Molar Ratio Calculator
A free mole ratio calculator for stoichiometry: type any balanced chemical equation and convert mole-to-mole, mass-to-mass (grams-to-grams), find the limiting reactant and the theoretical yield — every result comes with step-by-step solutions so you can follow the math.
Step-by-step solution
Mole ratios in this equation
What Is a Molar Ratio?
A molar ratio (also called a mole ratio) is the ratio between the coefficients of any two substances in a balanced chemical equation. It tells you the exact proportion in which reactants combine and products form — the conversion factor at the heart of every stoichiometry calculation.
Because the ratio comes straight from the balanced equation, no memorization is needed: balance the equation, read the numbers in front of each formula, and you have every mole ratio the reaction offers.
Mole ratio definition in chemistry
One mole contains 6.022 × 10²³ particles (Avogadro's number). The coefficients in a balanced equation count moles, so the ratio 2:1 in 2H₂ + O₂ → 2H₂O is true whether you mean 2 molecules or 2 moles — scaling is what makes mole ratios so powerful for lab and industrial calculations.
How to Read Mole Ratios From a Balanced Equation
Take ammonia synthesis, N₂ + 3H₂ → 2NH₃. Reading coefficients in the balanced equation gives:
- N₂ : H₂ = 1 : 3 — 1 mole of nitrogen reacts with 3 moles of hydrogen
- H₂ : NH₃ = 3 : 2 — 3 moles of hydrogen produce 2 moles of ammonia
- N₂ : NH₃ = 1 : 2 — 1 mole of nitrogen produces 2 moles of ammonia
Any pair works in either direction: the ratio H₂:N₂ is simply 3:1. This calculator parses your equation and lists every coefficient ratio automatically in the results panel.
Why the equation must be balanced first
An unbalanced equation gives wrong ratios. H₂ + O₂ → H₂O misleadingly suggests a 1:1 H₂:O₂ ratio, but the balanced 2H₂ + O₂ → 2H₂O shows the true 2:1 ratio. The balance badge above the calculator checks atom counts on both sides and warns you before any calculation runs.
Mole-to-Mole Conversions: The 3 Steps
- Write the balanced equation and identify the given and target substances.
- Read the mole ratio from the coefficients (target coefficient ÷ given coefficient).
- Multiply: moles of target = moles given × (coefficient of target ÷ coefficient of given).
Example: 5 mol KClO₃ decomposing via 2KClO₃ → 2KCl + 3O₂ gives 5 × (3/2) = 7.5 mol O₂. Select the "Mole → Mole" tab above to run any such conversion.
Mass-to-Mass (Grams-to-Grams) Stoichiometry
Mole ratios apply to moles, never directly to grams. The bridge is molar mass, with the fundamental relation:
- Convert the given mass to moles: n = m ÷ M.
- Apply the mole ratio from the coefficients.
- Convert product moles back to grams: m = n × M.
Example: 16 g CH₄ burning via CH₄ + 2O₂ → CO₂ + 2H₂O gives 43.8910 g CO₂ (16 ÷ 16.043 = 0.99732 mol CH₄ → 0.99732 mol CO₂ → × 44.009 g/mol). The "Mass → Mass" tab shows each intermediate value.
Limiting Reactant and Theoretical Yield
When two or more reactants are supplied, one runs out first — the limiting reactant. It alone determines how much product can form (the theoretical yield); the others are excess reactants.
How to find the limiting reactant
- Convert every reactant to moles.
- For each, compute the product moles it could make: n(product) = n(reactant) × coef(product) ÷ coef(reactant).
- The reactant yielding the least product is limiting.
- Theoretical yield = that product amount, in moles or × M in grams.
Use the "Limiting Reactant" tab above with any number of reactants and mixed mol/gram inputs.
Worked Examples With Answers
Example 1 — Mole → mole
How much O₂ reacts with 4 mol H₂? (2H₂ + O₂ -> 2H₂O)
Mole ratio H₂:O₂ = 2:1, so 4 × (1/2) = 2 mol O₂. The same 4 mol H₂ makes 4 mol H₂O (ratio 2:2).
Example 2 — Mass → mass
What mass of CO₂ forms from 10 g CaCO₃? (CaCO₃ -> CaO + CO₂)
M(CaCO₃) = 100.086 g/mol → n = 10 ÷ 100.086 = 0.09991 mol. 1:1 ratio → 0.09991 mol CO₂ × 44.009 g/mol = 4.3971 g CO₂.
Example 3 — Limiting reactant
28 g N₂ + 8 g H₂ → NH₃? (N₂ + 3H₂ -> 2NH₃)
N₂ could make 1.999 mol NH₃; H₂ could make 2.6455 mol NH₃. N₂ is limiting. Theoretical yield = 1.999 mol × 17.031 g/mol = 34.045 g NH₃.
Example 4 — Grams of Al → grams of AlCl₃
What mass of AlCl₃ forms from 54 g Al? (2Al + 3Cl₂ -> 2AlCl₃)
n(Al) = 54 ÷ 26.982 = 2.0013 mol → 1:1 → 2.0013 mol AlCl₃ × 133.332 g/mol = 266.8419 g AlCl₃.
Molar Ratio vs Mass Ratio vs Mole Fraction
| Concept | Definition | Example (2H₂ + O₂ → 2H₂O) |
|---|---|---|
| Molar (mole) ratio | Coefficient ÷ coefficient | H₂ : O₂ = 2 : 1 |
| Mass ratio | (coef × M) ÷ (coef × M) | H₂ : O₂ ≈ 1 : 7.94 |
| Mole fraction | n(substance) ÷ n(total mixture) | Depends on the mixture, not the equation |
The classic trap: the mole ratio H₂:O₂ is 2:1, but the mass ratio is about 1:7.94 because oxygen atoms are far heavier. Always convert through moles — never apply a mole ratio directly to grams.
Common Molar Masses (g/mol)
Built-in reference used by the calculator's mass conversions (IUPAC 2021 atomic weights):
| Compound | Formula | Molar mass | Compound | Formula | Molar mass |
|---|---|---|---|---|---|
| Water | H₂O | 18.015 | Carbon dioxide | CO₂ | 44.009 |
| Sodium chloride | NaCl | 58.44 | Calcium carbonate | CaCO₃ | 100.086 |
| Sulfuric acid | H₂SO₄ | 98.072 | Sodium hydroxide | NaOH | 39.997 |
| Ammonia | NH₃ | 17.031 | Methane | CH₄ | 16.043 |
| Glucose | C₆H₁₂O₆ | 180.156 | Hydrogen chloride | HCl | 36.458 |
| Oxygen | O₂ | 31.998 | Nitrogen | N₂ | 28.014 |
| Calcium oxide | CaO | 56.077 | Aluminium chloride | AlCl₃ | 133.332 |
| Potassium chlorate | KClO₃ | 122.545 | Iron(III) oxide | Fe₂O₃ | 159.687 |
Hydrates are supported too — e.g. CuSO₄·5H₂O parses to 249.677 g/mol — as are parentheses like Al₂(SO₄)₃ (342.132 g/mol) and bracket complexes like K₄[Fe(CN)₆].
Frequently Asked Questions
What is a molar ratio in chemistry?
A molar ratio (mole ratio) is the ratio of the coefficients of any two substances in a balanced chemical equation. In 2H₂ + O₂ → 2H₂O the molar ratio of H₂ to O₂ is 2:1, meaning 2 moles of hydrogen react with 1 mole of oxygen. It is the conversion factor at the heart of every stoichiometry calculation.
How do you find the molar ratio from a balanced equation?
Read the coefficients in front of each formula. In N₂ + 3H₂ → 2NH₃ the coefficient of N₂ is 1 and of H₂ is 3, so the molar ratio N₂:H₂ is 1:3. No calculation is needed — the balanced equation hands you every mole ratio directly. This calculator parses your equation and lists each ratio automatically.
How many moles of O₂ react with 4 moles of H₂?
2 moles. From 2H₂ + O₂ → 2H₂O the molar ratio H₂:O₂ is 2:1, so 4 mol H₂ × (1 mol O₂ / 2 mol H₂) = 2 mol O₂. The same 4 mol of H₂ produces 4 mol of H₂O, since the H₂:H₂O ratio is 2:2.
How many grams of CO₂ form from 10 g of CaCO₃?
4.3971 g. CaCO₃ → CaO + CO₂ has a 1:1 mole ratio. First convert to moles: 10 g ÷ 100.086 g/mol = 0.09991 mol CaCO₃, giving 0.09991 mol CO₂. Then back to grams: 0.09991 mol × 44.009 g/mol = 4.3971 g CO₂.
How do you calculate theoretical yield?
Theoretical yield is the maximum product mass the limiting reactant can make: convert the limiting reactant to moles, apply the mole ratio to get product moles, then multiply by the product's molar mass. Example: 28 g N₂ with excess H₂ gives 28 ÷ 28.014 = 0.9995 mol N₂ → 1.9990 mol NH₃ → 1.9990 × 17.031 = 34.045 g NH₃ theoretical yield. Percent yield = (actual ÷ theoretical) × 100.
How do you tell which reactant is limiting?
For each reactant, calculate how much product it could make; the one that makes the least is limiting. With 28 g N₂ and 8 g H₂ making ammonia (N₂ + 3H₂ → 2NH₃), N₂ can make 34.045 g NH₃ while H₂ could make more — so N₂ is the limiting reactant and H₂ is in excess. This calculator runs that comparison for you across any number of reactants.
Is molar ratio the same as mole fraction?
No. A molar ratio compares two substances via equation coefficients (e.g. H₂:O₂ = 2:1 in water formation), while a mole fraction is one substance's moles divided by the total moles in a mixture. Molar ratios come from the balanced equation; mole fractions describe a mixture's composition.
Does the equation have to be balanced to use mole ratios?
Yes — an unbalanced equation gives wrong ratios. H₂ + O₂ → H₂O is not balanced (2 O on the left, 1 on the right); the correct 2H₂ + O₂ → 2H₂O gives H₂:O₂ = 2:1, while the unbalanced form would misleadingly suggest 1:1. This tool checks atom balance automatically and warns you before calculating.
How do you convert grams to moles?
Divide mass by molar mass: n = m ÷ M. For example, 54 g of aluminium (M = 26.982 g/mol) is 54 ÷ 26.982 = 2.0013 mol Al. That 54 g of Al then produces 266.8419 g of AlCl₃ via 2Al + 3Cl₂ → 2AlCl₃.
What is an excess reactant?
The reactant left over after the limiting reactant runs out. In 2H₂ + O₂ → 2H₂O with 10 g H₂ (4.9603 mol) and 1 mol O₂, oxygen is limiting — it caps water production at 2 mol (36.03 g) — while hydrogen is in excess and some remains unreacted.
What is the molar mass of Al₂(SO₄)₃?
342.132 g/mol. Add the atoms: 2×Al (2 × 26.982) + 3×S (3 × 32.06) + 12×O (12 × 15.999) = 342.132 g/mol. Parentheses multiply everything inside, which the parser handles automatically.
Is mole ratio the same as mass ratio?
No — and confusing them is the most common stoichiometry mistake. In 2H₂ + O₂ → 2H₂O the mole ratio H₂:O₂ is 2:1, but the mass ratio is (2 × 2.016) : 31.998 = 4.032 : 31.998, i.e. about 1 : 7.94. Always convert through moles; never apply a mole ratio directly to grams.
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