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Using Chemical Formulas

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Using Chemical Formulas

- 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.

- 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.

- 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.

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

- 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.

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

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.

- 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

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

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

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

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

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

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?

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?

- 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.

- 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.

Percentage Composition of Iron Oxides

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.

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%).