original hypothesis that was proposed by Amadeo Avogadro was that 'equal volumes of gases, at the same temperature and pressure, contain the same number of molecules'. His ideas were not accepted by the scientic community and it was only four years after his death, that his original hypothesis was accepted and that it became known as 'Avogadro's Law'. In honour of his contribution to science, the number of particles in one mole was named Avogadro's number. 2.1 Moles and mass 1. Complete the following table: Element Relative atomic mass (u) Sample mass (g) Number of moles in the sample Hydrogen Magnesium Carbon Chlorine Nitrogen Click here for the solution 1 2. How many atoms are there in... a. 1 mole of a substance b. 2 moles of calcium c. 5 moles of phosphorus d. 24, 31 g of magnesium e. 24, 02 g of carbon Click here for the solution 2 Table 1 3 Molar Mass Denition 3: Molar mass Molar mass (M) is the mass of 1 mole of a chemical substance. The unit for molar mass is grams per mole or g mol 1. You will remember that when the mass, in grams, of an element is equal to its relative atomic mass, the sample contains one mole of that element. This mass is called the molar mass of that element. You may sometimes see the molar mass written as M m. We will use M in this book, but you should be aware of the alternate notation
3 OpenStax-CNX module: m It is worth remembering the following: On the periodic table, the relative atomic mass that is shown can be interpreted in two ways. 1. The mass of a single, average atom of that element relative to the mass of an atom of carbon. 2. The mass of one mole of the element. This second use is the molar mass of the element. Element Relative atomic mass (u) Molar mass (g mol 1 ) Magnesium 24,31 24,31 24,31 Lithium 6,94 6,94 6,94 Oxygen Nitrogen 14,01 14,01 14,01 Iron 55,85 55,85 55,85 Mass of one mole of the element (g) Table 2: The relationship between relative atomic mass, molar mass and the mass of one mole for a number of elements. Exercise 1: Calculating the number of moles from mass (Solution on p. 8.) Calculate the number of moles of iron (F e) in a 11, 7 g sample. Exercise 2: Calculating mass from moles (Solution on p. 8.) You have a sample that contains 5 moles of zinc. 1. What is the mass of the zinc in the sample? 2. How many atoms of zinc are in the sample? 3.1 Moles and molar mass 1. Give the molar mass of each of the following elements: a. hydrogen b. nitrogen c. bromine Click here for the solution 3 2. Calculate the number of moles in each of the following samples: a. 21, 62 g of boron (B) b. 54, 94 g of manganese (Mn) c. 100, 3 g of mercury (Hg) d. 50 g of barium (Ba) e. 40 g of lead (P b) Click here for the solution
4 OpenStax-CNX module: m An equation to calculate moles and mass in chemical reactions The calculations that have been used so far, can be made much simpler by using the following equation: m (mass of substance in g) n (number of moles) = M ( molar mass of substance in g mol 1) (1) tip: Remember that when you use the equation n = m M, the mass is always in grams (g) and molar mass is in grams per mol (g mol 1 ). The equation can also be used to calculate mass and molar mass, using the following equations: and m = n M (2) M = m n (3) The following diagram may help to remember the relationship between these three variables. You need to imagine that the horizontal line is like a 'division' sign and that the vertical line is like a 'multiplication' sign. So, for example, if you want to calculate 'M', then the remaining two letters in the triangle are 'm' and 'n' and 'm' is above 'n' with a division sign between them. In your calculation then, 'm' will be the numerator and 'n' will be the denominator. Figure 1 Exercise 3: Calculating moles from mass (Solution on p. 8.) Calculate the number of moles of copper there are in a sample that weighs 127 g. Exercise 4: Calculating mass from moles (Solution on p. 8.) You are given a 5 mol sample of sodium. What mass of sodium is in the sample? Exercise 5: Calculating atoms from mass (Solution on p. 8.) Calculate the number of atoms there are in a sample of aluminium that weighs 80, 94 g. 4.1 Some simple calculations 1. Calculate the number of moles in each of the following samples: a. 5, 6 g of calcium b. 0, 02 g of manganese c. 40 g of aluminium Click here for the solution 5 2. A lead sinker has a mass of 5 g. a. Calculate the number of moles of lead the sinker contains. b. How many lead atoms are in the sinker? 5
5 OpenStax-CNX module: m Click here for the solution 6 3. Calculate the mass of each of the following samples: a. 2, 5 mol magnesium b. 12 mol lithium c. 4, atoms of silicon Click here for the solution 7 5 Molecules and compounds So far, we have only discussed moles, mass and molar mass in relation to elements. But what happens if we are dealing with a molecule or some other chemical compound? Do the same concepts and rules apply? The answer is 'yes'. However, you need to remember that all your calculations will apply to the whole molecule. So, when you calculate the molar mass of a molecule, you will need to add the molar mass of each atom in that compound. Also, the number of moles will also apply to the whole molecule. For example, if you have one mole of nitric acid (HNO 3 ), it means you have 6, molecules of nitric acid in the sample. This also means that there are 6, atoms of hydrogen, 6, atoms of nitrogen and (3 6, ) atoms of oxygen in the sample. In a balanced chemical equation, the number that is written in front of the element or compound, shows the mole ratio in which the reactants combine to form a product. If there are no numbers in front of the element symbol, this means the number is '1'. e.g. N 2 + 3H 2 2NH 3 In this reaction, 1 mole of nitrogen reacts with 3 moles of hydrogen to produce 2 moles of ammonia. Exercise 6: Calculating molar mass (Solution on p. 8.) Calculate the molar mass of H 2 SO 4. Exercise 7: Calculating moles from mass (Solution on p. 9.) Calculate the number of moles there are in 1 kg of MgCl 2. Exercise 8: Calculating the mass of reactants and products (Solution on p. 9.) Barium chloride and sulphuric acid react according to the following equation to produce barium sulphate and hydrochloric acid. BaCl 2 + H 2 SO 4 BaSO 4 + 2HCl If you have 2 g of BaCl What quantity (in g) of H 2 SO 4 will you need for the reaction so that all the barium chloride is used up? 2. What mass of HCl is produced during the reaction? 5.1 Group work : Understanding moles, molecules and Avogadro's number Divide into groups of three and spend about 20 minutes answering the following questions together: 1. What are the units of the mole? Hint: Check the denition of the mole. 2. You have a 56 g sample of iron sulphide (F es) a. How many moles of F es are there in the sample? b. How many molecules of F es are there in the sample? c. What is the dierence between a mole and a molecule?
6 OpenStax-CNX module: m The exact size of Avogadro's number is sometimes dicult to imagine. a. Write down Avogadro's number without using scientic notation. b. How long would it take to count to Avogadro's number? You can assume that you can count two numbers in each second. Khan academy video on the mole - 1 This media object is a Flash object. Please view or download it at < Figure More advanced calculations 1. Calculate the molar mass of the following chemical compounds: a. KOH b. FeCl 3 c. Mg (OH) 2 Click here for the solution 8 2. How many moles are present in: a. 10 g of Na 2 SO 4 b. 34 g of Ca (OH) 2 c. 2, molecules of CH 4? Click here for the solution 9 3. For a sample of 0, 2 moles of potassium bromide (KBr), calculate... a. the number of moles of K + ions b. the number of moles of Br ions Click here for the solution You have a sample containing 3 moles of calcium chloride. a. What is the chemical formula of calcium chloride? b. How many calcium atoms are in the sample? Click here for the solution Calculate the mass of: a. 3 moles of NH 4 OH b. 4, 2 moles of Ca (NO 3 ) 2 Click here for the solution , 2 g sulphur reacts with an unknown quantity of zinc according to the following equation: Zn + S ZnS a. What mass of zinc will you need for the reaction, if all the sulphur is to be used up?
7 OpenStax-CNX module: m b. What mass of zinc sulphide will this reaction produce? Click here for the solution Calcium chloride reacts with carbonic acid to produce calcium carbonate and hydrochloric acid according to the following equation: CaCl 2 + H 2 CO 3 CaCO 3 + 2HCl If you want to produce 10 g of calcium carbonate through this chemical reaction, what quantity (in g) of calcium chloride will you need at the start of the reaction? Click here for the solution
8 OpenStax-CNX module: m Solutions to Exercises in this Module Solution to Exercise (p. 3) If we look at the periodic table, we see that the molar mass of iron is 55, 85 g mol 1. This means that 1 mole of iron will have a mass of 55, 85 g. Step 2. If 1 mole of iron has a mass of 55, 85 g, then: the number of moles of iron in 111, 7 g must be: There are 2 moles of iron in the sample. Solution to Exercise (p. 3) 111, 7g 1 = 2 mol (4) 55, 85g mol Molar mass of zinc is 65, 38 g mol 1, meaning that 1 mole of zinc has a mass of 65, 38 g. Step 2. If 1 mole of zinc has a mass of 65, 38 g, then 5 moles of zinc has a mass of: 65, 38 g 5 mol = 326, 9 g (answer to a) Step , = 30, (5) (answer to b) Solution to Exercise (p. 4) n = m M (6) Step 2. There are 2 moles of copper in the sample. n = , 55 = 2 (7) Solution to Exercise (p. 4) m = n M (8) Step 2. M Na = 22, 99 g mol 1 Therefore, The sample of sodium has a mass of 114, 95 g. Solution to Exercise (p. 4) m = 5 22, 99 = 114, 95 g (9) n = m M Step 2. Number of atoms in 3 mol aluminium = 3 6, There are 18, aluminium atoms in a sample of 80, 94 g. Solution to Exercise (p. 5) 80, 94 = = 3 moles (10) 26, 98 Hydrogen = 1, 008 g mol 1 ; Sulphur = = 32, 07 g mol 1 ; Oxygen = 16 g mol 1
9 OpenStax-CNX module: m Step 2. Solution to Exercise (p. 5) M (H2SO 4) = (2 1, 008) + (32, 07) + (4 16) = 98, 09 g mol 1 (11) n = m M (12) Step 2. a. Convert mass into grams m = 1kg 1000 = 1000 g (13) Step 3. b. Calculate the molar mass of MgCl 2. M (MgCl2 ) = 24, 31 + (2 35, 45) = 95, 21 g mol 1 (14) There are 10, 5 moles of magnesium chloride in a 1 kg sample. Solution to Exercise (p. 5) n = 1000 = 10, 5 mol (15) 95, 21 n = m M = 2 = 0, 0096 mol (16) 208, 24 Step 2. According to the balanced equation, 1 mole of BaCl 2 will react with 1 mole of H 2 SO 4. Therefore, if 0, 0096 mol of BaCl 2 react, then there must be the same number of moles of H 2 SO 4 that react because their mole ratio is 1:1. Step 3. m = n M = 0, , 086 = 0, 94 g (17) (answer to 1) Step 4. According to the balanced equation, 2 moles of HCl are produced for every 1 mole of the two reactants. Therefore the number of moles of HCl produced is (2 0, 0096), which equals 0, 0096 moles. Step 5. m = n M = 0, , 73 = 0, 69 g (18) (answer to 2)
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