Balance chemical equations, find limiting reagents, calculate theoretical yield, determine percent yield, and solve stoichiometry problems with step-by-step solutions and visualizations for chemistry homework and lab work.
Enter a balanced equation and known amounts to calculate stoichiometry, find limiting reagent, and determine theoretical yield.
n = m/M (mass → moles)
n = M·V (solution)
n = PV/(RT) (gas)
Divide moles by coefficient
Smallest ratio = limiter
Controls max product
% = (actual/theoretical) × 100
Ideal = 100%
Typical = 60-90%
Stoichiometry is the quantitative foundation of chemistry—the mathematical relationship between reactants and products in chemical reactions. At its core lies the law of conservation of mass: atoms are neither created nor destroyed in chemical reactions, only rearranged. This means every atom present in reactants must appear in products, making balanced chemical equations essential for all quantitative chemistry work.
Balancing chemical equations is the first critical step in stoichiometry. An unbalanced equation like H₂ + O₂ → H₂O violates conservation of mass (2 oxygen atoms on left, 1 on right). The balanced version, 2 H₂ + O₂ → 2 H₂O, satisfies the requirement: 4 H atoms and 2 O atoms on each side. The coefficients (2, 1, 2) tell you the mole ratio—for every 1 mole of O₂, you need 2 moles of H₂ to produce 2 moles of H₂O.
Once equations are balanced, stoichiometry lets you answer practical questions: How many grams of product can I make? Which reactant will run out first (the limiting reagent)? How much excess reagent remains? What's my percent yield if I only get 15 grams instead of the theoretical 20 grams? These calculations are essential for lab work, industrial synthesis, environmental chemistry, and biochemistry—anywhere chemical reactions happen.
Our calculator combines equation balancing with comprehensive stoichiometry features. Enter your reaction, specify what you have (mass, moles, solution volume, or gas conditions), and get instant results: balanced equation with coefficients, limiting reagent identification, theoretical yield predictions, excess amounts, and visual mole ratio diagrams. It's your complete tool for chemistry homework, exam prep, lab planning, and conceptual understanding.
Stoichiometry bridges the microscopic world of atoms and molecules (measured in moles, where 1 mole = 6.022 × 10²³ particles) to the macroscopic world of grams, liters, and lab equipment you can see and measure. For students, mastering stoichiometry means mastering chemistry problem-solving. For professionals, it means predicting reaction outcomes, optimizing yields, and scaling processes from bench to industrial scale.
This tool handles all major stoichiometry scenarios: mass-to-mass conversions, solution stoichiometry with molarity, gas stoichiometry with ideal gas law (PV = nRT), limiting reagent determination, theoretical and percent yield calculations, and excess reagent analysis. Whether you're balancing simple synthesis reactions, complex combustion equations, or multi-step reaction sequences, this calculator provides accurate, step-by-step guidance to build your chemistry confidence.
This calculator is designed to handle the full workflow from balancing equations to predicting reaction outcomes. Here's a comprehensive guide to each calculation mode:
Type your reaction in standard chemical notation. The calculator accepts various input formats:
Example inputs:
H2 + O2 -> H2O
C3H8 + O2 -> CO2 + H2O (propane combustion)
Fe + O2 -> Fe2O3 (rust formation)
NaOH + H2SO4 -> Na2SO4 + H2O (neutralization)
Click "Balance" or submit the form. The calculator automatically finds the smallest whole-number coefficients that satisfy conservation of mass. The balanced equation shows coefficients in front of each species. If balancing fails, you'll get an error message—check for typos in formulas or impossible reactions.
Example: Propane combustion
Input: C3H8 + O2 → CO2 + H2O
Balanced: C₃H₈ + 5 O₂ → 3 CO₂ + 4 H₂O
Coefficients mean: 1 mol propane + 5 mol oxygen → 3 mol CO₂ + 4 mol water
For each reactant, enter what you have using one of four input methods:
Example: Reacting hydrogen gas with oxygen gas
H₂: 2.0 g (mass mode)
O₂: 1.5 L at 1 atm, 25°C (gas mode)
Calculator converts both to moles, then applies stoichiometry
The calculator identifies which reactant limits the reaction (runs out first) and computes the maximum product you can make (theoretical yield). Results include:
Example: 2 H₂ + O₂ → 2 H₂O with 2 g H₂ and 32 g O₂
H₂: 2 g / 2.016 g/mol = 0.992 mol → ratio = 0.992/2 = 0.496
O₂: 32 g / 32 g/mol = 1.0 mol → ratio = 1.0/1 = 1.0
Limiting reagent: H₂ (smaller ratio)
Theoretical yield H₂O: 0.992 mol H₂ × (2 mol H₂O / 2 mol H₂) × 18.015 g/mol = 17.87 g
If you performed the reaction and measured actual product mass, enter it to compute percent yield:
% Yield = (Actual Yield / Theoretical Yield) × 100%
Typical lab yields: 60-90%. Values >100% suggest impure product or measurement errors. Values <50% may indicate side reactions, incomplete reaction, or transfer losses.
Understanding the math behind stoichiometry helps you solve problems confidently and troubleshoot when things don't work out. Here are the core formulas and concepts:
Balancing ensures atom conservation. The process conceptually:
Example: Balance C₃H₈ + O₂ → CO₂ + H₂O
Let coefficients be: a C₃H₈ + b O₂ → c CO₂ + d H₂O
C balance: 3a = c
H balance: 8a = 2d → d = 4a
O balance: 2b = 2c + d
Set a = 1: c = 3, d = 4, then 2b = 2(3) + 4 = 10 → b = 5
Result: C₃H₈ + 5 O₂ → 3 CO₂ + 4 H₂O
Mass ↔ Moles: n = m / M
where n = moles, m = mass (g), M = molar mass (g/mol)
Solution: n = M × V
where M = molarity (mol/L), V = volume (L)
Gas: PV = nRT → n = PV / (RT)
where P = pressure, V = volume, T = temperature (K), R = 0.08206 L·atm/(mol·K)
Ratioi = molesi / coefficienti
The reactant with the smallest ratio is the limiting reagent
Example: 2 Al + 3 Cl₂ → 2 AlCl₃
Given: 5 mol Al, 6 mol Cl₂
Al ratio: 5 mol / 2 = 2.5
Cl₂ ratio: 6 mol / 3 = 2.0
Cl₂ is limiting (2.0 < 2.5)
Max AlCl₃: 6 mol Cl₂ × (2 mol AlCl₃ / 3 mol Cl₂) = 4 mol
nproduct = nlimiting × (coeffproduct / coefflimiting)
massproduct = nproduct × Mproduct
Example: N₂ + 3 H₂ → 2 NH₃
Given: 2 mol N₂, 4 mol H₂ (H₂ is limiting: 4/3 = 1.33 < 2/1 = 2)
nNH₃ = 4 mol H₂ × (2 mol NH₃ / 3 mol H₂) = 2.67 mol NH₃
massNH₃ = 2.67 mol × 17.03 g/mol = 45.4 g
% Yield = (Actual Yield / Theoretical Yield) × 100%
Example: Theoretical yield = 45.4 g, actual yield = 38.2 g
% Yield = (38.2 / 45.4) × 100% = 84.1%
(Good lab result—typical organic synthesis yields are 60-85%)
Stoichiometry isn't just a classroom exercise—it's the foundation for real chemistry in labs, industry, and everyday life. Here are detailed scenarios where this calculator helps:
Balancing equations and solving stoichiometry problems are core skills tested on every chemistry exam. Use this calculator to check your manual work, verify limiting reagent identification, and confirm theoretical yields. Practice with textbook problems: balance the equation by hand, solve for products, then verify with the calculator. Build confidence by understanding where you make mistakes—coefficient errors, mole ratio confusion, or unit conversion issues.
Before starting a synthesis, you need to know how much of each reactant to order. Enter your balanced equation and desired product amount (work backwards from product to reactants using stoichiometry). The calculator tells you exact masses or volumes needed. Add 10-20% extra to account for losses and ensure you have excess of cheaper, non-limiting reagents. This prevents costly mid-synthesis reagent shortages.
After running a reaction, you measure actual product yield. Calculate percent yield to assess efficiency. Low yields (<50%) suggest problems: incomplete reaction (not enough time, wrong temperature), side reactions consuming reactants, product decomposition, or transfer losses. Use yield data to optimize: adjust reaction time, temperature, catalyst concentration, or purification methods. Track yields over multiple trials to evaluate improvements.
Combustion reactions (fuel + O₂ → CO₂ + H₂O) power vehicles and generate energy. Balance equations like C₈H₁₈ + O₂ → CO₂ + H₂O (octane combustion) to determine oxygen requirements and CO₂ emissions. Calculate: how many grams of CO₂ does burning 1 gallon of gasoline produce? Environmental chemistry applications include carbon footprint analysis and air quality studies.
Neutralization reactions (acid + base → salt + water) are fundamental in analytical chemistry. Balance equations like H₂SO₄ + NaOH → Na₂SO₄ + H₂O (note the 1:2 mole ratio due to sulfuric acid being diprotic). For titrations, use stoichiometry to calculate unknown concentrations: if 25.0 mL of 0.1 M NaOH neutralizes 12.5 mL H₂SO₄, what's the acid molarity? Stoichiometry handles the mole ratio conversion.
When two solutions mix and form an insoluble product (precipitate), stoichiometry predicts how much precipitate forms. Example: AgNO₃ + NaCl → AgCl ↓ + NaNO₃. If you mix 50 mL of 0.1 M AgNO₃ with 50 mL of 0.15 M NaCl, which is limiting? How many grams of AgCl precipitate? Used in qualitative analysis (identifying ions), water hardness testing, and gravimetric quantification.
Reactions involving gases require ideal gas law integration. Ammonia synthesis (Haber process): N₂ + 3 H₂ → 2 NH₃. If you react 100 L N₂ gas at 200°C and 200 atm with excess H₂, how many moles of NH₃ form? How many liters at STP? Gas stoichiometry is critical in industrial chemistry: ammonia production for fertilizers, chlorine manufacturing, and petroleum refining all depend on accurate gas volume predictions.
Pharmaceutical chemists use stoichiometry to scale reactions from milligrams (research) to kilograms (production). Multi-step synthesis requires calculating yields at each step—if Step 1 gives 80% yield, Step 2 gives 70%, and Step 3 gives 90%, overall yield is 0.80 × 0.70 × 0.90 = 50.4%. Limiting reagent calculations ensure expensive reagents (chiral catalysts, rare intermediates) aren't wasted. Quality control demands precise stoichiometry to meet pharmaceutical purity standards.
Subscripts are part of the chemical formula and define the compound's identity. Changing H₂O to H₂O₂ turns water into hydrogen peroxide—a completely different substance. ONLY change coefficients (the numbers in front of formulas). H₂ + O₂ → H₂O becomes 2 H₂ + O₂ → 2 H₂O, NOT H₂ + O₂ → H₃O or other nonsense formulas.
In 2 Ca(OH)₂, the coefficient 2 applies to the entire formula: you get 2 Ca, 4 O, and 4 H atoms (not 2 Ca, 2 O, 2 H). Parentheses indicate groupings—the subscript outside applies to everything inside. Common in ionic compounds like Al₂(SO₄)₃: this means 2 Al, 3 SO₄ groups → 2 Al, 3 S, 12 O total. Always expand formulas carefully before balancing.
The limiting reagent runs out first and determines maximum product—it's NOT the reagent you have less of by mass. You might have 100 g of one reactant and 10 g of another, but the 100 g one could still be limiting if its coefficient in the balanced equation is very large. Always convert to moles, divide by coefficients, and compare ratios. Smallest ratio = limiting. Largest ratio = most excess.
You MUST balance the equation before doing any mole ratio calculations. Using unbalanced coefficients (or assuming all coefficients are 1) gives completely wrong answers. For H₂ + O₂ → H₂O, if you assume 1:1:1 ratio instead of 2:1:2, you'll predict half the actual water produced. Always verify your equation is balanced (count atoms on both sides) before proceeding to stoichiometry.
Stoichiometry requires consistent units. Common errors: using mL instead of L for gas volume (1000 mL = 1 L), forgetting to convert °C to K (K = °C + 273.15), using kPa instead of atm for pressure (1 atm = 101.325 kPa), or mixing molarity (M = mol/L) with moles. Always check your units match the formula requirements. When in doubt, use dimensional analysis to verify units cancel correctly.
While (s), (l), (g), (aq) labels don't affect atom counts when balancing, they DO matter for stoichiometry calculations. Gaseous reactants use PV = nRT; aqueous use molarity; solids use mass. If you treat a gas like a solid (trying to measure "grams" of O₂ gas directly), you'll get nonsense. Also, precipitation and solubility rules depend on states—AgCl(s) precipitates from Ag⁺(aq) + Cl⁻(aq).
While solving, you might get fractional coefficients like ½ O₂. This is mathematically correct but unconventional. Multiply ALL coefficients by the smallest number that clears fractions. For C₃H₈ + 5 O₂ → 3 CO₂ + 4 H₂O, if you initially got ½, 5/2, 3/2, 2, multiply everything by 2. Final answer uses whole numbers unless the problem specifically asks for fractional form.
Percent yield = (actual / theoretical) × 100%, NOT (actual / starting material) or (actual / limiting reagent mass). Theoretical yield is the maximum product mass calculated from stoichiometry of the limiting reagent. If you got 15 g product but theoretical was 20 g, yield is 75%. Getting >100% means errors—either your actual measurement is wrong (impure product) or theoretical calculation was wrong.
Molar mass must match the actual formula. For Ca(OH)₂, M = 40.08 + 2(16.00) + 2(1.008) = 74.096 g/mol, NOT 40.08 + 16 + 1 = 57.08. Also, use updated periodic table values: C = 12.011 (not 12.0), H = 1.008 (not 1.0). Small differences compound in large molecules. Our calculator uses the latest IUPAC values automatically, but if you're doing manual calculations, verify your molar masses.
Some equations are chemically impossible and can't be balanced. Example: H₂ + O₂ → H₂O₂ + H₂O (trying to make both products from the same reactants usually fails). If your balancing attempts give non-integer or negative coefficients, check for typos in formulas or reconsider if the reaction is actually feasible. Not all combinations of reactants and products are valid chemical reactions. Consult reaction type rules (single replacement, double replacement, etc.).
If a polyatomic ion appears on both sides unchanged (e.g., SO₄²⁻ in neutralizations), treat it as a single unit rather than balancing S and O separately. For H₂SO₄ + NaOH → Na₂SO₄ + H₂O, balance Na, H, and "SO₄" as a group. This simplifies complex equations significantly. However, if the ion breaks apart (like NH₄⁺ decomposing), you must balance individual atoms.
Learn to recognize reaction types: combustion (fuel + O₂ → CO₂ + H₂O), single replacement (A + BC → AC + B), double replacement (AB + CD → AD + CB), synthesis (A + B → AB), decomposition (AB → A + B). Each type has predictable product patterns. For example, combustion of hydrocarbons ALWAYS gives CO₂ and H₂O. Knowing patterns helps you write correct products before balancing, reducing errors.
Don't become dependent on automated balancing—exams require manual work. Practice balancing equations by inspection (trial and error with atoms) or algebraic method (setting up equations). Use the calculator to check your answer and identify where you went wrong if it doesn't match. Over time, you'll develop intuition for which element to balance first (usually start with the most complex molecule or the element appearing in fewest species).
Visualize the limiting reagent as a "bottleneck" in production. If making sandwiches with 2 slices bread + 1 slice cheese, and you have 10 bread slices and 3 cheese slices, cheese limits you to 3 sandwiches (with 4 bread slices left over). Same principle: mole ratios from coefficients tell you the "recipe"; actual moles you have determine how many "batches" you can make. The ingredient (reactant) that runs out first limits total output.
Set up stoichiometry problems as a chain of conversion factors: grams A → moles A → moles B → grams B. Each arrow is a conversion factor (molar mass or mole ratio). Write units explicitly and cancel them: (g A) × (1 mol A / M_A g) × (coeff B mol B / coeff A mol A) × (M_B g / 1 mol B) = g B. Units guide you—if they don't cancel to your target unit, you made an error.
Stoichiometry gives maximum (thermodynamic limit) product. Equilibrium (K, ΔG) tells you if the reaction actually proceeds far enough to reach that maximum. Kinetics (rate, activation energy) tells you how fast you get there. For reversible reactions, stoichiometry calculates theoretical yield assuming completion, but equilibrium may prevent 100% conversion. Use stoichiometry + Le Châtelier's principle to predict how changing conditions (pressure, temperature) affects yield.
Stoichiometric coefficients (1, 2, 3) are exact numbers (infinite sig figs). Molar masses from periodic table have 4-5 sig figs. Your final answer precision should match your measured data—if you weighed reactants to ±0.01 g (2 decimal places), report yield to 2-3 sig figs. Don't report 18.456732 g when your measurement uncertainty is ±0.1 g. Proper sig figs reflect real measurement limitations.
Complex redox (oxidation-reduction) reactions often can't be balanced by inspection. Use the half-reaction method: separate into oxidation and reduction halves, balance atoms and charges in each half, then combine. For acidic solutions, add H⁺ and H₂O to balance H and O. For basic solutions, add OH⁻ and H₂O. Example: MnO₄⁻ + Fe²⁺ → Mn²⁺ + Fe³⁺ requires balancing O with H₂O and H with H⁺, then electrons, then combining half-reactions. Our calculator can handle many redox equations automatically.
Use stoichiometry to analyze environmental impact: calculate CO₂ emissions from fossil fuel combustion, determine fertilizer requirements for nitrogen fixation (Haber process), or estimate wastewater neutralization needs. For green chemistry, optimize atom economy: (molecular weight of desired product / total molecular weight of all products) × 100%. Reactions with higher atom economy waste less material—a key metric in sustainable chemical manufacturing.
Keep a notebook or digital file of frequently used balanced equations: combustion of alkanes, common acids/bases neutralizations, metal oxide formations, precipitation reactions, redox pairs. Include molar masses of common compounds (H₂O, CO₂, NaCl, H₂SO₄, NaOH). This reference speeds homework and lab calculations. Over time, you'll memorize the most common ones, making you faster and more confident in exams and lab situations.
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Calculate pressure, volume, temperature, and moles using PV = nRT for gas stoichiometry problems.
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Convert between units for mass, moles, volume, pressure, and temperature in stoichiometry calculations.
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