Using Chemical Formulas

1. Using Chemical Formulas

2. The chemical formula for water is H2O. • How many atoms of hydrogen and oxygen are there in one water molecule? H2O 1 oxygen atom 2 hydrogen atoms • How might you calculate the mass of a water molecule, given the atomic masses of hydrogen and oxygen? • In this section, you will learn how to carry out these and other calculations for any compound.

3. Using Chemical Formulas • As well as indicating the elements and the relative numbers of atoms or ions of each element in a compound, chemical formulas can also be used to calculate formula mass, molar mass, and the percent composition of a compound.

4. Formula Mass • 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. • The units for formula mass are atomic massunits (amu). • The mass of a water molecule, H2O, can be referred to as a molecular mass. • The mass of one formula unit of an ionic compound, such as NaCl, is not a molecular mass.

5. Example: Find the formula mass for H2O. H2O has 2 hydrogen atoms and 1 oxygen atom. Atomic mass of hydrogen = 1.01 amu Atomic mass of oxygen = 16.00 amu 2.02 amu 2 hydrogen atoms x 1.01 amu = 1 oxygen atom x 16.00 amu = 16.00 amu Total 18.02amu Formula mass of H2O

6. Molar Masses • The molar mass of a substance is equal to the mass in grams of one mole, or 6.02 x 1023 particles, of the substance. • Units for molar mass are g/mol. • 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 that compound. • A compound’s molar mass is numericallyequal to its formula mass.

7. Example: Find the molar mass for KClO3. KClO3 has 1 potassium (K) atom, 1 chlorine atom (Cl), and 3 oxygen (O) atoms. Atomic mass of potassium = 39.10 amu Atomic mass of chlorine = 35.45 amu Atomic mass of oxygen = 16.00 amu 39.10 amu 35.45 amu 48.00 amu 1 potassium atom x 39.10 amu = 1 chlorine atom x 35.45 amu = 3 oxygen atoms x 16.00 amu = Total 122.55 amu

8. Since a compound’s molar mass is numerically equal to its formula mass (KClO3 = 122.55 amu) the molar mass of KClO3 would be Numerically equivalent to formula mass but units are different. 122.55 g/mol This tells us that if we have one mole of KClO3 we would have 122.55 g of KClO3 or 6.02 x 1023 formula units of KClO3.

9. 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 moles to grams, multiply the amount in moles by the molar mass. • Amount in moles x molar mass (g/mol) = mass in grams

10. Example: What is the mass in grams of 2.50 mol of oxygen (O2) gas? Given: 2.50 mol O2 Unknown: mass of O2 in grams Solution: mol O2→ grams O2

11. Determine the molar mass of O2. O2 has 2 oxygen atoms. Atomic mass of O is 16.00 amu. 2 oxygen atoms x 16.00 = 32.00 amu Remember that molar mass is numerically equal to the formula mass so the molar mass of O2 = 32.00 g/mol. g O2 32.00 80.0 g O2 2.50 mol O2 x = 1 mol O2

12. Ibuprofen, C13H18O2, is the active ingredient in many nonprescription pain relievers. Its molar mass is 206.31 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? 1 mol C13H18O2 33 g C13H18O2 x = 0.16 mol C13H18O2 206.31 g C13H18O2

13. b. How many molecules of ibuprofen are in the bottle? Remember we have 0.16 mol. 6.02 x 1023 molecules 0.16 mol C13H18O2 x = 9.6 x 1022 1 mol molecules C13H18O2

14. c. What is the total mass in grams of carbon in 33 g of ibuprofen? To start, determine the number of moles of carbon per 1 mole of C13H18O2. There are 13 moles of carbon per 1 mole of C13H18O2. Two conversion factors are needed to solve problem: number of moles of carbon per mole of C13H18O2 and the molar mass of carbon. 13 moles C 12.01 g C 1 mol C13H18O2 1 mol C

15. 13 mol C 12.01 g C 0.16 mol C13H18O2 x x 1 mol C 1 mol C13H18O2 25 g C = • Problem: • Consider a sample of 10.0 g of the gaseous hydrocarbon C3H4 to answer the following questions. • How many moles are present in the sample? • How many molecules are present in the C3H4 sample? • What is the total mass in grams of carbon in the sample?

16. Additional Problems: • How many molecules of aspirin, C9H8O4, are there in 0.165 moles of aspirin? • If we have 6.54 x 108 molecules HCN, how many moles of HCN are there? • What is the total mass of nitrogen in 1.25 moles of Zn(NO3)2?

17. Percent Composition • It is often useful to know the percentage by mass of a particular element in a compound. • For example, suppose the compound potassium chlorate, KClO3, were to be used as a source of oxygen. It would be useful to know the percentage of oxygen in the compound. • To find the mass percentage of an element in a compound, the following equation can be used.

18. The mass percentage of an element in a compound is the same regardless of the sample’s size. • The percentage of an element in a compound can be calculated by determining how many grams of the element are present in one mole of the compound. • The percentage by mass of each element in a compound is known as the percentage composition of the compound.

19. Percentage Composition of Iron Oxides

20. Example: Find the percentage composition of copper(I) sulfide, Cu2S. 1) Find the molar mass of the compound. Cu2S has 2 copper atoms and 1 sulfur atom. The atomic mass of copper is 63.55 amu and the atomic mass of sulfur is 32.07 amu. 127.1 amu 32.07 amu 2 copper atoms x 63.55 amu = 1 sulfur atom x 32.07 amu = The formula mass of Cu2S = 159.2 amu. The molar mass of Cu2S = 159.2 g/mol.

21. 2) Use the mass of each element present in one mole of the compound to calculate the mass percentage of each element. 2 atoms of Cu = 127.1 g 1 atom of S = 32.07 g Molar mass of Cu2S = 159.2 g. A good check is to see if the results add up to about 100%. (Because of rounding, the total may not always be exactly 100%).