Stoichiometry - The Math of Chemistry

Don't freak out. The math isn't too compllicated.

Mostly there is some multiplying and dividing.

Pay attention to the units and get them to cancel out when you can. That will lead you to the right answers.

Be ready to cross-multiply and divide to get answers.

The Mole

A mole is unit for measuring large amounts of small particles
Atoms are too tiny to see and they tend to exist in massive groups that can be observed
We use moles (mols) for calculations
- It's like a dozen, just for many more atoms or molecules
1 mol = 6.022 x 10²³ molecules
- This is known as Avogadro's number
Use this in ratio form:
- 6.022x10²³ molecules
  1 mol

In a balanced equation, the coefficients represent the ratio of moles
2H₂ + O₂ → 2H₂O
The ratio is 2 : 1 : 2
- It takes 2 moles of H₂ to react with 1 mole of O₂ to produce 2 moles of H₂O

To get the formula mass of a molecule, simply add up the atomic masses of its atoms
Use the masses on the periodic table
- Don't forget about the subscripts
CO₂: carbon has a mass of 12.011, oxygen is 15.9994, so…
- 12.011 + (15.9994)x2 → 12.011 + 31.9988 → 44.0098 amu
H₂S: hydrogen has a mass of 1.00794, sulfur has a mass of 32.065, so…
- (1.00794)x2 + 32.065 → 2.01588 + 32.065 → 34.08088 amu
C₆H₁₂O₆: carbon is 12.011, hydrogen is 1.00794, oxygen is 15.9994, so…
- (12.011)x6 + (1.00794)x12 + (15.9994)x6 → 72.066 + 12.09528 + 95.9964 → 180.15768 amu

Gram Formula Mass is the mass per mole of a substance
Follow the process for finding the formula mass
Convert that value to g/mol (grams per mole)
Formula mass of Mg₃P₂:
- (24.305)x3 + (30.97376)x2 → 72.915 + 64.94752 → 134.86252 amu
Molar mass: 134.86252 g/mol
Remember that this actually means it's 134.86252 grams per 1 mole:
- 134.86252 g
  1 mol
- This ratio format will be helpful for calculations

How many moles of H₂O are produced when 8 moles of O2 are reacted?
2H₂ + O₂ → 2H₂O
This is based on a simple ratio from the coefficients
1 mol O₂ = 2 mol H₂O ← from the coefficients
8 mol O₂ x mol H₂O ← from the moles given
(1)x mol H₂O = (2)8 → 16 mol H₂O produced

How many moles of H₂O are produced given a mass of 80g O₂?
2H₂ + O₂ → 2H₂O
We have grams of O₂, but we need moles, then convert to H₂O
GFM of O₂ is 31.9988 ^g/^mol → 80g O₂ x ^{1 mol}/^31.9988 g → 2.5 mol O₂
Use a simple ratio based on the coefficients, then cross multiply
1 mol O₂ = 2 mol H₂O ← from the coefficients 2.5 mol O₂ x mol H₂O ← from the grams given converted to mol
(1)x mol H₂O = (2)2.500 → 5.0 mol H₂O produced

Molecular formula shows the exact numbers of atoms bonded
- Ex: C₆H₁₂O₆
Empirical formula shows the lowest ratio of those bonded atoms
- Ex: CH₂O
If given the empirical formula and the molecular mass, you can determine the molecular formula
Example: You have the empirical formula C₃H₈ and the molecular mass of 176 g.
What is the molecular formula?
First get the formula mass for the empirical formula (C₃H₈)
- (12)x3 + (1)x8 → 44
Divide the molecular mass by the empirical formula mass
- ¹⁷⁶/₄₄ → 4
This means the atom numbers in the empirical formula need to be multiplied by 4
- C_3x4H_8x4 → C₁₂H₃₂ is the molecular formula

Percent is always "part over whole times 100%"
- This is no different
- This formula is given on Reference Table T
Example 1: What is the percent composition of oxygen in H₂O?
We need the mass of oxygen [15.9994 g/mol]
We need the gram formula mass of H₂O [18.01528 g/mol]
Part → 15.9994 → 0.88810166 x 100% → 88.81% O₂
Whole 18.01528
Example 2: What is the percent composition of hydrogen in H₂O?
We need the mass of hydrogen [2 x 1.00794 g/mol → 2.01588 g/mol]
- Don't forget about the subscript!!
We need the formula mass of H₂O [18.01528 g/mol]
Part → 2.01588 → 0.11189834 x 100% → 11.19% H₂
Whole 18.01528
Let's check!
- H₂O is only H and O. We solved for oxygen in the last problem.
- 88.81% oxygen + 11.19% hydrogen → 100%
  - This may not be perfect in some problems due to rounding

Concentration, or strength of a solution, can be represented in different ways
- molarity (M)
- percent by volume
- percent by mass
- parts per million (ppm)
High concentration (i.e. higher molarity) = concentrated
Low concentration (i.e. lower molarity) = dilute

Preparing a Solution from Molarity
Ex: You need 2 liters of 0.4M NaOH
- Think: How many grams of NaOH do you need to add to the water?
First, use the molarity formula to figure out how many moles you need
- M = ^mol/_L → 0.4 = ^mol/₂ → mol = 0.8 mol
Next, get the gram formula mass of NaOH (we'll simplify with whole #s)
- Na (23) + O (16) + H (1) → 40 ^g/_mol
Finally, multiply the GFM by the number of moles to get moles to cancel
- 40 ^g/_mol x 0.8 mol → 32 grams
What does this mean?
You need to add 32 grams of NaOH to 2 liters of water to make 0.4M NaOH

Percent by volume is a measure of a substance in mL versus 100 mL of water times 100%
- Remember: percent is "part over whole times 100%"
Example: You have 12 mL of HCl. What is its percent by volume?
% by volume = 12 mL HCl → 0.12 x 100% → 12%
100 mL H₂O
If you are given a different volume of water, use that value instead of 100 mL

Percent by mass is a measure of a substance in grams versus amount of water in grams of water times 100%
- Remember: percent is "part over whole times 100%"
- This formula is given to you on Reference Table T
You need to add the mass of solute to the mass of solvent
Example: You have 13 g of NaCl in 150 g of H₂O. What is its percent by mass?
% by mass = 13 g NaCl → 13 g → 0.0797546 x 100% → 7.975%
(13 g NaCl + 150 g H₂O) 163 g

Parts per million (ppm) is a measure of how much solute there is in a solution
- This is very similar to percent by mass
- You need the amount of solute and the mass of the entire solution
- Multiply by 1,000,000 (one million)
- This formula is given to you on Reference Table T
Example: How many parts per million of NaOH are there when 92 g are dissolved in 50 mL water?
ppm = 92 g NaOH → 92 g → 0.6479 x 1000000 → 6.479x105 ppm
(92 g NaOH + 50 g H₂O) 142 g