Stoichiometry and Limiting Reactant: Study Notes for General Chemistry

Stoichiometry

Introduction to Stoichiometry

Stoichiometry is a fundamental concept in chemistry that involves the calculation of quantities of reactants and products in chemical reactions. These calculations are based on balanced chemical equations, which ensure the conservation of mass and atoms.

• Definition: Stoichiometry is the quantitative relationship between reactants and products in a chemical reaction.

• Balanced Chemical Equation: All stoichiometric calculations must use a balanced equation to ensure correct ratios.

• Conversion Steps: Calculations often involve converting between moles, mass, and number of particles.

Example Conversion Path:

• Mass → Moles → Moles (other substance) → Mass

Formula:

• $\text{Moles} = \frac{\text{Mass}}{\text{Molar Mass}}$

Limiting Reactant and Excess Reactant

Real-World Stoichiometry

In practical chemical reactions, reactants are not always present in exact stoichiometric ratios. One reactant may be completely consumed first, limiting the amount of product formed. This is known as the limiting reactant.

• Limiting Reactant: The reactant that is completely consumed first, thus limiting the amount of product formed.

• Excess Reactant: The reactant(s) that remain after the limiting reactant is used up.

• Theoretical Yield: The maximum amount of product that can be formed from the limiting reactant, assuming complete reaction.

Identifying the Limiting Reactant:

• Calculate the amount of product each reactant could produce.

• The reactant that produces the least amount of product is the limiting reactant.

Calculating Theoretical and Actual Yield

Yield Calculations

Not all reactions proceed with 100% efficiency. The actual yield is the amount of product actually obtained from a reaction, while the theoretical yield is the maximum possible amount calculated from stoichiometry.

• Actual Yield: The measured amount of product obtained from a reaction.

• Theoretical Yield: The calculated maximum amount of product possible, based on the limiting reactant.

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

Formula:

• $\text{Percent Yield} = \frac{\text{Actual Yield}}{\text{Theoretical Yield}} \times 100\%$

Worked Examples

Example 2: Haber Process

The Haber Process involves the reaction of nitrogen and hydrogen gases to form ammonia. Stoichiometry can be used to determine the mass of hydrogen gas required to form a given amount of ammonia.

• Balanced Equation: $N_2 (g) + 3H_2 (g) \rightarrow 2NH_3 (g)$

• Calculation: Find grams of $H_2$ needed for $1.00 \times 10^3$ g $NH_3$.

Your Turn 2: Potassium Chlorate and Phosphorus

Given 52.9 g of potassium chlorate ($KClO_3$) and excess phosphorus, calculate the mass of tetraphosphorus decoxide ($P_4O_{10}$) produced.

• Balanced Equation: $KClO_3 (s) + P_4 (s) \rightarrow P_4O_{10} (s) + KCl (s)$

• Answer: 36.8 g $P_4O_{10}$

Example 3: Limiting Reactant Calculation

Consider the reaction:

• $2Sb (s) + 3I_2 (g) \rightarrow 2SbI_3 (s)$

Determine the limiting reactant and theoretical yield when 1.20 g of Sb and 2.40 g of $I_2$ are mixed. Also, calculate the mass of excess reactant left after the reaction.

Your Turn 3: Silver Salt Formation

Given 25.0 g $Ag_2SO_4$ and 50.0 g $C_6H_5N_2^+$, calculate the mass of $AgC_6H_5N_2SO_4$ produced, assuming 100% yield.

• Answer: 71.4 g $AgC_6H_5N_2SO_4$

Summary on Limiting Reactant (LR)

• Calculate the amount of product formed if the first reactant is completely consumed.

• Repeat for other reactants.

• The reactant that produces the least product is the limiting reactant.

• The other reactant(s) are in excess.

Actual Yield and Percent Yield

• Actual yield is usually less than theoretical yield due to incomplete reactions or losses.

• Percent yield quantifies reaction efficiency.

• $\text{Percent Yield} = \frac{\text{Actual Yield}}{\text{Theoretical Yield}} \times 100\%$

Example 4: Percent Yield Calculation

Given a percent yield of 78.2% for the reaction in Example 3, calculate the mass of $SbI_3$ formed.

Your Turn 4: Percent Yield for Silver Salt

If 21.5 g of $AgC_6H_5N_2SO_4$ is obtained from the reaction in Your Turn 3, calculate the percent yield.

• Answer: 30.1%

Summary Table: Key Stoichiometry Concepts

Concept	Definition	Formula
Stoichiometry	Quantitative relationship between reactants and products	$\text{Moles} = \frac{\text{Mass}}{\text{Molar Mass}}$
Limiting Reactant	Reactant that is completely consumed first	Compare product amounts from each reactant
Theoretical Yield	Maximum possible product from limiting reactant	Based on stoichiometric calculation
Actual Yield	Measured product obtained	Experimental value
Percent Yield	Efficiency of reaction	$\text{Percent Yield} = \frac{\text{Actual Yield}}{\text{Theoretical Yield}} \times 100\%$

Additional info: Some chemical equations and answers were inferred from context and standard stoichiometry problems.