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Theoretical Yield Calculator

Determine the maximum amount of product that can be formed from a chemical reaction using stoichiometric ratios. Enter reactant mass, molar masses, and stoichiometric coefficients.

Theoretical yield is the maximum amount of product a chemical reaction can produce if it runs to completion with zero loss. It's a stoichiometric ceiling, not a real-world result — but knowing the ceiling is what lets you measure how well a reaction actually performs. Without a theoretical yield, you can't compute percent yield, can't plan how much starting material to use, and can't compare reactions across different scales or conditions.

The math is straightforward: convert reactant mass to moles using its molar mass, scale by the reaction's stoichiometric ratio (the coefficients in the balanced equation), then convert moles of product back to mass using the product's molar mass. The trickiest part for new students isn't the math but identifying the limiting reagent — when you have multiple reactants, only the one that runs out first sets the theoretical yield. The others are "in excess" and don't constrain how much product forms.

This calculator handles the standard "one limiting reagent" case. Enter the limiting reagent's mass and molar mass, the product's molar mass, and the stoichiometric coefficients from the balanced equation. The output is the theoretical yield in grams — the maximum product mass if the reaction went perfectly. Combine with the percent-yield calculator after the experiment to grade your actual performance.

Inputs

e.g. NaCl = 58.44

e.g. Na = 22.99

Results

Theoretical Yield

3.934 g

Moles Product

0.17112 mol

Mole Ratio

1.00

Theoretical Yield Results

ParameterValue
Reactant Mass10.0000 g
Reactant Molar Mass58.4400 g/mol
Moles of Reactant0.171116 mol
Mole Ratio (product/reactant)1/1 = 1.0000
Moles of Product0.171116 mol
Product Molar Mass22.9900 g/mol
Theoretical Yield3.9339 g
Theoretical Yield (mg)3933.95 mg
Last updated:

Formula

**Theoretical yield from stoichiometry:** 1. Moles of reactant = mass_reactant / molar_mass_reactant 2. Moles of product = moles_reactant × (product_coeff / reactant_coeff) 3. Theoretical yield (g) = moles_product × molar_mass_product **Combined:** theoretical_yield = (mass_reactant / molar_mass_reactant) × (product_coeff / reactant_coeff) × molar_mass_product **Example: limestone decomposition** CaCO₃ → CaO + CO₂ Heat 25.0 g of CaCO₃ (molar mass 100.09 g/mol) to decompose. Theoretical CaO (56.08 g/mol): - moles CaCO₃ = 25.0 / 100.09 = 0.2498 mol - moles CaO produced = 0.2498 × (1/1) = 0.2498 mol (1:1 stoichiometry) - mass CaO = 0.2498 × 56.08 = **14.01 g** **Example: synthesis of ammonia** N₂ + 3H₂ → 2NH₃ Starting with 5.0 g H₂ (molar mass 2.016 g/mol). Theoretical NH₃ (17.03 g/mol): - moles H₂ = 5.0 / 2.016 = 2.480 mol - moles NH₃ from H₂ = 2.480 × (2/3) = 1.653 mol - mass NH₃ = 1.653 × 17.03 = **28.15 g** theoretical (Assumes H₂ is limiting; check N₂ availability separately.) **Identifying the limiting reagent (when two or more reactants are given):** For each reactant, compute "moles available / coefficient." The reactant with the smallest ratio is limiting. **Example: 2 H₂ + O₂ → 2 H₂O. Given 4 g H₂ and 16 g O₂:** - H₂: 4/2.016 = 1.984 mol, ÷ 2 = 0.992 - O₂: 16/32.0 = 0.500 mol, ÷ 1 = 0.500 - O₂ has smaller ratio → O₂ is limiting. - Theoretical H₂O = 0.500 × (2/1) × 18.015 = 18.02 g **Theoretical yield in moles (alternative form):** Sometimes it's cleaner to leave the answer in moles: theoretical_yield_moles = (mass_reactant / molar_mass_reactant) × (product_coeff / reactant_coeff) Then multiply by molar mass only at the end if you need grams. **Atom economy (related but different):** atom_economy = (molar_mass_desired_product / sum_of_all_reactant_molar_masses_in_balanced_eq) × 100 Atom economy is a property of the reaction itself (can't be exceeded). Percent yield is a property of how well a particular run went (can be).

How to use this calculator

  1. Balance the chemical equation first. The coefficients (reactant_coeff, product_coeff) come from the balanced equation.
  2. Identify the limiting reagent by computing (moles available / coefficient) for each reactant. Smallest ratio = limiting.
  3. Enter the limiting reagent's mass and molar mass.
  4. Enter the product's molar mass (use the molar mass calculator if needed).
  5. Enter both coefficients from the balanced equation.
  6. Output is theoretical mass of product. Use with percent-yield calculator after experiment.

Worked examples

Combustion of methane

**Scenario:** Burn 10.0 g of methane (CH₄, 16.04 g/mol) completely: CH₄ + 2 O₂ → CO₂ + 2 H₂O. Find theoretical CO₂ (44.01 g/mol). **Calculation:** Moles CH₄ = 10.0 / 16.04 = 0.6235 mol. Moles CO₂ = 0.6235 × (1/1) = 0.6235 mol. Mass CO₂ = 0.6235 × 44.01 = 27.44 g theoretical CO₂. **Result:** 10 g methane combusts completely to 27.44 g CO₂ (and ~22.5 g water). A typical residential gas stove burning 1 kg methane per day releases ~2.7 kg CO₂.

Limestone for industrial lime

**Scenario:** Industrial lime kiln: 1 ton (1000 kg) of CaCO₃ (100.09 g/mol). Reaction: CaCO₃ → CaO + CO₂. Theoretical CaO (56.08 g/mol)? **Calculation:** Moles CaCO₃ = 1,000,000 g / 100.09 = 9991 mol. Moles CaO = 9991 × (1/1) = 9991 mol. Mass CaO = 9991 × 56.08 = 560,400 g = 560.4 kg. **Result:** 1 ton limestone gives 560 kg lime theoretically. Industrial yields ~95%, so actual delivery is ~530 kg. The other 440 kg "lost" is CO₂ released — a major source of industrial emissions from cement and lime production.

Limiting reagent in a Grignard synthesis

**Scenario:** Grignard reaction: 2.5 g RMgBr (175 g/mol) + 1.2 g aldehyde (148 g/mol) → alcohol product (200 g/mol). Stoichiometry 1:1:1. **Calculation:** Moles RMgBr = 2.5/175 = 0.01429 mol. Moles aldehyde = 1.2/148 = 0.00811 mol. Aldehyde has fewer moles → limiting. Theoretical product = 0.00811 × 200 = 1.62 g. **Result:** Theoretical yield is 1.62 g (limited by aldehyde). If Grignard typical yield is 70%, expect ~1.13 g actual. The excess Grignard (0.62 g, half unreacted) is consumed in workup or unwanted side reactions. Sometimes adding excess Grignard improves yield; sometimes it causes more side products — it depends on the specific substrate.

When to use this calculator

**Calculate theoretical yield to:**

- **Set up experiments correctly**: ensure you have enough starting material to produce the target product mass. - **Choose the right scale**: if a paper reports 65% yield at 5 g scale, plan starting material accordingly when scaling up. - **Compute percent yield**: actual / theoretical × 100, the standard metric for reaction efficiency. - **Identify the limiting reagent**: which reactant runs out first determines maximum product. - **Plan reagent ordering**: convert "I need 50 g of product" backward into "I need 75 g of starting material" via known yields. - **Compare reaction conditions**: same theoretical yield, different actual yields = different efficiency. - **Industrial process optimization**: knowing the theoretical ceiling sets the target for improvement.

**Steps for stoichiometric problem-solving:**

1. **Write the balanced equation.** No way around this. 2. **Identify limiting reagent** if multiple reactants are given. 3. **Convert reactant mass to moles** using molar mass. 4. **Apply stoichiometric ratio** (product coefficient / limiting reagent coefficient). 5. **Convert product moles to mass** using product molar mass. 6. **Sanity check**: does the answer make sense? Theoretical yield should never exceed the combined mass of reactants minus byproducts.

**Common reaction patterns:**

- **1:1 stoichiometry**: product_coeff/reactant_coeff = 1. Mass scales linearly through molar mass ratio. - **2:1 (two products from one reactant, like 2 H + O → 2 H₂O)**: product moles = 2 × reactant moles. - **N₂ + 3 H₂ → 2 NH₃**: ratio (2/3) for NH₃ from H₂, (2/1) for NH₃ from N₂. - **Combustion**: CₐHᵦ + (a + b/4) O₂ → a CO₂ + (b/2) H₂O. Coefficients depend on the hydrocarbon.

**Theoretical yield in industrial chemistry:**

- **Haber process** (NH₃): theoretical yield is 100% per pass, but equilibrium limits to ~15%; unconverted reactants are recycled. The plant's "real-world" yield approaches 100% overall through recycling. - **Ostwald process** (HNO₃): catalytic oxidation of NH₃; theoretical 100%, real-world 95-97% per pass. - **Contact process** (H₂SO₄): theoretical 100%, real-world >99% via SO₂/SO₃ recycling. - **Petroleum cracking**: theoretical varies with feedstock; real-world yields constrained by side reactions and thermodynamics.

Common mistakes to avoid

  • Skipping balancing. Coefficients in an unbalanced equation give meaningless theoretical yields.
  • Identifying the wrong limiting reagent. Always compare (moles available / coefficient), not just moles or mass.
  • Mixing up product and reactant molar masses. Both go into the formula but in different places.
  • Using mass ratio instead of mole ratio. The stoichiometric ratio is moles-to-moles; mass-to-mass requires going through moles.
  • Forgetting hydrate corrections. CuSO₄·5H₂O is much heavier than CuSO₄ — if you weigh the hydrate but calculate using anhydrous molar mass, your theoretical yield will be wrong.
  • Computing theoretical with too few significant figures. Theoretical yields propagate through percent yield calculations; carry 4 sig figs.
  • Assuming theoretical yield is fixed for a reaction. It depends on which starting material is limiting — change the starting masses, change the theoretical yield.

Frequently Asked Questions

Sources & further reading

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