Stoichiometry and Molar Mass Notes

Stoichiometry Introduction

• Stoichiometry involves quantitative relationships and ratios.

• It connects knowledge of formulas, the periodic table, and dimensional analysis.

• If given 50 grams of a substance, molar mass can be used to find moles.

• Example: Molar mass of $H_2$ is $2.016$ grams per mole.

• Mole to mole ratio: 2 moles of $H<em>2O$ for every 2 moles of $H</em>2$ burned.

• Molar mass of $H_2O$ is $18.016$ grams per mole.

• Quantitative relationships allow determining the amount of product formed from a given amount of reactant.

• Balancing chemical equations correctly is crucial; otherwise, everything gets messed up.

• Stoichiometry is more complex than simply adding masses; the numbers in the balanced equation matter.

Atomic and Molar Mass

• Atomic mass is measured in AMUs (atomic mass units), which are too small for practical use.

• A mole is a unit, similar to a dozen, but represents an astronomically large number.

• One mole of a substance is equal to $6.022 \times 10^{23}$ particles (Avogadro's number).

• Analogy: Having $6.022 \times 10^{23}$ dollars and spending a million dollars every second for 100 years, you would still have enough money to give everyone on the planet a million dollars.

• Moles are more useful than individual atomic masses because atoms are so small.

• Molar mass is the mass in grams of one mole of a substance.

• Units of molar mass are grams per mole (g/mol).

• Molar masses are found on the periodic table as the numbers with decimal places.

• Molar mass is used to "count" atoms by weighing them, similar to how candy is charged per pound rather than per piece.

Calculating Molar Mass

Example: Calcium Carbonate ($CaCO_3$)

1. Identify the number of each element in the compound:

   • 1 Calcium (Ca)

   • 1 Carbon (C)

   • 3 Oxygens (O)

2. Find the molar mass of each element on the periodic table:

   • Ca: ~40.078 g/mol (rounded to 40 for simplicity in the example)

   • C: 12.011 g/mol

   • O: 15.999 g/mol (rounded to 16 for simplicity in the example)

3. Multiply the molar mass of each element by the number of atoms of that element in the compound:

   • Ca: $1 \times 40 = 40$ g/mol

   • C: $1 \times 12.011 = 12.011$ g/mol

   • O: $3 \times 16 = 48$ g/mol

4. Add the results together to find the molar mass of the compound:

   • $40 + 12.011 + 48 = 100.011$ g/mol

Comparison of Atomic Mass and Molar Mass

• Atomic mass (AMU): Mass of a single atom at the atomic level.

• Molar mass (grams): Mass of one mole of a substance at the macroscopic level.

Example: Sulfuric Acid ($H<em>2SO</em>4$)

1. Identify the number of each element in the compound:

   • 2 Hydrogen (H)

   • 1 Sulfur (S)

   • 4 Oxygens (O)

2. Find the molar mass of each element on the periodic table:

   • H: ~1 g/mol

   • S: ~32.06 g/mol

   • O: ~16 g/mol

3. Multiply the molar mass of each element by the number of atoms of that element in the compound:

   • H: $2 \times 1 = 2$ g/mol

   • S: $1 \times 32.06 = 32.06$ g/mol

   • O: $4 \times 16 = 64$ g/mol

4. Add the results together to find the molar mass of the compound:

   • $2 + 32.06 + 64 = 98.06$ g/mol

Example: Water ($H_2O$)

• 2 Hydrogens: $2 \times 1 = 2$ g/mol

• 1 Oxygen: $1 \times 16 = 16$ g/mol

• Molar mass of $H_2O$: $2 + 16 = 18$ g/mol

Example: Chloroform ($CHCl_3$)

• 1 Carbon: $1 \times 12.011 = 12.011$ g/mol

• 1 Hydrogen: $1 \times 1.008 = 1.008$ g/mol

• 3 Chlorines: $3 \times 35.453 = 106.359$ g/mol

• Molar mass of $CHCl_3$: $12.011 + 1.008 + 106.359 = 119.378$ g/mol

Example: Ibuprofen ($C<em>{13}H</em>{18}O_2$)

• 13 Carbons: $13 \times 12.011 = 156.143$ g/mol

• 18 Hydrogens: $18 \times 1.008 = 18.144$ g/mol

• 2 Oxygens: $2 \times 15.999 = 31.998$ g/mol

Molar mass of Ibuprofen: 206.285 g/mol

Example: Aluminum Sulfate ($Al<em>2(SO</em>4)_3$)

• 2 Aluminum: $2 \times 26.98 = 53.96$ g/mol

• 3 Sulfurs: $3 \times 32.06 = 96.18$ g/mol

• 12 Oxygens: $12 \times 15.999 = 191.988$ g/mol

• Molar mass of $Al<em>2(SO</em>4)_3$: 342.128 g/mol

Examples of Determining Molar Mass

1. Carbon Monoxide (CO): 1 Carbon + 1 Oxygen = ~ 29 grams/mole . (12 +16 =28)

2. Sulfur Trioxide ($SO_3$): ~ 84 grams/mole

3. Ammonium Sulfate ($(NH<em>4)</em>2SO_4$): ~ 132 grams/mole

4. Oxygen Gas ($O_2$): ~ 32 grams/mole .

5. Silver Nitrate ($AgNO_3$): ~170 grams per mole

It is important to write molar masses with correct units (grams/mole).