1. Chapter 7-3: Using Chemical Formulas Coach Kelsoe Chemistry Pages 237-244

2. Section 7-3 Objectives Calculate the formula mass or molar mass of any given compound. Use molar mass to convert between mass in grams and amount in moles of a chemical compound. Calculate the number of molecules, formula units, or ions in a given molar amount of a chemical compound. Calculate the percentage composition of a given chemical compound.

3. Using Chemical Formulas A chemical formula indicates the elements as well as the number of atoms or ions of each element present in a compound. Chemical formulas also allow chemists to calculate a number of characteristic values for a given compound. In this section we will learn how to use chemical formulas to calculate the formula mass, molar mass, and percentage composition by mass of a compound.

4. Formula Masses Just like atoms have an average atomic mass, a molecule, formula unit, or an ion have a characteristic average mass. We can find the average atomic mass of a molecule, formula unit, or an ion by adding the atomic masses of ALL the atoms found. For example, water (H 2 O): H has a mass of 1.01; O has a mass of 16.00 So water has an atomic mass of 18.02.

5. Formula Mass The mass of a water molecule can be correctly referred to as a molecular mass. The mass of one NaCl formula unit is NOT a molecular mass because it is not a molecular compound; it is an ionic compound. The formula mass of any molecule, formula unit, or ion is the sum of the average atomic masses of all the atoms represented in its formula.

6. Sample Problem 1 Find the formula mass of potassium chlorate, KClO 3. 1 K atom = 39.10 amu 1 Cl atom = 35.45 amu 3 O atoms = (3)(16.00 amu) = 48.00 amu Formula mass = 122.55 Find the formula masses of the following: H 2 SO 4 Ca(NO 3 ) 2 PO 4 3- MgCl 2 98.08 amu 164.10 amu 94.97 amu 95.21 amu

7. Molar Masses The molar mass of a substance is equal to the mass in grams of one mole, or approximately 6.022 x 10 23 particles, of the substance. For example, the molar mass of pure calcium, Ca, is 40.08 g/mol because one mole of calcium atoms has a mass of 40.08 grams. The molar mass of a compound is calculated by summing the masses of the elements present in a mole of the molecules or formula units that make up the compound.

8. Molar Masses For example, one mole of water molecules contains exactly two moles of H atoms and one mole of O atoms. Two moles of H = (2)(1.01 g/mol) = 2.02 g/mol One mole of O = 16.00 g/mol Molar mass of H 2 O = 18.02 g/mol A compound’s molar mass is numerically equal to its formula mass. The only difference is the units: amu or g/mol.

9. Sample Problem 2 What is the molar mass of barium nitrate, Ba(NO 3 ) 2 ? 1 mol Ba = 137.33 g 2 mol N = (2)(14.01 g) = 28.02 g 6 mol O = (6)(16.00 g) = 96.00 g Molar mass of Ba(NO 3 ) 2 = 261.35 g/mol

10. Sample Problem 2 How many atoms of each element are there in one mole of the following: Al 2 S 3 NaNO 3 Ba(OH) 2 Find the molar mass of each of the compounds listed above. 150.17 g/mol 85.00 g/mol 171.35 g/mol 2 mol Al, 3 mol S 1 mol Na, 1 mol N, 3 mol O 1 mol Ba, 2 mol O, 2 mol H

11. Molar Mass as a Conversion Factor The molar mass of a compound can be used as a conversion factor to relate an amount in moles to a mass in grams for a given substance. To convert a known amount of a compound in moles to a mass in grams, multiply the amount in moles by the molar mass. Amount in moles x molar mass (g/mol) = mass in grams

12. Sample Problem 3 What is the mass in grams of 2.50 mol of oxygen gas, O 2 ? 2 mol O x 16.00 g/mol = 32.00 gram 2.50 mol O 2 x 32.00 g/mol = 80.0 g O 2 What is the mass in grams of 3.04 mol of ammonia vapor, NH 3 ? 1 mol N = 14.00 g; 3 mol H = 3.03 g 1 mol NH 3 = 17.03 g 3.04 mol NH 3 x 17.03 g = 51.8 g

13. Molar Mass as a Conversion Factor To convert a known mass of a compound in grams to an amount in moles, the mass must be divided by the molar mass. A simpler way of doing this is to set the equation up so that the units cancel.

14. Sample Problem 4 Ibuprofen, C 13 H 18 O 2, is the active ingredient in many nonprescription pain relievers. Its molar mass is 206.29 g/mol. (a) If the tablets in a bottle contain a total of 33 g of ibuprofen how many moles of ibuprofen are in the bottle? (b) How many particles of ibuprofen are in the bottle? (c) What is the total mass in grams of carbon in 33 g of ibuprofen?

15. Sample Problem 4 (a) If the tablets in a bottle contain 33 g of ibuprofen, how many moles of ibuprofen are in the bottle? Given: 33 g of C 13 H 18 O 2, mol. mass 206.29 g/mol Unknown: moles C 13 H 18 O 2 33 g C 13 H 18 O 2 x 1 mol/206.29 g = 0.16 mol

16. Sample Problem 4 (b) How many particles of ibuprofen are in the bottle? Given: 33 g of C 13 H 18 O 2, mol. mass 206.29 g/mol Unknown: particles C 13 H 18 O 2 0.16 mol C 13 H 18 O 2 x 6.022 x 10 23 particles/mol 9.6 x 10 22 particles C 13 H 18 O 2

17. Sample Problem 4 (c) What is the total mass in grams of carbon in 33 g of ibuprofen? Given: 33 g of C 13 H 18 O 2, mol. mass 206.29 g/mol Unknown: total mass of C 0.16 mol C 13 H 18 O 2 x 13 mol c/ 1 mol C 13 H 18 O 2 x 12.01 g C/1 mol C 25 g C

18. Sample Problem 5 How many moles are there in 6.60 g (NH 4 ) 2 SO 4 ? 0.0500 mol (NH 4 ) 2 SO 4 How many molecules are there in 25.0 g of H 2 SO 4 ? 1.53 x 10 23 molecules What is the mass in grams of 6.25 mol of copper(II) nitrate? 1170 g

19. Percentage Composition It is often useful to know the percentage by mass of a particular element in a chemical compound. For example, suppose the compound potassium chlorate, KClO 3, were to be used as a source of oxygen. We would need to know how much oxygen we could get out of the amount of potassium chlorate we have.

20. Percentage Composition To find the mass percentage of an element in a compound, we can divide the mass of the element in a sample of the compound by the total mass of the sample and multiplying it by 100. The mass percentage is the same no matter how big or how small the sample is.

21. Percentage Composition Since this is the case, we can find the percentage of an element in a compound by determining how many grams of the element are present in one mole of the compound, then dividing this value by the molar mass of the compound and multiplying by 100. The percentage by mass of each element in a compound is known as the percentage composition of the compound.

22. Sample Problem 6 Find the percentage composition of copper(I) sulfide, Cu 2 S. Molar mass of CuS 2 =159.2 g 2 mol Cu x 63.55 g Cu/1 mol = 127.1 g Cu 1 mol S x 32.07 g/1 mol = 32.07 g S P.C. Of Cu = 127.1 g/159.2 g x 100 = 79.84% P.C. of S = 32.07 g/159.2 g x 100 = 20.14%

23. Sample Problem 7 Find the percentage composition of the following: PbCl 2 74.51% Pb 25.49% Cl Ba(NO 3 ) 2 52.546% Ba 10.72% N 36.73% O