Limiting Reactant and Mole-to-Mole Comparisons in Chemical Reactions

Quantities in Chemical Reactions

Limiting Reactant Concept

The limiting reactant is the reactant that is completely consumed in a chemical reaction and determines the maximum amount of product that can be formed. The other reactant(s) are considered excess reactants, which remain after the completion of the reaction.

• Limiting Reactant: The reactant that runs out first and thus limits the amount of product formed.

• Excess Reactant: The reactant(s) that are not completely used up in the reaction.

• Theoretical Yield: The maximum amount of product that can be formed from the limiting reactant, assuming complete reaction and 100% yield.

To determine which reactant is limiting, compare the amount of product each reactant can produce using stoichiometry.

Mole-to-Mole Comparison

Stoichiometry allows us to relate quantities of reactants and products in a chemical reaction using balanced equations. The key step is converting given quantities to moles and using mole ratios from the balanced equation.

• Mole Ratio: The ratio of moles of one substance to moles of another as indicated by the coefficients in the balanced chemical equation.

• Conversion Steps:

  1. Convert given quantities to moles.

  2. Use mole ratios to determine the amount of product or other reactant.

  3. Compare the amounts to identify the limiting reactant.

  4. Calculate the theoretical yield based on the limiting reactant.

Example: Limiting Reactant Calculation

Reaction: Chromium(III) oxide reacts with hydrogen sulfide to produce chromium(III) sulfate and water.

$Cr_2O_3 (s) + 3 H_2S (g) \rightarrow Cr_2(SO_4)_3 (s) + 3 H_2O (l)$

• Given: 10.0 g $Cr_2O_3$, 10.0 g $H_2S$

• Find: Maximum mass of $Cr_2(SO_4)_3$ and $H_2O$ that can be formed

Steps:

1. Convert grams of each reactant to moles using molar mass.

2. Use mole ratios from the balanced equation to determine which reactant produces less product (limiting reactant).

3. Calculate the mass of product formed from the limiting reactant.

Example Calculation:

• Moles of $Cr_2O_3$: $\frac{10.0\ g}{152.0\ g/mol} = 0.0658\ mol$

• Moles of $H_2S$: $\frac{10.0\ g}{34.1\ g/mol} = 0.293\ mol$

• From the equation, 1 mol $Cr_2O_3$ reacts with 3 mol $H_2S$.

• Calculate how much product each reactant can produce and identify the limiting reactant.

Additional info: The limiting reactant is the one that produces the least amount of product. The excess reactant is left over after the reaction is complete.

Practice Problems

• Example 1: Acrylonitrile ($C_3H_3N$) is produced by the reaction:

  • $2 C_3H_6 + 2 NH_3 + 3 O_2 \rightarrow 2 C_3H_3N + 6 H_2O$

  • If 12.0 g $C_3H_6$, 10.0 g $NH_3$, and 5.0 g $O_2$ react, what mass of acrylonitrile can be produced?

  • Answer: 15.1 g

• Example 2: Aluminum reacts with iron(III) chloride:

  • $2 Al + 3 FeCl_3 \rightarrow 2 AlCl_3 + 3 Fe$

  • If 150 g of $Al$ are reacted with 400 g $FeCl_3$, what is the mass of the excess reactant remaining?

  • Answer: 8.8 g

Summary Table: Limiting Reactant Steps

Step	Description
1	Convert all reactant quantities to moles
2	Use mole ratios to determine which reactant produces less product
3	Identify the limiting reactant
4	Calculate theoretical yield from limiting reactant