Chemical reactions involve the rearrangement of atoms. The Law of Conservation of Mass dictates that matter cannot be created or destroyed in a chemical reaction. Therefore, the number of atoms of each element must be the same on both the reactant side (the starting materials) and the product side (the substances formed).
Balancing a chemical equation involves adding coefficients (numbers placed in front of chemical formulas) to ensure that the number of atoms of each element is equal on both sides. We never change the subscripts within a chemical formula, as that would change the identity of the substance.
How this Calculator Works:
This calculator uses a systematic approach, often involving matrix algebra or a system of linear equations, to determine the smallest whole-number coefficients that satisfy the conservation of mass for each element present in the reaction. The process generally involves:
Identifying all unique elements in the unbalanced equation.
Assigning a variable coefficient to each chemical species (reactants and products).
For each element, creating an equation representing the total number of atoms of that element on the reactant side must equal the total number on the product side.
Solving the resulting system of linear equations. If the system is underdetermined (which is common for chemical reactions), we typically set one coefficient to 1 and solve for the others, then scale them to the smallest whole numbers.
Example: The Formation of Water
Let's balance the formation of water from hydrogen and oxygen:
Unbalanced equation: H2 + O2 → H2O
Elements involved: Hydrogen (H), Oxygen (O).
Assigning coefficients: a H2 + b O2 → c H2O
Setting up equations:
For Hydrogen (H): 2a = 2c (2 atoms of H on left per 'a' molecules, 2 atoms of H on right per 'c' molecules)
For Oxygen (O): 2b = c (2 atoms of O on left per 'b' molecules, 1 atom of O on right per 'c' molecules)
Solving this system (e.g., setting c = 2):
If c = 2, then 2a = 2(2) => a = 2.
If c = 2, then 2b = 2 => b = 1.
The coefficients are a=2, b=1, c=2.
Balanced equation: 2 H2 + 1 O2 → 2 H2O or commonly written as 2 H2 + O2 → 2 H2O.
Use Cases:
Stoichiometry calculations in chemistry.
Predicting reaction yields.
Understanding reaction mechanisms.
Educational purposes for students learning chemistry.
function balanceReaction() {
var reactantsInput = document.getElementById("reactants").value.trim();
var productsInput = document.getElementById("products").value.trim();
var resultDiv = document.getElementById("result");
if (!reactantsInput || !productsInput) {
resultDiv.textContent = "Please enter both reactants and products.";
return;
}
var unbalancedEquation = reactantsInput + " -> " + productsInput;
var balancedEquation = "";
try {
var result = parseAndBalance(unbalancedEquation);
if (result && result.balancedEquation) {
balancedEquation = result.balancedEquation;
resultDiv.textContent = "Balanced Equation: " + balancedEquation;
} else {
resultDiv.textContent = "Could not balance the equation. Please check the chemical formulas and format.";
}
} catch (e) {
console.error("Error balancing equation:", e);
resultDiv.textContent = "An error occurred. Ensure formulas are correctly written (e.g., H2O, C6H12O6, Fe3O4).";
}
}
// Basic chemical formula parser and element counter
function parseFormula(formula) {
var elements = {};
var regex = /([A-Z][a-z]*)(\d*)/g;
var match;
while ((match = regex.exec(formula)) !== null) {
var element = match[1];
var count = match[2] ? parseInt(match[2]) : 1;
elements[element] = (elements[element] || 0) + count;
}
return elements;
}
// Function to solve system of linear equations using Gaussian elimination (simplified for this context)
// This is a placeholder for a more robust solver. Real-world balancing often requires libraries or more complex algorithms.
// For simplicity and to avoid external libraries, this example will use a simplified approach that works for many common cases.
// A full Gaussian elimination solver would be significantly more complex.
// This simplified approach attempts to find coefficients by iterating or by setting up a system and solving it.
// Due to the complexity of a full matrix solver in pure JS without libraries, this part is a conceptual implementation.
// A common approach involves setting up a matrix where columns represent elements and rows represent compounds,
// and then solving the system Ax = 0. This is non-trivial to implement robustly from scratch.
// For this example, we'll use a common strategy:
// 1. Identify all unique elements.
// 2. Count atoms of each element in each compound.
// 3. Set up a system of linear equations.
// 4. Solve the system.
// THIS IS A HIGHLY SIMPLIFIED SOLVER FOR DEMONSTRATION. A PRODUCTION-READY SOLVER
// WOULD NEED A ROBUST NUMERICAL LIBRARY FOR GAUSSIAN ELIMINATION OR SIMILAR.
function gcd(a, b) {
return b === 0 ? a : gcd(b, a % b);
}
function lcm(a, b) {
return (a * b) / gcd(a, b);
}
function findCoefficients(matrix, numVars) {
// This is where the actual Gaussian elimination or similar algorithm would go.
// For this simplified example, we will attempt a rudimentary approach for common cases.
// This approach is NOT guaranteed to work for all chemical reactions, especially complex ones.
var numEqs = matrix.length;
var numCols = matrix[0].length;
// Try to set the last variable to 1 and solve backwards
// This is a very naive approach and likely to fail for many cases.
// A proper implementation requires a full solver.
// For demonstration, we'll use a pre-calculated common approach for simple reactions,
// or rely on external logic if a true solver isn't feasible here.
// The challenge is implementing a reliable matrix solver in vanilla JS.
// Let's attempt a very basic system solver if it's simple enough.
// For a general solution, external libraries are usually preferred.
// Placeholder for a full Gaussian elimination solver.
// A proper implementation would involve:
// 1. Forward elimination to get Row Echelon Form.
// 2. Back substitution to find the solution.
// This is complex to implement robustly here.
// Trying a common pattern for simple reactions:
// If we have N compounds and M elements, we have N equations and M variables.
// We can often set one variable and solve.
// For this scope, let's assume a simplified scenario or provide a known solution pattern.
// Since a robust matrix solver is outside the scope of a simple inline script without libraries,
// we will simulate a successful balancing for common examples if it can be detected.
// A real-world application would use a dedicated math library.
// Example: H2 + O2 -> H2O
// Elements: H, O
// Compounds: H2, O2, H2O
// Matrix might look like:
// H2 O2 H2O
// H:[2, 0,-2] (2a + 0b – 2c = 0)
// O:[0, 2,-1] (0a + 2b – 1c = 0)
// Solving 2a = 2c and 2b = c. Set c=2, then a=2, b=1. -> 2 H2 + O2 -> 2 H2O
// The logic below is a conceptual attempt and will not solve all cases.
// It's more of a placeholder for the complex numerical algorithm.
// A practical solution often involves using a library like 'numeric.js' or 'math.js'.
// Without them, robust solving is very difficult.
// Fallback to a simpler direct counting approach that might work for some cases:
// This is NOT a general solver.
return null; // Indicate that a full solver is needed.
}
// This parseAndBalance function will try to use a known approach or simulate balancing
// for common cases. It highlights the complexity of implementing a general solver.
function parseAndBalance(equation) {
var parts = equation.split('->');
if (parts.length !== 2) {
throw new Error("Invalid equation format. Use 'reactants -> products'.");
}
var reactantsStr = parts[0].trim();
var productsStr = parts[1].trim();
var reactantFormulas = reactantsStr.split('+').map(f => f.trim()).filter(f => f.length > 0);
var productFormulas = productsStr.split('+').map(f => f.trim()).filter(f => f.length > 0);
var allFormulas = reactantFormulas.concat(productFormulas);
var uniqueElements = new Set();
var formulaData = []; // [{ formula: 'H2', elements: { H: 2 }, isReactant: true }, …]
// Parse reactants
for (var i = 0; i < reactantFormulas.length; i++) {
var formula = reactantFormulas[i];
var elements = parseFormula(formula);
formulaData.push({ formula: formula, elements: elements, isReactant: true, index: formulaData.length });
for (var el in elements) {
uniqueElements.add(el);
}
}
// Parse products
for (var i = 0; i H2O
// Compounds: H2, O2, H2O (indices 0, 1, 2)
// Elements: H, O (indices 0, 1)
// Matrix:
// H2 O2 H2O
// H:[ 2, 0,-2] (2*a + 0*b – 2*c = 0)
// O:[ 0, 2,-1] (0*a + 2*b – 1*c = 0)
var matrix = [];
for (var j = 0; j < numElements; j++) {
var row = [];
var element = elementList[j];
for (var k = 0; k […row]); // Copy matrix
var pivotRow = 0;
var pivotCol = 0;
while (pivotRow < numElements && pivotCol < numCompounds) {
// Find pivot: Find row with largest absolute value in current column below or at pivotRow
var maxRow = pivotRow;
for (var i = pivotRow + 1; i Math.abs(augmentedMatrix[maxRow][pivotCol])) {
maxRow = i;
}
}
// Swap rows if necessary
if (maxRow !== pivotRow) {
var temp = augmentedMatrix[pivotRow];
augmentedMatrix[pivotRow] = augmentedMatrix[maxRow];
augmentedMatrix[maxRow] = temp;
}
var pivotValue = augmentedMatrix[pivotRow][pivotCol];
// If pivot is zero, move to next column
if (Math.abs(pivotValue) < 1e-9) { // Use tolerance for floating point comparison
pivotCol++;
continue;
}
// Normalize pivot row (optional but good practice)
// for (var j = pivotCol; j < numCompounds; j++) {
// augmentedMatrix[pivotRow][j] /= pivotValue;
// }
// Eliminate other rows
for (var i = 0; i < numElements; i++) {
if (i !== pivotRow) {
var factor = augmentedMatrix[i][pivotCol] / pivotValue;
for (var j = pivotCol; j < numCompounds; j++) {
augmentedMatrix[i][j] -= factor * augmentedMatrix[pivotRow][j];
}
}
}
pivotRow++;
pivotCol++;
}
// Now `augmentedMatrix` is roughly in Reduced Row Echelon Form (or close enough for underdetermined system)
// We need to extract coefficients. The last column that is not a zero vector will be our free variable.
// This part is tricky: We need to identify dependent and independent variables.
// A common approach is to set the last variable as a parameter (e.g., k) and solve.
var coefficients = new Array(numCompounds).fill(0);
// Find a non-zero row to start back-substitution
var freeVarCol = -1;
for(var c = 0; c < numCompounds; c++) {
var isZeroCol = true;
for(var r = 0; r 1e-9) {
isZeroCol = false;
break;
}
}
if (!isZeroCol) {
freeVarCol = c; // Potential free variable column
}
}
if (freeVarCol === -1) { // Should not happen for valid chemical equations
// If all columns are zero, it implies redundancy or error.
// Try a default common multiplier if no clear free variable.
// Fallback: Try setting last coefficient to 1.
coefficients[numCompounds – 1] = 1;
} else {
// Set the free variable (last dependent one found) to a placeholder value, e.g., 1
coefficients[freeVarCol] = 1;
}
// Back-substitution to find other coefficients
for (var i = numElements – 1; i >= 0; i–) {
var pivotFound = false;
for (var j = 0; j 1e-9) { // Found pivot for this row
var pivotValue = augmentedMatrix[i][j];
var rhs = 0; // Right hand side is 0 for Ax=0
// Subtract contributions from already determined variables
for (var k = j + 1; k < numCompounds; k++) {
rhs -= augmentedMatrix[i][k] * coefficients[k];
}
// Calculate the current variable's coefficient
// If this column was the free variable, it's already set.
if (j === freeVarCol) {
// coefficients[j] = coefficients[j]; // already set
} else {
coefficients[j] = rhs / pivotValue;
}
pivotFound = true;
break; // Move to the next row (element)
}
}
}
// — Scaling to Smallest Whole Numbers —
// Find the least common multiple of denominators, or scale based on smallest fraction.
// This part requires careful handling of floating point numbers.
var commonMultiplier = 1;
var denominatorScale = 1;
// Find the smallest fractional part or a scaling factor
var scalingFactors = [];
for (var i = 0; i 0) {
denominatorScale = scalingFactors.reduce((a, b) => lcm(a, b));
}
// Apply denominator scale and then find GCD of all coefficients to simplify
var scaledCoeffs = coefficients.map(c => c * denominatorScale);
var finalGcd = 0;
for (var i = 0; i 0).
// Try setting a default coefficient if possible.
// If scaling resulted in all zeros, it's an issue with the solver or input.
return { balancedEquation: "Error: Could not determine coefficients." };
}
var finalCoefficients = scaledCoeffs.map(c => c / finalGcd);
// Format the balanced equation
var balancedReactants = [];
for (var i = 0; i < reactantFormulas.length; i++) {
var coeff = finalCoefficients[i];
balancedReactants.push((coeff === 1 ? "" : coeff) + reactantFormulas[i]);
}
var balancedProducts = [];
for (var i = 0; i " + balancedProducts.join(" + ")
};
}
// Example Usage (for testing during development)
// console.log(parseAndBalance("H2 + O2 -> H2O")); // Expected: 2 H2 + O2 -> 2 H2O
// console.log(parseAndBalance("Fe + Cl2 -> FeCl3")); // Expected: 2 Fe + 3 Cl2 -> 2 FeCl3
// console.log(parseAndBalance("C2H6 + O2 -> CO2 + H2O")); // Expected: 2 C2H6 + 7 O2 -> 4 CO2 + 6 H2O
// console.log(parseAndBalance("Al + H2SO4 -> Al2(SO4)3 + H2")); // Expected: 2 Al + 3 H2SO4 -> Al2(SO4)3 + 3 H2
// console.log(parseAndBalance("P4 + O2 -> P2O5")); // Expected: P4 + 5 O2 -> 2 P2O5