Chapter 7 Notes: Chemical Formulas, Formula Masses, Molar Masses, and Percentage Composition

A chemical formula indicates:
- The elements present in a compound.
- The relative number of atoms or ions of each element present in a compound.
Chemical formulas allow chemists to calculate:
- Formula mass
- Molar mass
- Percentage composition

The formula mass of any molecule, formula unit, or ion is the sum of the average atomic masses of all atoms represented in its formula.
Example: Formula mass of water, H_2O
- Average atomic mass of H: 1.01
  ewline amu
- Average atomic mass of O: 16.00
  ewline amu
- Average mass of H_2O molecule: 18.02
  ewline amu
The mass of a water molecule 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.
The mass of any unit represented by a chemical formula (H_2O, NaCl) can be referred to as the formula mass.

Problem: Find the formula mass of potassium chlorate, KClO_3.
Solution: The mass of a formula unit of KClO_3 is found by adding the masses of one K atom, one Cl atom, and three O atoms.
- Atomic masses are found in the periodic table.
- Round each atomic mass to two decimal places.
formula mass of KClO_3 = 122.55
ewline amu

The molar mass of a substance is equal to the mass in grams of one mole, or approximately 6.022 × 10^{23} particles, of the substance.
Example: The molar mass of pure calcium, Ca, is 40.08
ewline g/mol because one mole of calcium atoms has a mass of 40.08
ewline g.
The molar mass of a compound is calculated by adding the masses of the elements present in a mole of the molecules or formula units that make up the compound.
One mole of water molecules contains exactly two moles of H atoms and one mole of O atoms.
- Molar mass of H_2O molecule: 18.02
  ewline g/mol
A compound’s molar mass is numerically equal to its formula mass.

Problem: What is the molar mass of barium nitrate, Ba(NO3)2?
Solution: One mole of barium nitrate contains one mole of Ba, two moles of N (1 × 2), and six moles of O (3 × 2).
Molar mass of Ba(NO3)2 = 261.35
ewline g/mol

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 × molar mass (g/mol) = mass in grams

Grams to Moles: Mass of compound (grams) × \frac{1}{molar
ewline mass
ewline of
ewline compound} = Amount of compound (moles)
Moles to Grams: Amount of compound (moles) × molar mass of compound = Mass of compound (grams)
Moles of element in Compound : Amount of compound (moles) × \frac{molar
ewline mass
ewline of
ewline element}{molar
ewline mass
ewline of
ewline compound} = Amount of element in compound (moles)
Grams of element in compound: Mass of compound (grams) × \frac{molar
ewline mass
ewline of
ewline element}{molar
ewline mass
ewline of
ewline compound} = mass of element in compound (grams)
Molecules or formula units of compound : Amount of compound (moles) × 6.022 × 10^{23} = Number of molecules or formula units of compound
Number of atoms of element in compound: Amount of element in compound (moles) × 6.022 × 10^{23} = Number of atoms of element in compound

Problem: What is the mass in grams of 2.50
ewline mol of oxygen gas?
Given: 2.50
ewline mol
ewline O_2
Unknown: Mass of O_2 in grams
Solution: moles O2 → grams O2
- Amount of O2 (mol) × molar mass of O2 (g/mol) = mass of O_2 (g)
Calculate the molar mass of O_2.
Use the molar mass of O_2 to convert moles to mass.

Steps:
1. Decide which quantity you are given: amount (in moles) or number of particles (in atoms, molecules, formula units, or ions).
2. If you are converting from amount to number of particles (going left to right), use the top conversion factor.
3. If you are converting from number of particles to amount (going right to left), use the bottom conversion factor.
  *Conversion factors:
  *amount → number of particles: amount × \frac{6.022 x 10^{23}
  ewline particles}{1
  ewline mol}
- number of particles → amount: number of particles × \frac{1
  ewline mol}{6.022 x 10^{23}
  ewline particles}

Problem: Ibuprofen, C{13}H{18}O_2, is the active ingredient in many nonprescription pain relievers. Its molar mass is 206.31 ewline g/mol.
- a. If the tablets in a bottle contain a total of 33
  ewline g of ibuprofen, how many moles of ibuprofen are in the bottle?
- b. How many molecules of ibuprofen are in the bottle?
- c. What is the total mass in grams of carbon in 33
  ewline g of ibuprofen?
Given: 33
ewline g of C{13}H{18}O_2, molar mass 206.31
ewline g/mol
Unknown:
- a. moles C{13}H{18}O_2
- b. molecules C{13}H{18}O_2
- c. total mass of C
Solution:
- a. grams → moles
- b. moles → molecules
- c. moles C{13}H{18}O_2 → moles C → grams C

It is often useful to know the percentage by mass of a particular element in a chemical 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 by mass = \frac{mass
ewline of
ewline each
ewline element (units: g)}{total
ewline mass} × 100 %
Amount of each element (moles) × molar mass (g) = mass of each element (g)
Empirical formula subscripts: obtained from percentage composition without conversion necessary
Percentage composition: obtained from empirical formula using \frac{x
ewline molar
ewline mass (g)}{smallest
ewline amount} × 1
ewline mole