Calculation of the Limiting Reagent

Understanding the Calculation of the Limiting Reagent in Chemical Reactions

The calculation of the limiting reagent determines the reactant that limits product formation. It is essential for precise stoichiometric analysis.

This article explores detailed formulas, common values, and real-world examples for expert-level understanding.

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  • Calculate the limiting reagent when 5 moles of H2 react with 3 moles of O2.
  • Determine the limiting reagent in a reaction with 10 g of Na and 15 g of Cl2.
  • Find the limiting reagent for 2 moles of N2 and 6 moles of H2 in ammonia synthesis.
  • Calculate the limiting reagent when 4 moles of Fe react with 3 moles of S.

Comprehensive Tables of Common Values in Limiting Reagent Calculations

ReactantMolar Mass (g/mol)Common Reaction CoefficientTypical Amounts Used (moles)Density (g/cmĀ³)State at Room Temperature
Hydrogen (H2)2.01621 – 100.00008988Gas
Oxygen (O2)31.99811 – 100.001429Gas
Sodium (Na)22.99020.5 – 50.97Solid
Chlorine (Cl2)70.90610.5 – 50.003214Gas
Nitrogen (N2)28.01411 – 100.0012506Gas
Hydrogen Sulfide (H2S)34.0810.1 – 21.363Gas
Iron (Fe)55.84510.5 – 57.874Solid
Sulfur (S)32.0610.5 – 52.07Solid
Carbon Dioxide (CO2)44.0111 – 100.001977Gas
Water (H2O)18.01511 – 101.00Liquid

Fundamental Formulas for Calculating the Limiting Reagent

Calculating the limiting reagent requires understanding the stoichiometric relationships between reactants. The key is to compare the mole ratios of reactants used to those required by the balanced chemical equation.

1. Mole Ratio Comparison Formula

The limiting reagent is identified by comparing the actual mole ratio of reactants to the stoichiometric mole ratio:

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<span style=”font-weight:bold;”>Limiting Reagent Condition:</span>
If
(nA / a) < (nB / b), then A is limiting reagent.
Else, B is limiting reagent.

Where:
nA = moles of reactant A available
a = stoichiometric coefficient of A in balanced equation
nB = moles of reactant B available
b = stoichiometric coefficient of B in balanced equation
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This formula can be extended to multiple reactants by comparing each reactant’s mole ratio to its coefficient.

2. Calculating Moles from Mass

Often, reactants are given in mass rather than moles. Use the molar mass to convert:

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n = m / M

Where:
n = number of moles (mol)
m = mass of substance (g)
M = molar mass (g/mol)
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3. Calculating Theoretical Yield Based on Limiting Reagent

Once the limiting reagent is identified, the theoretical yield of product can be calculated:

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nproduct = (nlimiting Ɨ c) / a

Where:
nproduct = moles of product formed
nlimiting = moles of limiting reagent
a = stoichiometric coefficient of limiting reagent
c = stoichiometric coefficient of product
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The mass of product can then be found by multiplying moles by molar mass of the product.

4. Percent Yield Calculation

In practical scenarios, the actual yield is often less than theoretical. Percent yield quantifies efficiency:

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Percent Yield = (Actual Yield / Theoretical Yield) Ɨ 100%
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Detailed Explanation of Variables and Their Common Values

  • n (moles): The amount of substance, typically measured in moles. Commonly ranges from 0.1 to 10 moles in laboratory settings.
  • m (mass): Mass of the reactant or product, measured in grams. Values depend on the scale of the reaction.
  • M (molar mass): Mass of one mole of a substance, in g/mol. For example, H2O = 18.015 g/mol, O2 = 31.998 g/mol.
  • a, b, c (stoichiometric coefficients): Numbers from the balanced chemical equation representing mole ratios.
  • Actual Yield: The experimentally obtained amount of product, usually less than theoretical yield.

Real-World Applications of Limiting Reagent Calculations

Case Study 1: Combustion of Hydrogen Gas

Consider the reaction:

2 H2 (g) + O2 (g) ā†’ 2 H2O (l)

Suppose 5 moles of hydrogen gas react with 3 moles of oxygen gas. Determine the limiting reagent and the theoretical amount of water produced.

Step 1: Identify mole ratios

  • Hydrogen coefficient (a) = 2
  • Oxygen coefficient (b) = 1

Step 2: Calculate mole ratio for each reactant

  • Hydrogen: nH2 / a = 5 / 2 = 2.5
  • Oxygen: nO2 / b = 3 / 1 = 3

Since 2.5 < 3, hydrogen is the limiting reagent.

Step 3: Calculate moles of water produced

Using the formula:

nH2O = (nH2 Ɨ c) / a = (5 Ɨ 2) / 2 = 5 moles

Therefore, 5 moles of water are theoretically produced.

Step 4: Calculate mass of water produced

Molar mass of water = 18.015 g/mol

Mass = moles Ɨ molar mass = 5 Ɨ 18.015 = 90.075 g

Result: Hydrogen limits the reaction, producing 90.075 g of water.

Case Study 2: Synthesis of Ammonia via Haber Process

Reaction:

N2 (g) + 3 H2 (g) ā†’ 2 NH3 (g)

Given 2 moles of nitrogen and 6 moles of hydrogen, find the limiting reagent and theoretical ammonia yield.

Step 1: Stoichiometric coefficients

  • Nitrogen (a) = 1
  • Hydrogen (b) = 3

Step 2: Calculate mole ratios

  • Nitrogen: 2 / 1 = 2
  • Hydrogen: 6 / 3 = 2

Both ratios are equal, so neither reactant is limiting; both are consumed completely.

Step 3: Calculate moles of ammonia produced

Using nitrogen as reference:

nNH3 = (nN2 Ɨ c) / a = (2 Ɨ 2) / 1 = 4 moles

Molar mass of NH3 = 17.031 g/mol

Mass = 4 Ɨ 17.031 = 68.124 g

Result: Both reactants are limiting equally, producing 68.124 g of ammonia.

Additional Considerations and Advanced Insights

In industrial and laboratory settings, precise limiting reagent calculations are critical for optimizing resource use and minimizing waste. Factors such as purity of reactants, reaction conditions (temperature, pressure), and side reactions can affect actual yields.

Advanced stoichiometric calculations may incorporate:

  • Activity coefficients: Adjusting for non-ideal behavior in solutions or gases.
  • Equilibrium constants: For reversible reactions, determining extent of reaction.
  • Reaction kinetics: Rate laws influencing how quickly limiting reagent is consumed.
  • Mass transfer limitations: In heterogeneous reactions, affecting reagent availability.

Understanding these factors enhances the accuracy of limiting reagent calculations beyond simple mole ratio comparisons.

Useful External Resources for Further Study