Calculate theoretical mass from balanced equation

Quantitative chemistry • Yield and atom economy

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How does excess reagent affect the theoretical mass calculation when only one reactant mass is given?

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When only one reactant mass is given, that reactant acts as the limiting reagent and any other reagents are implicitly in excess; theoretical mass uses the given reactant amount.

Key concepts

What you'll likely be quizzed about

Balanced equations and mole ratios

A balanced chemical equation shows the relative number of moles of each substance that react or form. The coefficients in the equation give direct mole ratios that link reactants and products. Because mole ratios are fixed by stoichiometry, change in the amount of one substance causes proportional change in the amount of another according to those coefficients. Accurate use of the mole ratio causes correct conversion between moles of reactant and moles of product. Incorrect balancing or ignoring coefficients causes incorrect theoretical mass results.

Moles and molar mass (Mr)

Moles measure amount of substance and connect mass to the number of particles. Molar mass (Mr) gives mass per mole in grams per mole, calculated from relative atomic masses. Division of mass by molar mass converts grams to moles; multiplication of moles by molar mass converts moles back to grams. Because conversion between mass and moles uses Mr, errors in Mr values cause proportional errors in calculated theoretical mass. Consistent units and correct Mr values ensure accurate calculations.

Step-by-step calculation procedure

Step 1: Ensure the equation is balanced so the mole ratio between reactant and product is correct. Step 2: Calculate moles of the given reactant by dividing its mass by its molar mass. Step 3: Use the mole ratio from the balanced equation to find moles of product. Step 4: Convert moles of product to mass by multiplying by the product's molar mass. Following the steps in order gives the theoretical mass because each step logically follows: balancing determines ratio, ratio links amounts, and molar mass links moles and mass.

Limiting reagent and single reactant data

The limiting reagent is the reactant that runs out first and therefore limits the amount of product formed. When only one reactant mass is given, that reactant is treated as the limiting reagent unless the problem statement indicates otherwise. When masses of more than one reactant are provided, calculation of moles and comparison using mole ratios identifies the limiting reagent. Correct identification of the limiting reagent causes the theoretical mass calculation to use the correct starting amount. Incorrect identification causes overestimation of the theoretical mass.

Units, significant figures and assumptions

All masses use grams and molar masses use g mol-1. Moles are unitless amounts. Final theoretical mass must include correct units (g). Significant figures follow the precision of the given data; rounding during intermediate steps can cause small errors, so round only at the final step where possible. Theoretical mass assumes complete reaction, no side reactions and pure substances. Deviations from these assumptions in real experiments cause actual yield to be lower than the theoretical mass.

Key notes

Important points to keep in mind

Always balance the equation before any quantitative work.

Convert given mass to moles using moles = mass ÷ Mr.

Use mole ratios from the balanced equation to convert moles of reactant to moles of product.

Convert moles of product to mass using mass = moles × Mr and include units (g).

Identify the limiting reagent when more than one reactant mass is provided.

Assume complete reaction for theoretical mass; real yields are usually lower.

Keep units consistent: grams for mass, g mol-1 for molar mass.

Avoid premature rounding; round final answer to the correct significant figures.

Check arithmetic by reversing the final mass to moles and comparing with intermediate mole values.

Check that coefficients used in ratios are for the balanced equation, not for simplified or altered forms.