Stoichiometry, limiting and excess reactants, conversion and yield

Balanced equations, limiting and excess reactants, percent excess, fractional conversion, and yield and selectivity for single and multiple reactions.

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Why it matters

Raw materials are the largest cost in most chemical plants, so engineers must know exactly how much of each reactant is needed, which one runs out first, how much is converted per pass and how much of it ends up as the desired product. Stoichiometry, limiting and excess reactants, conversion, yield and selectivity are the language of every reactor material balance and plant performance report.

Key ideas

Balanced equation and stoichiometric ratio. A balanced equation such as N₂ + 3H₂ → 2NH₃ gives the molar ratio in which species react and form (1 : 3 : 2). Mass is conserved, moles in general are not. Stoichiometric coefficients ν_i are taken negative for reactants and positive for products.

Limiting reactant. The reactant that would be used up first if the reaction went to completion. Find it by dividing each reactant's feed moles by its stoichiometric coefficient: the smallest ratio n_i,0 / |ν_i| is limiting. If all ratios are equal, the feed is stoichiometric and no reactant is in excess.

Excess reactant and percent excess. Any other reactant is in excess. Percent excess compares its feed with the amount needed to react completely with the limiting reactant (the theoretical requirement), regardless of how much actually reacts. In combustion this is called percent excess air.

Fractional conversion. X_A = (moles of A reacted) / (moles of A fed). Conversion is defined for a specific reactant – conversions of different reactants differ unless the feed is stoichiometric. Single-pass and overall conversion differ in recycle processes (see the recycle topic).

Yield and selectivity (multiple reactions). When side reactions occur, not all reacted material forms the desired product D:

  • Yield based on feed: moles of D formed / moles of D that could form if all limiting reactant fed went to D.
  • Yield based on consumption: moles of D formed / moles of D that could form from the reactant actually consumed (fractional yield).
  • Selectivity: moles of D formed / moles of undesired product U formed (or, in some books, moles of reactant converted to D / moles converted in total). Definitions vary between textbooks – read each problem's definition and state the one you use.

Choice of basis. Start with 100 mol (or kmol) of feed or of the limiting reactant, then scale.

Formulas

  • limiting reactant = min over reactants of (n_i,0 / |ν_i|)
  • % excess = (n_fed − n_theoretical) / n_theoretical × 100 – n_theoretical needed to consume all limiting reactant.
  • X_A = (n_A,0 − n_A) / n_A,0 – fractional conversion of A.
  • n_i = n_i,0 + ν_i·ξ – amount of i after reaction; ξ extent of reaction (mol), ν_i stoichiometric coefficient.
  • Y_feed = n_D / (n_A,0 × (ν_D/|ν_A|)) – yield based on feed.
  • Y_reacted = n_D / ((n_A,0 − n_A) × (ν_D/|ν_A|)) – yield based on reactant consumed.
  • S_D/U = n_D / n_U – selectivity of D relative to U.
  • Y_feed = X_A × Y_reacted

Worked examples

Example 1 (standard). An ammonia reactor is fed 100 kmol/h N₂ and 360 kmol/h H₂. The conversion of N₂ is 25 %. Find the limiting reactant, the percent excess, the outlet flows and the conversion of H₂. Reaction: N₂ + 3H₂ → 2NH₃.

  1. Ratios: N₂ 100 / 1 = 100; H₂ 360 / 3 = 120. N₂ has the smaller ratio, so N₂ is limiting.
  2. H₂ needed for all N₂: 3 × 100 = 300 kmol/h. % excess H₂ = (360 − 300) / 300 × 100 = 20 %.
  3. N₂ reacted = 0.25 × 100 = 25 kmol/h, so ξ = 25 kmol/h.
  4. Outlet: N₂ = 100 − 25 = 75; H₂ = 360 − 3 × 25 = 285; NH₃ = 0 + 2 × 25 = 50 kmol/h; total 410 kmol/h.
  5. Conversion of H₂ = 75 / 360 = 0.208.

Answer: N₂ limiting, 20 % excess H₂; outlet 75 N₂, 285 H₂, 50 NH₃ kmol/h; X_H₂ = 20.8 %

Example 2 (GATE level). Ethylene is oxidised to ethylene oxide (EO), with some complete combustion: C₂H₄ + ½O₂ → C₂H₄O and C₂H₄ + 3O₂ → 2CO₂ + 2H₂O. The feed is 100 mol C₂H₄ and 100 mol O₂. The ethylene conversion is 50 % and the yield of EO based on ethylene fed is 40 %. Find the outlet composition, the fractional yield based on ethylene reacted and the selectivity of EO relative to ethylene burned.

  1. C₂H₄ reacted = 0.50 × 100 = 50 mol. EO formed = 0.40 × 100 = 40 mol (ξ₁ = 40).
  2. C₂H₄ burned = 50 − 40 = 10 mol (ξ₂ = 10).
  3. O₂ used: 0.5 × 40 + 3 × 10 = 20 + 30 = 50 mol; O₂ left = 100 − 50 = 50 mol.
  4. CO₂ = 2 × 10 = 20 mol; H₂O = 2 × 10 = 20 mol; C₂H₄ left = 50 mol.
  5. Outlet total = 50 + 50 + 40 + 20 + 20 = 180 mol. Mole fractions: C₂H₄ 0.278, O₂ 0.278, EO 0.222, CO₂ 0.111, H₂O 0.111.
  6. Fractional yield (on C₂H₄ reacted) = 40 / 50 = 0.80. Selectivity = 40 mol EO / 10 mol C₂H₄ burned = 4.0.
  7. Check: Y_feed = X × Y_reacted = 0.50 × 0.80 = 0.40 ✓.

Answer: Outlet 50 C₂H₄, 50 O₂, 40 EO, 20 CO₂, 20 H₂O (mol); yield on reacted 80 %; selectivity 4.0

Common mistakes

  • Picking the limiting reactant by comparing masses or raw moles instead of moles divided by coefficients.
  • Calculating percent excess from the amount actually reacted instead of the amount theoretically required.
  • Quoting a conversion without saying which reactant it refers to.
  • Mixing yield-on-feed and yield-on-consumed definitions.
  • Forgetting that unreacted excess reactant and inerts leave in the product stream.
  • Using an unbalanced equation or molar masses that are wrong (SO₂ is 64 g/mol, not 32).

For GATE CH

Typical questions give a feed and a conversion and ask for outlet flows or composition, percent excess, or the yield and selectivity in a two-reaction system. Practise setting up a table of species with feed, change (in terms of extents) and outlet, and checking an element balance at the end.

Quick check

  1. For 2A + B → C with 6 mol A and 2 mol B fed, which is limiting?
  2. In question 1, what is the percent excess of the other reactant?
  3. 4 mol H₂ and 2 mol O₂ react completely (2H₂ + O₂ → 2H₂O). How much water forms?
  4. If X = 0.6 and the yield on reactant consumed is 0.75, what is the yield on feed?
  5. Is conversion defined for products or reactants?

Answers: 1. B (2/1 = 2 < 6/2 = 3); 2. 50 % excess A; 3. 4 mol (feed is stoichiometric); 4. 0.45; 5. reactants.

Interview questions

All Process Calculations interview questions

Try answering each one aloud before you open it.

  1. 1.What is stoichiometry in chemical engineering?Concept

    Stoichiometry is the calculation of reactants and products in chemical reactions. It involves using balanced chemical equations to determine the proportions of substances involved in reactions. This is essential for designing chemical processes and ensuring that reactions proceed efficiently.

  2. 2.Explain the concept of limiting and excess reactants.Concept

    In a chemical reaction, the limiting reactant is the substance that is completely consumed first, limiting the amount of product formed. The excess reactant is the substance that remains after the reaction has completed. Identifying the limiting reactant is crucial for calculating the theoretical yield of a reaction.

  3. 3.What is meant by conversion in chemical reactions?Concept

    Conversion in chemical reactions refers to the fraction or percentage of a reactant that is transformed into products. It is a measure of the efficiency of a reaction and is calculated as the amount of reactant consumed divided by the initial amount of reactant.

  4. 4.Define yield in the context of chemical reactions.Concept

    Yield is the amount of product obtained from a chemical reaction. It is often expressed as a percentage of the theoretical maximum amount of product that could be formed, based on the limiting reactant. Yield can be affected by factors such as reaction conditions and purity of reactants.

  5. 5.Why is it important to identify the limiting reactant in industrial chemical processes?Application

    Identifying the limiting reactant is important because it determines the maximum amount of product that can be formed. This helps in optimizing the use of raw materials, reducing waste, and improving the cost-effectiveness of the process. It also aids in designing reactors and scaling up processes.

  6. 6.What happens if a chemical reaction is carried out with an excess of one reactant?Application

    If a reaction is carried out with an excess of one reactant, the excess reactant will remain unreacted after the limiting reactant is completely consumed. This can lead to increased costs and the need for additional separation and purification steps to remove the excess reactant from the product.

  7. 7.How does temperature affect the yield of a chemical reaction?Application

    Temperature can significantly affect the yield of a chemical reaction. Increasing the temperature generally increases the reaction rate, which can lead to higher yields if the reaction is kinetically controlled. However, for equilibrium reactions, higher temperatures may shift the equilibrium position, potentially reducing yield if the reaction is exothermic.

  8. 8.Calculate the theoretical yield of water when 4 mol of hydrogen react with 2 mol of oxygen.Numerical

    For 2H₂ + O₂ → 2H₂O, divide each feed by its coefficient: H₂ 4 / 2 = 2 and O₂ 2 / 1 = 2. The ratios are equal, so the feed is exactly stoichiometric and neither reactant is limiting or in excess. At complete reaction 4 mol H₂ give 4 mol H₂O (72 g).

  9. 9.A reaction has a theoretical yield of 100 grams but only produces 80 grams of product. What is the percent yield?Numerical

    Percent yield is calculated using the formula: (actual yield / theoretical yield) × 100%. Here, the actual yield is 80 grams and the theoretical yield is 100 grams. Percent yield = (80 / 100) × 100% = 80%.

  10. 10.Explain how stoichiometry is used in designing chemical reactors.Application

    Stoichiometry is used in designing chemical reactors by determining the proportions of reactants needed to achieve desired product yields. It helps in calculating the reactor size, residence time, and conditions required for optimal conversion and yield. Accurate stoichiometric calculations ensure efficient use of resources and energy in the reactor design.

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