Stoichiometry

Learning Objectives

  • Understand the mole concept and molar mass.
  • Balance chemical equations.
  • Perform stoichiometric calculations.
  • Determine limiting reactants and percent yield.
  • Calculate empirical and molecular formulas.
The mathematics of chemical equations, essential for determining the precise amounts of reactants and products.

Introduction to Stoichiometry

Stoichiometry allows engineers to calculate the precise amounts of reactants and products involved in chemical reactions. In civil engineering, this is vital for designing concrete mixes, treating wastewater, and predicting the corrosion of steel structures.

The Mole Concept

Avogadro's Number and Molar Mass

  • Mole (mol): The SI unit for amount of substance. One mole contains exactly 6.02214076×10236.02214076 \times 10^{23} specified elementary entities.
  • Avogadro constant (NAN_A): Exactly 6.02214076×1023 mol−16.02214076 \times 10^{23} \, \text{mol}^{-1}.

  • Molar Mass (MM): The mass of one mole of a substance (g/mol).

    • Calculated by summing atomic masses from the periodic table.
    • Example: Molar mass of Water (H2OH_2O) = (2×1.008)+15.999=18.015 g/mol(2 \times 1.008) + 15.999 = 18.015 \, \text{g/mol}.

Formula Weights and Molecular Weights

Quantifying Mass

Before performing stoichiometric calculations, one must be able to quantify the mass of a substance based on its chemical formula.

Calculating Formula and Molecular Weights

  • Formula Weight: The sum of the atomic weights of the atoms in the chemical formula of a substance. Usually applied to ionic compounds (e.g., NaClNaCl).
  • Molecular Weight: The sum of the atomic weights of the atoms in a molecule. Usually applied to molecular/covalent compounds (e.g., H2OH_2O).
  • Both are numerically equivalent to the Molar Mass (MM) of the substance in g/mol.

Some Simple Patterns of Chemical Reactivity

Predicting Products

Predicting the products of a chemical reaction is a fundamental skill. Three common patterns cover many basic reactions:

Common Reaction Types

  • Combination Reactions: Two or more substances react to form one product (A+B→CA + B \rightarrow C).

    • Example: 2Mg+O2→2MgO2Mg + O_2 \rightarrow 2MgO (Burning of magnesium).

  • Decomposition Reactions: One substance undergoes a reaction to produce two or more other substances (C→A+BC \rightarrow A + B).

    • Example: CaCO3→CaO+CO2CaCO_3 \rightarrow CaO + CO_2 (Heating limestone to produce quicklime).

  • Combustion Reactions: Rapid reactions that produce a flame, usually involving O2O_2 from the air as a reactant. Combustion of hydrocarbons produces CO2CO_2 and H2OH_2O.

    • Example: CH4+2O2→CO2+2H2OCH_4 + 2O_2 \rightarrow CO_2 + 2H_2O (Combustion of methane).

Balancing Chemical Equations

Balancing Fundamentals

Chemical equations are the symbolic representation of the transformation of reactants into products. Because matter cannot be created or destroyed (the Law of Conservation of Mass), every equation must be balanced, meaning the number of atoms of each element must be identical on both the reactant and product sides.

Unbalanced Equation

Example of an unbalanced equation.

Unbalanced:Fe(s)+O2(g)→Fe2O3(s)\text{Unbalanced:} \quad Fe(s) + O_2(g) \rightarrow Fe_2O_3(s)

Steps to Balance

  1. Count atoms of each element on both sides. (Fe: 1 vs 2; O: 2 vs 3).

  2. Adjust coefficients to equalize atoms.

    • Balance Fe: 2Fe+O2→Fe2O32Fe + O_2 \rightarrow Fe_2O_3. (Fe balanced).
    • Balance O: The LCM of 2 and 3 is 6. Put 3 in front of O2O_2 and 2 in front of Fe2O3Fe_2O_3.
    • 2Fe+3O2→2Fe2O32Fe + 3O_2 \rightarrow 2Fe_2O_3.
    • Re-check Fe: 22 vs 2×2=42 \times 2 = 4. Adjust Fe to 4.

Balanced Equation

Example of a balanced equation.

Balanced:4Fe(s)+3O2(g)→2Fe2O3(s)\text{Balanced:} \quad 4Fe(s) + 3O_2(g) \rightarrow 2Fe_2O_3(s)

Quantitative Information from Balanced Equations

Quantitative Relationships

A balanced chemical equation provides quantitative relationships among the reactants and products. The coefficients in the balanced equation indicate both the relative numbers of molecules (or formula units) and the relative numbers of moles involved in the reaction.

Mole Ratios

The coefficients from the balanced equation form mole ratios, which act as conversion factors between reactants and products.

Example: For 2H2+O2→2H2O2H_2 + O_2 \rightarrow 2H_2O, the mole ratio of H2H_2 to O2O_2 is 2:12:1, and H2H_2 to H2OH_2O is 2:22:2 (or 1:11:1).

Standard Stoichiometric Conversion Process:

  1. Grams of Reactant A →\rightarrow Moles of Reactant A (using Molar Mass of A)
  2. Moles of Reactant A →\rightarrow Moles of Product B (using Mole Ratio from equation)
  3. Moles of Product B →\rightarrow Grams of Product B (using Molar Mass of B)

Limiting Reactants and Yield

Industrial Relevance

In industrial processes, reactants are rarely mixed in exact stoichiometric ratios. One reactant will inevitably run out before the others.

Limiting Reactant

The substance that is completely consumed first in a reaction, determining the maximum theoretical amount of product that can be formed.

  1. Convert all given masses to moles.
  2. Divide the number of moles of each reactant by its stoichiometric coefficient in the balanced equation.
  3. The reactant with the smallest ratio is the limiting reactant.
  4. Use the moles of the limiting reactant to calculate the theoretical yield.

Stoichiometry & Limiting Reagents

Adjust the initial amounts of reactants to see which one limits the reaction and how much product is formed.

Initial Reactants (moles)

0 mol
0 mol
Hint: For every 1 mole of O₂, you need 2 moles of H₂.

Adjust inputs and click "Run Reaction"

Percent Yield and Theoretical Yield

Reactions rarely go to completion due to side reactions, incomplete mixing, or losses during recovery.

%Yield=Actual YieldTheoretical Yield×100%\% \text{Yield} = \frac{\text{Actual Yield}}{\text{Theoretical Yield}} \times 100\%
  • Actual Yield: The amount experimentally obtained in practice.
  • Theoretical Yield: The maximum amount calculated from stoichiometry assuming 100% efficiency.
Find the Limiting Reactant and Calculate Yield

Trace mass or mole inputs through coefficient-normalized comparison to the theoretical product amount and, when actual yield is known, percent yield.

Start with a balanced equation, amounts for every reactant, and a selected product. Convert each mass to moles; keep amounts already in moles. For each reactant compute n_i/nu_i, where n_i is its amount in moles and nu_i is its coefficient in the balanced equation. The smallest ratio sets the maximum reaction extent; tied minima are co-limiting. If all ratios are equal within the reported precision, the reactants are in stoichiometric proportions and none is in excess. For the selected product with coefficient nu_p, theoretical product moles are min(n_i/nu_i) times nu_p. Convert to the requested units. Calculate percent yield only when actual yield is provided, using the same units for actual and theoretical amounts: (actual/theoretical) times 100%. This workflow assumes complete reactant quantities, a balanced equation, and a selected product; it does not determine reaction rate or equilibrium.

Find the Limiting Reactant and Calculate YieldTrace mass or mole inputs through coefficient-normalized comparison to the theoretical product amount and, when actual yield is known, percent yield.. Start with a balanced equation, amounts for every reactant, and a selected product. Convert each mass to moles; keep amounts already in moles. For each reactant compute n_i/nu_i, where n_i is its amount in moles and nu_i is its coefficient in the balanced equation. The smallest ratio sets the maximum reaction extent; tied minima are co-limiting. If all ratios are equal within the reported precision, the reactants are in stoichiometric proportions and none is in excess. For the selected product with coefficient nu_p, theoretical product moles are min(n_i/nu_i) times nu_p. Convert to the requested units. Calculate percent yield only when actual yield is provided, using the same units for actual and theoretical amounts: (actual/theoretical) times 100%. This workflow assumes complete reactant quantities, a balanced equation, and a selected product; it does not determine reaction rate or equilibrium.. Balanced equation, reactant quantities, and target product → Convert each reactant mass to moles; keep amounts already in moles; Convert each reactant mass to moles; keep amounts already in moles → For each reactant, calculate nᵢ/νᵢ; For each reactant, calculate nᵢ/νᵢ → Are all nᵢ/νᵢ values equal within precision?; Are all nᵢ/νᵢ values equal within precision? — Yes → Reactants are stoichiometric; none is in excess; Are all nᵢ/νᵢ values equal within precision? — No → Smallest ratio is limiting; ties are co-limiting; Reactants are stoichiometric; none is in excess → Calculate theoretical product moles from the minimum ratio and product coefficient; Smallest ratio is limiting; ties are co-limiting → Calculate theoretical product moles from the minimum ratio and product coefficient; Calculate theoretical product moles from the minimum ratio and product coefficient → Convert theoretical product to the requested units; Convert theoretical product to the requested units → Is actual product yield provided?; Is actual product yield provided? — Yes → Use matching units; calculate actual/theoretical × 100%; Is actual product yield provided? — No → Report theoretical yield only; Use matching units; calculate actual/theoretical × 100% → Yield calculation complete; Report theoretical yield only → Yield calculation complete

Balanced equation, reactant quantities, and target product → Convert each reactant mass to moles; keep amounts already in moles; Convert each reactant mass to moles; keep amounts already in moles → For each reactant, calculate nᵢ/νᵢ; For each reactant, calculate nᵢ/νᵢ → Are all nᵢ/νᵢ values equal within precision?; Are all nᵢ/νᵢ values equal within precision? — Yes → Reactants are stoichiometric; none is in excess; Are all nᵢ/νᵢ values equal within precision? — No → Smallest ratio is limiting; ties are co-limiting; Reactants are stoichiometric; none is in excess → Calculate theoretical product moles from the minimum ratio and product coefficient; Smallest ratio is limiting; ties are co-limiting → Calculate theoretical product moles from the minimum ratio and product coefficient; Calculate theoretical product moles from the minimum ratio and product coefficient → Convert theoretical product to the requested units; Convert theoretical product to the requested units → Is actual product yield provided?; Is actual product yield provided? — Yes → Use matching units; calculate actual/theoretical × 100%; Is actual product yield provided? — No → Report theoretical yield only; Use matching units; calculate actual/theoretical × 100% → Yield calculation complete; Report theoretical yield only → Yield calculation complete

  • Balanced equation, reactant quantities, and target product: terminator
  • Convert each reactant mass to moles; keep amounts already in moles: process
  • For each reactant, calculate nᵢ/νᵢ: process
  • Are all nᵢ/νᵢ values equal within precision?: decision
  • Reactants are stoichiometric; none is in excess: process
  • Smallest ratio is limiting; ties are co-limiting: process
  • Calculate theoretical product moles from the minimum ratio and product coefficient: process
  • Convert theoretical product to the requested units: process
  • Is actual product yield provided?: decision
  • Use matching units; calculate actual/theoretical × 100%: process
  • Report theoretical yield only: terminator
  • Yield calculation complete: terminator

Empirical and Molecular Formulas from Analyses

Formula Determination

Engineers may need to determine the chemical formula of an unknown substance (e.g., a newly synthesized polymer or an environmental pollutant) from experimental data, such as elemental mass percentages.

Formulas

  • Empirical Formula: The simplest whole-number ratio of atoms in a compound.
  • Molecular Formula: The exact number of atoms of each element in a molecule. It is a whole-number multiple of the empirical formula.
  1. Assume a 100 g100 \, \text{g} sample if given mass percentages.
  2. Convert masses to moles.
  3. Divide by the smallest number of moles to find the ratio.
  4. Multiply to get whole numbers if necessary.
Key Takeaways
  • Balancing equations ensures mass conservation.
  • The Limiting Reactant determines the maximum product possible; calculate it by comparing mole/coefficient ratios.
  • Percent Yield measures process efficiency.
  • Empirical Formulas show the simplest ratio, while Molecular Formulas show the exact counts of atoms.
  • Stoichiometric calculations are foundational for material estimation in engineering projects.

References