Stoichiometry Made Easy Study Notes

Introduction to Stoichiometry

• Definition of Stoichiometry: The study of the quantitative relationships between reactants and products in a chemical reaction. It utilizes mole ratios to determine these relationships.

• The Foundation of Stoichiometry: To accurately reflect the Law of Conservation of Matter, all chemical reactions must be BALANCED before stoichiometric calculations can be performed.

• Conversion Factors: The balanced chemical equation serves as the primary conversion factor in every stoichiometry problem.

• Mnemonic/Analogy: A chemist's favorite plant is the "Stoichiome-tree."

• Conceptual Example (Grilled Cheese): To understand the proportional nature of stoichiometry, consider the production of a grilled cheese sandwich. If the recipe requires 2 slices of bread for 1 sandwich ($2 \, \text{slices} : 1 \, \text{sandwich}$), then to make $7$ grilled cheese sandwiches, you would need:

  • $7 \times 2 = 14 \, \text{slices of bread}$.

The Mole and Standard Conversion Values

• The Mole (mol): The central unit of measurement in stoichiometry that allows for conversion between particles, mass, and volume.

• Molar Volume of a Gas: At Standard Temperature and Pressure (STP), $1 \, \text{mol}$ of any gas occupies $22.4 \, \text{L}$.

• Molar Mass: $1 \, \text{mol}$ of a substance is equal to its molar mass (calculated from the periodic table in grams).

• Avogadro's Number: $1 \, \text{mol}$ is equal to $6.02 \times 10^{23}$ particles (atoms, molecules, or formula units).

Mole Ratios

• Definition: A mole ratio is the ratio of the numbers of moles of any two substances in a balanced chemical equation.

• Structure: Mole ratios are written as fractions where the coefficients from the balanced equation are used as the numerator and denominator.

• Function as a Bridge: The mole ratio acts as a bridge that allows a chemist to move from the GIVEN unit and substance to the NEEDED unit and substance.

• Identification Practice: Using the reaction $6 \, \text{NaCl} + \text{Fe}_3(\text{PO}_4)_2 \rightarrow 2 \, \text{Na}_3\text{PO}_4 + 3 \, \text{FeCl}_2$:

  • Mole ratio of sodium chloride to iron(II) chloride: $\frac{6 \, \text{mol NaCl}}{3 \, \text{mol FeCl}_2}$.

  • Mole ratio of sodium phosphate to sodium chloride: $\frac{2 \, \text{mol Na}_3\text{PO}_4}{6 \, \text{mol NaCl}}$.

  • Mole ratio of iron(II) phosphate to sodium chloride: $\frac{1 \, \text{mol Fe}_3(\text{PO}_4)_2}{6 \, \text{mol NaCl}}$.

The Stoichiometry Roadmap

Stoichiometry follows a logical flow to convert from Substance A to Substance B:

• Start at Substance A: This could be given in Particles, Mass (grams), or Volume (liters).

• Convert to Moles of A: Use molar mass, Avogadro's number, or $22.4 \, \text{L}$ to find the moles of the given substance.

• The Mole Ratio Bridge (Coefficients): Use the coefficients from the balanced chemical equation to convert Moles of Substance A into Moles of Substance B.

• Convert to Needed Units for Substance B: Once in moles of B, convert to the final required units (Particles, Mass, or Volume) using the appropriate conversion factor.

Stoichiometry Practice Problems

Mole-Mole Calculations

• Reaction: $\text{NH}_4\text{NO}_3 \rightarrow \text{N}_2\text{O} + 2\text{H}_2\text{O}$

  • Question: How many moles of water are produced if you start with $4.27 \, \text{moles}$ of ammonium nitrate?

• Reaction: $2\text{KNO}_3 + \text{PbSO}_4 \rightarrow \text{K}_2\text{SO}_4 + \text{Pb}(\text{NO}_3)_2$

  • Question: How many moles of potassium sulfate are produced if you start with $2.25 \, \text{moles}$ of lead (II) sulfate?

• Reaction: $6\text{NaCl} + \text{Fe}_3(\text{PO}_4)_2 \rightarrow 2\text{Na}_3\text{PO}_4 + 3\text{FeCl}_2$

  • Question: If iron (II) phosphate reacts with $2.56 \, \text{moles}$ of sodium chloride, how many moles of sodium phosphate are made?

Mass-Mole Calculations

• Reaction: $2\text{AgI} + \text{Fe}_2(\text{CO}_3)_3 \rightarrow 2\text{FeI}_3 + 3\text{Ag}_2\text{CO}_3$ (balancing required)

  • Question: How many grams of silver carbonate are produced if you start with $3.67 \, \text{moles}$ of silver iodide?

Mass-Mass Calculations

• Reaction: $\text{AgNO}_3 + \text{NaCl} \rightarrow \text{AgCl} + \text{NaNO}_3$

  • Question: How many grams of silver chloride can be produced from the reaction of $17.0 \, \text{g}$ of silver nitrate with excess sodium chloride?

• Reaction: $\text{BaCl}_2 + \text{H}_2\text{SO}_4 \rightarrow 2\text{HCl} + \text{BaSO}_4$

  • Question: How many grams of hydrochloric acid can be produced from the reaction of $17.0 \, \text{g}$ of barium chloride with excess sulfuric acid?

Mass-Particles Calculations

• Reaction: $\text{PbCl}_2 + \text{Li}_2\text{SO}_4 \rightarrow \text{PbSO}_4 + 2\text{LiCl}$

  • Question: Calculate the grams of lithium chloride produced from $6.8 \times 10^{21}$ formula units of lithium sulfate.

Particles-Volume and Volume-Particle Calculations

• Reaction: $\text{C}_3\text{H}_8 + 5\text{O}_2 \rightarrow 4\text{H}_2\text{O} + 3\text{CO}_2$

  • Question: How many liters of carbon dioxide are produced from $9.8 \times 10^{14}$ molecules of propane in excess oxygen?

• Reaction: $\text{CH}_4 + 2\text{O}_2 \rightarrow 2\text{H}_2\text{O} + \text{CO}_2$

  • Question: How many particles of carbon dioxide are produced from $273 \, \text{mL}$ of oxygen?

Limiting and Excess Reactants

• Limiting Reactant: This reactant is completely consumed in a chemical reaction. It is the factor that determines the maximum amount of product that can be formed.

• Excess Reactant: This reactant is not completely used up; there will always be some amount remaining after the reaction has finished.

• Practice Problem 1: In the reaction $2\text{Cu} + \text{S} \rightarrow \text{Cu}_2\text{S}$, what is the limiting reactant when $80.0 \, \text{g}$ of $\text{Cu}$ reacts with $25.0 \, \text{g S}$? How many grams of $\text{Cu}_2\text{S}$ can be formed?

• Practice Problem 2: When $4.00 \, \text{g}$ of silver reacts with $4.00 \, \text{g}$ of sulfur ($\text{S}_8$), what mass of silver sulfide ($\text{Ag}_2\text{S}$) is produced? What is the limiting reactant?

• Practice Problem 3 (Comparison): $2\text{NaCl} + \text{Mg}(\text{NO}_3)_2 \rightarrow 2\text{NaNO}_3 + \text{MgCl}_2$

  • If $3.6 \, \text{g}$ of $\text{NaCl}$ is combined with $2.6 \, \text{g}$ of $\text{Mg}(\text{NO}_3)_2$, the stoichiometry is calculated as follows:

    • From $\text{NaCl}$: $3.6 \, \text{g NaCl} \times (\frac{1 \, \text{mol}}{58.44 \, \text{g}}) \times (\frac{2 \, \text{mol NaNO}_3}{2 \, \text{mol NaCl}}) \times (\frac{85 \, \text{g NaNO}_3}{1 \, \text{mol}}) = 5.2 \, \text{g NaNO}_3$

    • From $\text{Mg}(\text{NO}_3)_2$: $2.6 \, \text{g Mg}(\text{NO}_3)_2 \times (\frac{1 \, \text{mol}}{148.33 \, \text{g}}) \times (\frac{2 \, \text{mol NaNO}_3}{1 \, \text{mol Mg}(\text{NO}_3)_2}) \times (\frac{85 \, \text{g NaNO}_3}{1 \, \text{mol}}) = 3.0 \, \text{g NaNO}_3$ (rounded).

    • Limiting Reactant: $\text{Mg}(\text{NO}_3)_2$.

    • Excess Reactant: $\text{NaCl}$.

Percent Yield

• Theoretical Yield: The maximum amount of product that could be produced, calculated using stoichiometry.

• Actual Yield: The actual amount of product produced in an experiment (this is usually given in a problem's text or measured physically in a lab).

• Percent Yield Definition: The ratio of the actual yield to the theoretical yield expressed as a percentage.

• Formula: $\text{Percent Yield} = (\frac{\text{Actual Yield}}{\text{Theoretical Yield}}) \times 100$

• Practice Problem: Determine the percent yield for the reaction between $3.74 \, \text{g}$ of sodium and excess oxygen if $4.34 \, \text{g}$ of sodium oxide is recovered.

Advanced Scenarios and Excess Calculations

• Calculation of Excess Remaining: In the reaction $\text{SiCl}_4 + 2\text{Mg} \rightarrow \text{Si} + 2\text{MgCl}_2$:

  • Given: $185 \, \text{g}$ of silicon tetrachloride and $58.0 \, \text{g}$ of magnesium reacts to produce $30.6 \, \text{g}$ of silicon.

  • Identified: $\text{SiCl}_4$ is the limiting reactant.

  • Objective: Calculate how much of the excess reactant ($\text{Mg}$) is left over.

• Molecular Analysis: Combustion of Butane: $2\text{C}_4\text{H}_{10} + 13\text{O}_2 \rightarrow 8\text{CO}_2 + 10\text{H}_2\text{O}$.

  • Question 1: How many molecules of carbon dioxide can be produced when $15$ molecules of Butane are combusted by $20$ molecules of $\text{O}_2$?

  • Question 2: What is the limiting reactant?

  • Question 3: How many molecules of excess reactant are left over?