Balancing Chemical Equations Calculator with Steps

:root {
–primary-color: #004a99;
–success-color: #28a745;
–background-color: #f8f9fa;
–text-color: #333;
–border-color: #ddd;
–shadow-color: rgba(0, 0, 0, 0.1);
}

body {
font-family: ‘Segoe UI’, Tahoma, Geneva, Verdana, sans-serif;
background-color: var(–background-color);
color: var(–text-color);
line-height: 1.6;
margin: 0;
padding: 0;
display: flex;
flex-direction: column;
align-items: center;
}

.container {
width: 95%;
max-width: 960px;
margin: 20px auto;
padding: 20px;
background-color: #fff;
border-radius: 8px;
box-shadow: 0 4px 15px var(–shadow-color);
display: flex;
flex-direction: column;
align-items: center;
}

header {
width: 100%;
text-align: center;
margin-bottom: 30px;
padding-bottom: 20px;
border-bottom: 1px solid var(–border-color);
}

h1 {
color: var(–primary-color);
margin-bottom: 10px;
}

h2, h3 {
color: var(–primary-color);
margin-top: 25px;
margin-bottom: 15px;
}

.calculator-section {
width: 100%;
margin-bottom: 40px;
padding: 30px;
border: 1px solid var(–border-color);
border-radius: 8px;
background-color: #fdfdfd;
}

.calculator-section h2 {
text-align: center;
margin-top: 0;
}

.input-group {
margin-bottom: 20px;
width: 100%;
}

.input-group label {
display: block;
margin-bottom: 8px;
font-weight: bold;
color: var(–primary-color);
}

.input-group input[type=”text”],
.input-group input[type=”number”],
.input-group select {
width: calc(100% – 20px);
padding: 12px;
border: 1px solid var(–border-color);
border-radius: 4px;
font-size: 1rem;
box-sizing: border-box;
}

.input-group input[type=”text”]:focus,
.input-group input[type=”number”]:focus,
.input-group select:focus {
outline: none;
border-color: var(–primary-color);
box-shadow: 0 0 0 2px rgba(0, 74, 153, 0.2);
}

.input-group .helper-text {
font-size: 0.85rem;
color: #666;
margin-top: 5px;
display: block;
}

.error-message {
color: #dc3545;
font-size: 0.85rem;
margin-top: 5px;
min-height: 1.2em; /* Prevent layout shift */
}

.button-group {
display: flex;
justify-content: center;
gap: 15px;
margin-top: 30px;
flex-wrap: wrap;
}

button {
padding: 12px 25px;
border: none;
border-radius: 5px;
cursor: pointer;
font-size: 1rem;
font-weight: bold;
transition: background-color 0.3s ease, transform 0.2s ease;
color: white;
}

button.primary {
background-color: var(–primary-color);
}

button.primary:hover {
background-color: #003366;
transform: translateY(-2px);
}

button.success {
background-color: var(–success-color);
}

button.success:hover {
background-color: #218838;
transform: translateY(-2px);
}

button.secondary {
background-color: #6c757d;
}

button.secondary:hover {
background-color: #5a6268;
transform: translateY(-2px);
}

.results-container {
width: 100%;
margin-top: 30px;
padding: 25px;
border: 1px solid var(–border-color);
border-radius: 8px;
background-color: #fefefe;
text-align: center;
}

.results-container h3 {
margin-top: 0;
color: var(–text-color);
}

#main-result {
font-size: 2.5rem;
font-weight: bold;
color: var(–success-color);
background-color: #e6f7ff;
padding: 15px 20px;
border-radius: 6px;
margin-bottom: 20px;
display: inline-block;
min-width: 200px;
}

.intermediate-results {
display: flex;
justify-content: space-around;
flex-wrap: wrap;
gap: 20px;
margin-bottom: 25px;
text-align: left;
}

.intermediate-results div {
flex: 1;
min-width: 150px;
padding: 15px;
border: 1px dashed var(–border-color);
border-radius: 5px;
background-color: #f9f9f9;
}

.intermediate-results span {
font-weight: bold;
color: var(–primary-color);
display: block;
font-size: 1.2rem;
}

.formula-explanation {
font-size: 0.9rem;
color: #555;
margin-top: 15px;
padding-top: 15px;
border-top: 1px solid var(–border-color);
}

table {
width: 100%;
border-collapse: collapse;
margin-top: 20px;
margin-bottom: 30px;
}

th, td {
padding: 12px 15px;
text-align: left;
border: 1px solid var(–border-color);
}

thead {
background-color: var(–primary-color);
color: white;
}

tbody tr:nth-child(even) {
background-color: #f2f2f2;
}

caption {
font-size: 1.1rem;
font-weight: bold;
color: var(–primary-color);
margin-bottom: 10px;
caption-side: top;
text-align: left;
}

canvas {
display: block;
margin: 20px auto;
border: 1px solid var(–border-color);
border-radius: 4px;
background-color: #fff;
}

.chart-legend {
text-align: center;
margin-top: 10px;
font-size: 0.9rem;
color: #555;
}

.chart-legend span {
display: inline-block;
margin: 0 10px;
}

.chart-legend .color-box {
display: inline-block;
width: 12px;
height: 12px;
margin-right: 5px;
vertical-align: middle;
border-radius: 3px;
}

.article-section {
width: 100%;
margin-top: 40px;
padding: 30px;
border: 1px solid var(–border-color);
border-radius: 8px;
background-color: #fefefe;
}

.article-section h2 {
text-align: left;
margin-top: 0;
}

.article-section p {
margin-bottom: 15px;
}

.article-section ul, .article-section ol {
margin-left: 20px;
margin-bottom: 15px;
}

.article-section li {
margin-bottom: 8px;
}

.faq-item {
margin-bottom: 20px;
padding: 15px;
border: 1px solid #eee;
border-radius: 5px;
background-color: #f9f9f9;
}

.faq-item h3 {
margin-top: 0;
margin-bottom: 10px;
color: var(–primary-color);
font-size: 1.1rem;
cursor: pointer;
}

.faq-item p {
margin-bottom: 0;
display: none; /* Hidden by default */
}

.faq-item.open p {
display: block;
}

.internal-links {
margin-top: 30px;
padding-top: 20px;
border-top: 1px solid var(–border-color);
}

.internal-links h3 {
text-align: left;
margin-top: 0;
}

.internal-links ul {
list-style: none;
padding: 0;
}

.internal-links li {
margin-bottom: 15px;
}

.internal-links a {
color: var(–primary-color);
text-decoration: none;
font-weight: bold;
}

.internal-links a:hover {
text-decoration: underline;
}

.internal-links p {
font-size: 0.9rem;
color: #555;
margin-top: 5px;
}

footer {
width: 100%;
text-align: center;
margin-top: 40px;
padding: 20px;
font-size: 0.9rem;
color: #777;
border-top: 1px solid var(–border-color);
}

/* Responsive adjustments */
@media (max-width: 768px) {
.container {
padding: 15px;
}
.button-group {
flex-direction: column;
align-items: center;
}
.intermediate-results {
flex-direction: column;
align-items: center;
}
.intermediate-results div {
width: 90%;
text-align: center;
}
.results-container {
padding: 15px;
}
#main-result {
font-size: 2rem;
}
}

Accurately balance chemical equations and understand the process with our comprehensive tool.

Chemical Equation Balancer

What is Balancing Chemical Equations?

Balancing chemical equations is a fundamental process in chemistry that ensures the law of conservation of mass is upheld. This law states 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) of a chemical equation. The process involves adding stoichiometric coefficients (numbers placed in front of chemical formulas) to balance the atoms without altering the chemical formulas themselves.

Who should use it? This tool is invaluable for high school students learning chemistry, university students in introductory chemistry courses, researchers, laboratory technicians, and anyone needing to accurately represent chemical reactions. It’s particularly useful for complex equations that are difficult to balance by inspection.

Common Misconceptions: A frequent misunderstanding is that balancing an equation changes the chemical identity of the substances involved. This is incorrect; balancing only adjusts the *quantity* of each substance participating in the reaction. Another misconception is that the coefficients represent mass ratios directly; they represent mole ratios, which can then be converted to mass ratios using molar masses.

Balancing Chemical Equations Formula and Mathematical Explanation

The core principle behind balancing chemical equations mathematically is to ensure that for each element, the total number of atoms on the reactant side equals the total number of atoms on the product side. We achieve this by assigning variables (coefficients) to each chemical species and setting up a system of linear equations.

Step-by-Step Derivation (Algebraic Method):

1. Write the Unbalanced Equation: Start with the correct chemical formulas for all reactants and products.
2. Assign Coefficients: Place variables (e.g., a, b, c, d) in front of each chemical formula. For example: a H₂ + b O₂ = c H₂O
3. Count Atoms of Each Element: For each element present, create an equation based on the conservation of atoms.
• For Hydrogen (H): In a H₂, there are 2a atoms. In c H₂O, there are 2c atoms. So, 2a = 2c.
• For Oxygen (O): In b O₂, there are 2b atoms. In c H₂O, there is 1c atom. So, 2b = c.
4. Solve the System of Equations: Set one coefficient to a simple integer (usually 1) and solve for the others. If fractions result, multiply all coefficients by the smallest integer that clears the fractions.
• Let c = 1.
• From 2a = 2c, we get 2a = 2(1), so a = 1.
• From 2b = c, we get 2b = 1, so b = 1/2.
5. Convert to Smallest Whole Numbers: Since we have a fraction (1/2), multiply all coefficients by 2.
• a = 1 * 2 = 2
• b = (1/2) * 2 = 1
• c = 1 * 2 = 2
6. Write the Balanced Equation: Substitute the whole number coefficients back into the equation: 2 H₂ + 1 O₂ = 2 H₂O (or simply 2 H₂ + O₂ = 2 H₂O).

Variable Explanations:

In the context of balancing chemical equations:

• Chemical Formula: Represents the types and number of atoms in a molecule (e.g., H₂O).
• Reactants: The substances that react together (left side of the equation).
• Products: The substances formed as a result of the reaction (right side of the equation).
• Stoichiometric Coefficient: The number placed in front of a chemical formula to balance the equation. It represents the relative number of moles (or molecules) of that substance involved in the reaction.

Variables Table:

Variable	Meaning	Unit	Typical Range
Chemical Equation String	Input string representing the unbalanced reaction.	String	N/A
Element Count (Reactants)	Number of atoms for each element on the reactant side.	Integer	≥ 0
Element Count (Products)	Number of atoms for each element on the product side.	Integer	≥ 0
Stoichiometric Coefficient	The multiplier for each chemical species to balance the equation.	Integer (or fraction during calculation)	≥ 1 (for balanced equation)
Mole Ratio	The relative number of moles of reactants and products.	Ratio	Positive Integers

Practical Examples (Real-World Use Cases)

Example 1: Combustion of Methane

Unbalanced Equation: CH₄ + O₂ = CO₂ + H₂O

Inputs:

• Chemical Equation: CH₄ + O₂ = CO₂ + H₂O

Calculation Steps:

1. Assign coefficients: a CH₄ + b O₂ = c CO₂ + d H₂O
2. Element counts:
   • C: a = c
   • H: 4a = 2d
   • O: 2b = 2c + d
3. Solve: Let a = 1. Then c = 1. From 4a = 2d, 4(1) = 2d, so d = 2. From 2b = 2c + d, 2b = 2(1) + 2, so 2b = 4, meaning b = 2.
4. Coefficients are all integers.

Outputs:

• Balanced Equation: CH₄ + 2 O₂ = CO₂ + 2 H₂O
• Reactants: CH₄, O₂
• Products: CO₂, H₂O
• Coefficients: 1, 2, 1, 2

Interpretation: This balanced equation tells us that one molecule (or mole) of methane reacts with two molecules (or moles) of oxygen to produce one molecule (or mole) of carbon dioxide and two molecules (or moles) of water. This is crucial for calculating the amount of oxygen needed for complete combustion or the amount of products formed.

Example 2: Synthesis of Ammonia (Haber Process)

Unbalanced Equation: N₂ + H₂ = NH₃

Inputs:

• Chemical Equation: N₂ + H₂ = NH₃

Calculation Steps:

1. Assign coefficients: a N₂ + b H₂ = c NH₃
2. Element counts:
   • N: 2a = c
   • H: 2b = 3c
3. Solve: Let c = 1. Then 2a = 1, so a = 1/2. From 2b = 3c, 2b = 3(1), so b = 3/2.
4. Clear fractions: Multiply by 2. a = 1, b = 3, c = 2.

Outputs:

• Balanced Equation: N₂ + 3 H₂ = 2 NH₃
• Reactants: N₂, H₂
• Products: NH₃
• Coefficients: 1, 3, 2

Interpretation: One mole of nitrogen gas reacts with three moles of hydrogen gas to produce two moles of ammonia. This stoichiometry is fundamental to the industrial production of ammonia, impacting yield calculations and resource management.

How to Use This Balancing Chemical Equations Calculator

Our calculator simplifies the process of balancing chemical equations. Follow these steps for accurate results:

1. Enter the Unbalanced Equation: In the “Enter Chemical Equation” field, type your chemical equation. Use standard chemical formulas (e.g., H2O, CO2, CH4). Use the ‘+’ symbol to separate multiple reactants or products, and use ‘=’ to represent the reaction arrow. For example: Fe + Cl2 = FeCl3 or C2H6 + O2 = CO2 + H2O.
2. Click “Balance Equation”: Once you have entered the equation, click the “Balance Equation” button.
3. Review the Results: The calculator will display:
   • Balanced Equation: The equation with the correct stoichiometric coefficients.
   • Reactants: A list of the chemical formulas on the left side.
   • Products: A list of the chemical formulas on the right side.
   • Coefficients: The numerical coefficients for each species in the balanced equation.
4. Understand the Steps: The “Explanation” section provides a brief overview of the algebraic method used.
5. Reset or Copy: Use the “Reset” button to clear the fields and start over. Use the “Copy Results” button to copy the balanced equation and coefficients for use elsewhere.

How to Read Results: The coefficients represent the mole ratios. For example, in 2 H₂ + O₂ = 2 H₂O, the coefficients 2, 1, and 2 indicate that 2 moles of hydrogen react with 1 mole of oxygen to form 2 moles of water.

Decision-Making Guidance: A correctly balanced equation is essential for stoichiometric calculations, such as determining theoretical yield, limiting reactants, and reaction efficiency. It ensures your chemical calculations are based on accurate molecular relationships.

Key Factors That Affect Balancing Chemical Equations

While the process of balancing itself is a mathematical procedure, several chemical and practical factors influence the *context* and *interpretation* of a balanced equation:

1. Correct Chemical Formulas: The most critical factor. If the formulas for reactants or products are incorrect (e.g., writing H₂O₂ instead of H₂O), the balancing process will yield an incorrect result, even if mathematically sound. This requires knowledge of chemical nomenclature and common compounds.
2. Physical States: While not directly affecting coefficients, the physical states (solid (s), liquid (l), gas (g), aqueous (aq)) are crucial for understanding reaction conditions and energy changes (e.g., in thermochemistry). They are often included alongside the balanced equation.
3. Reaction Conditions: Factors like temperature, pressure, and catalysts can influence whether a reaction proceeds and at what rate, but they don’t change the fundamental stoichiometry (the balanced coefficients). However, they are vital for practical implementation.
4. Complexity of the Equation: Simple reactions (like acid-base neutralization) are often easy to balance by inspection. Complex redox reactions or reactions involving many species may require more systematic methods like the algebraic approach or the ion-electron method, making calculators particularly useful.
5. Conservation Laws: The entire process hinges on the Law of Conservation of Mass. Understanding this fundamental principle is key to grasping why balancing is necessary.
6. Mole Ratios vs. Mass Ratios: Balanced coefficients represent mole ratios. To convert these to mass ratios, you must use the molar masses of each substance. This is a common point of confusion; balancing gives moles, not grams directly.
7. Polyatomic Ions: In some cases, polyatomic ions (like SO₄²⁻, NO₃⁻) can be treated as single units if they remain unchanged throughout the reaction, simplifying the balancing process. However, if they break apart, individual atoms must be balanced.
8. Redox Reactions: Balancing oxidation-reduction (redox) reactions often requires specialized methods (like the half-reaction method) in addition to or instead of the simple algebraic approach, as electron transfer is involved.

Frequently Asked Questions (FAQ)

What is the difference between balancing by inspection and using an algebraic method?

Balancing by inspection is a trial-and-error method, suitable for simpler equations. The algebraic method (used by this calculator) assigns variables and solves a system of equations, providing a systematic approach that works for all equations, especially complex ones.

Can a chemical equation have multiple balanced forms?

Technically, yes, if you multiply all coefficients by the same number. However, the “balanced” form typically refers to the one using the smallest possible whole number integers for the coefficients.

What if the calculator gives fractional coefficients?

Fractional coefficients often appear during the algebraic solving process. The final step is always to multiply all coefficients by the smallest integer that converts all fractions into whole numbers.

Does balancing an equation change the reaction?

No, balancing an equation does not change the identity of the reactants or products or the nature of the chemical reaction itself. It only adjusts the relative amounts (moles) of substances involved to satisfy the conservation of mass.

How do I handle polyatomic ions when balancing?

If a polyatomic ion (like SO₄²⁻ or PO₄³⁻) appears unchanged on both sides of the equation, you can often treat it as a single unit during balancing. However, if it dissociates or rearranges, you must balance the individual atoms within it.

What are stoichiometric coefficients used for?

Stoichiometric coefficients are used to calculate the quantitative relationships between reactants and products in a chemical reaction. They allow us to predict yields, determine limiting reactants, and understand reaction efficiency based on mole ratios.

Can this calculator balance redox reactions?

This calculator primarily uses the algebraic method, which works for most common reactions. For complex redox reactions, specialized methods like the half-reaction method might be necessary, which this specific tool may not fully implement beyond basic algebraic balancing.

What if I enter an invalid chemical formula?

The calculator relies on correct chemical formulas. If an invalid formula is entered (e.g., “H2O22”), it might not parse correctly or lead to an incorrect balancing result. Always ensure your formulas are chemically accurate.

Related Tools and Internal Resources

• Balancing Chemical Equations Calculator

  Our primary tool for balancing chemical equations with step-by-step guidance.

• Understanding Chemical Reactions

  Learn the fundamentals of chemical reactions, including types, energy changes, and reaction rates.

• Stoichiometry Explained

  Dive deeper into calculations involving quantitative relationships in chemical reactions.

• Molar Mass Calculator

  Calculate the molar mass of chemical compounds, essential for converting between moles and mass.

• Limiting Reactant Calculator

  Determine the limiting reactant in a chemical reaction based on initial amounts.

• Percent Yield Calculator

  Calculate the percent yield of a reaction by comparing theoretical and actual yields.

// Helper function to parse chemical formulas and count atoms
function parseFormula(formula) {
var atoms = {};
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], 10) : 1;
atoms[element] = (atoms[element] || 0) + count;
}
return atoms;
}

// Function to get unique elements from reactants and products
function getUniqueElements(reactants, products) {
var allElements = new Set();
reactants.forEach(function(formula) {
var parsed = parseFormula(formula);
for (var element in parsed) {
allElements.add(element);
}
});
products.forEach(function(formula) {
var parsed = parseFormula(formula);
for (var element in parsed) {
allElements.add(element);
}
});
return Array.from(allElements);
}

// Function to validate chemical formula syntax (basic check)
function isValidChemicalFormula(formula) {
if (!formula || formula.trim() === “”) return false;
// Basic check: starts with a capital letter, followed by optional lowercase, optional digits
var formulaRegex = /^([A-Z][a-z]*)(\d*)+$/;
var parts = formula.match(/([A-Z][a-z]*)(\d*)/g);
if (!parts) return false;
for (var i = 0; i 0;
}

// Function to validate the entire equation string
function validateEquationString(equationString) {
var parts = equationString.split(‘=’);
if (parts.length !== 2) return { valid: false, error: “Equation must contain exactly one ‘=’ sign.” };

var reactantStr = parts[0].trim();
var productStr = parts[1].trim();

if (reactantStr === “” || productStr === “”) return { valid: false, error: “Reactant and product sides cannot be empty.” };

var reactants = reactantStr.split(‘+’).map(function(s) { return s.trim(); });
var products = productStr.split(‘+’).map(function(s) { return s.trim(); });

if (reactants.some(function(r) { return r === “”; }) || products.some(function(p) { return p === “”; })) {
return { valid: false, error: “Empty chemical formulas found between ‘+’ signs.” };
}

for (var i = 0; i < reactants.length; i++) {
if (!isValidChemicalFormula(reactants[i])) {
return { valid: false, error: "Invalid chemical formula found on reactant side: " + reactants[i] };
}
}
for (var i = 0; i numEqs) {
// Try setting one variable to 1 and solving
// This is a heuristic and might fail for complex cases
var tempMatrix = matrix.map(function(row) { return row.slice(); });
// Try setting the last variable to 1
for(var i = 0; i < numVars; i++) {
tempMatrix[i][numVars – 1] = 1; // Set last coefficient to 1
}
// Adjust the constant terms based on this assumption
for(var r = 0; r < numEqs; r++) {
var sumOfKnowns = 0;
for(var c = 0; c < numVars; c++) {
if (c !== numVars – 1) { // Only sum known coefficients
sumOfKnowns += tempMatrix[c][r] * tempMatrix[c][numVars]; // coefficient * value
}
}
// This part is tricky without a full solver.
// A proper solver would handle free variables.
// For now, we'll rely on a simpler direct solving approach if possible.
}
// Fallback or simplified approach:
// Try to find a simple integer solution by setting one coefficient to 1.
// This is highly simplified. A real solver is needed for robustness.
}

// Simplified approach: Try to solve by setting one coefficient to 1 and back-substituting
// This is NOT a robust Gaussian elimination but a heuristic for common cases.
var coefficients = new Array(numVars).fill(0);
var assigned = new Array(numVars).fill(false);

// Try setting the first coefficient to 1
coefficients[0] = 1;
assigned[0] = true;

var solvedCount = 1;
var iterations = 0;
var maxIterations = numVars * 5; // Prevent infinite loops

while(solvedCount < numVars && iterations < maxIterations) {
iterations++;
var changed = false;
for(var i = 0; i < numVars; i++) {
if (assigned[i]) continue;

var currentEqSum = 0;
var unknownCount = 0;
var unknownIndex = -1;
var rhs = matrix[i][numVars]; // Right hand side

for(var j = 0; j < numVars; j++) {
var coeff = matrix[i][j];
if (coeff === 0) continue;

if (assigned[j]) {
currentEqSum += coeff * coefficients[j];
} else {
unknownCount++;
unknownIndex = j;
}
}

if (unknownCount === 1 && rhs !== null) { // Check if rhs is defined
var numerator = rhs – currentEqSum;
var denominator = matrix[unknownIndex][unknownIndex]; // Diagonal element

if (denominator !== 0) {
coefficients[unknownIndex] = numerator / denominator;
assigned[unknownIndex] = true;
solvedCount++;
changed = true;
}
}
}
// If no progress, try setting another variable or break
if (!changed && solvedCount < numVars) {
// Try setting the next unassigned variable to 1
for(var k=0; k < numVars; k++) {
if (!assigned[k]) {
coefficients[k] = 1;
assigned[k] = true;
solvedCount++;
changed = true;
break;
}
}
if (!changed) break; // Cannot solve further with this simple method
}
}

// Check if all variables were assigned
if (solvedCount < numVars) {
console.warn("Could not fully solve the system. Result might be incomplete or incorrect.");
// Attempt to return partial results or indicate failure
return null; // Indicate failure
}

// Convert to smallest whole numbers
var gcdVal = coefficients[0];
for (var i = 1; i < coefficients.length; i++) {
gcdVal = gcd(gcdVal, coefficients[i]);
}

// Find the smallest denominator if fractions exist
var minDenominator = 1;
for (var i = 0; i 1e-9) { // Check if it’s not an integer
var denominator = getDenominator(frac);
if (denominator > minDenominator) {
minDenominator = denominator;
}
}
}

// Multiply by minDenominator and then find GCD for final integers
var finalCoeffs = coefficients.map(function(c) { return c * minDenominator; });

var finalGcd = finalCoeffs[0];
for (var i = 1; i < finalCoeffs.length; i++) {
finalGcd = gcd(finalGcd, finalCoeffs[i]);
}

// Ensure final coefficients are positive integers
finalCoeffs = finalCoeffs.map(function(c) {
var val = Math.round(c / finalGcd);
// Ensure positivity, handle potential negative results from solver heuristic
return Math.abs(val);
});

return finalCoeffs;
}

// Helper GCD function
function gcd(a, b) {
a = Math.abs(a);
b = Math.abs(b);
while (b) {
var t = b;
b = a % b;
a = t;
}
return a;
}

// Helper to find the denominator of a fraction
function getDenominator(num) {
if (Math.abs(num – Math.round(num)) < 1e-9) return 1; // It's an integer
var tolerance = 1e-9;
var maxDenominator = 1000; // Limit search depth
for (var d = 2; d <= maxDenominator; d++) {
if (Math.abs(num * d – Math.round(num * d)) < tolerance) {
return d;
}
}
return maxDenominator; // Fallback
}

function balanceEquation() {
var equationInput = document.getElementById('chemicalEquation');
var equationString = equationInput.value;
var errorDiv = document.getElementById('chemicalEquationError');

var validationResult = validateEquationString(equationString);

if (!validationResult.valid) {
errorDiv.textContent = validationResult.error;
document.getElementById('main-result').textContent = "–";
document.getElementById('intermediate1').innerHTML = "Reactants–“;
document.getElementById(‘intermediate2’).innerHTML = “Products–“;
document.getElementById(‘intermediate3’).innerHTML = “Coefficients–“;
return;
}

errorDiv.textContent = “”; // Clear previous error

var reactants = validationResult.reactants;
var products = validationResult.products;
var uniqueElements = getUniqueElements(reactants, products);

var numVars = reactants.length + products.length; // Number of coefficients to find
var numEqs = uniqueElements.length; // Number of independent equations (one per element)

// Create the matrix for the system of linear equations
// Rows = elements, Columns = coefficients + 1 (for RHS)
// Initialize matrix with zeros
var matrix = [];
for (var i = 0; i < numEqs; i++) {
matrix.push(new Array(numVars + 1).fill(0));
}

// Populate the matrix
var elementIndexMap = {};
uniqueElements.forEach(function(el, index) {
elementIndexMap[el] = index;
});

var allFormulas = reactants.concat(products);
for (var i = 0; i = reactants.length;

for (var element in parsed) {
var elementIndex = elementIndexMap[element];
var count = parsed[element];
var sign = isProduct ? -1 : 1; // Reactants have positive contribution, products negative

// Place the count in the matrix, adjusted for product side
matrix[elementIndex][i] = sign * count;
}
}

// Set the right-hand side (RHS) of the equations.
// For a homogeneous system Ax=0, the RHS is typically all zeros.
// However, to solve it, we usually set one variable and solve.
// A common approach is to set the last variable’s coefficient to 1 and solve.
// Let’s adapt the matrix to solve for x_n = 1 (or similar)
// This requires modifying the matrix or using a solver that handles this.

// Simplified approach: Assume a solvable system and try to find coefficients.
// We need to transform the matrix or use a solver that handles Ax = 0 by setting one variable.
// Let’s try setting the last coefficient to 1 and adjusting the matrix.
// This is a heuristic. A proper solver is complex.

// A more direct approach for balancing:
// Set up equations: Sum(coeff_i * atoms_i_element_k) = 0 for each element k
// Example: a H2 + b O2 = c H2O
// H: 2a + 0b – 2c = 0 => 2a – 2c = 0
// O: 0a + 2b – 1c = 0 => 2b – c = 0
// Matrix:
// a b c
// H[ 2 0 -2 | 0 ]
// O[ 0 2 -1 | 0 ]
// We need to solve this homogeneous system. Set one variable (e.g., c=1) and solve.

// Let’s adjust the matrix setup for this:
// We have N coefficients (variables) and E elements (equations).
// We need N-1 independent equations to solve for N variables if we set one.
// Let’s set the last coefficient (index numVars-1) to 1.
// Then, for each element equation, move the term involving the last coefficient to the RHS.
var adjustedMatrix = [];
for (var r = 0; r < numEqs; r++) {
adjustedMatrix.push(new Array(numVars).fill(0)); // Now numVars columns (coefficients)
var rhs = 0;
for (var c = 0; c = reactants.length) ? -1 : 1; // Product side is negative

if (c === numVars – 1) { // Last coefficient
rhs = -sign * atomCount; // Move to RHS
} else {
adjustedMatrix[r][c] = sign * atomCount;
}
}
adjustedMatrix[r][numVars – 1] = rhs; // Place RHS in the last column for this row
}

// Now, adjustedMatrix[r][numVars-1] holds the RHS value for element r.
// The system is now: A’x’ = b, where x’ includes coefficients except the last one.
// This is still tricky. A robust solver is needed.

// Let’s try a simpler direct solving approach for common cases.
// Find the coefficient matrix A where Ax = 0.
var coefficientMatrix = [];
for (var elIndex = 0; elIndex < numEqs; elIndex++) {
var row = [];
for (var coeffIndex = 0; coeffIndex = reactants.length) ? -1 : 1; // Product side is negative
row.push(sign * count);
}
coefficientMatrix.push(row);
}

// Attempt to solve using a simplified solver function
var solvedCoefficients = solveSystem(coefficientMatrix);

if (!solvedCoefficients) {
errorDiv.textContent = “Could not automatically balance this equation. It might be too complex or require manual balancing.”;
document.getElementById(‘main-result’).textContent = “–“;
document.getElementById(‘intermediate1’).innerHTML = “Reactants–“;
document.getElementById(‘intermediate2’).innerHTML = “Products–“;
document.getElementById(‘intermediate3’).innerHTML = “Coefficients–“;
return;
}

// Format the balanced equation string
var balancedEquationString = “”;
for (var i = 0; i < reactants.length; i++) {
balancedEquationString += (solvedCoefficients[i] === 1 ? "" : solvedCoefficients[i]) + reactants[i] + (i < reactants.length – 1 ? " + " : " = ");
}
for (var i = 0; i < products.length; i++) {
balancedEquationString += (solvedCoefficients[reactants.length + i] === 1 ? "" : solvedCoefficients[reactants.length + i]) + products[i] + (i < products.length – 1 ? " + " : "");
}

// Display results
document.getElementById('main-result').textContent = balancedEquationString;
document.getElementById('intermediate1').innerHTML = "Reactants” + reactants.join(‘, ‘);
document.getElementById(‘intermediate2’).innerHTML = “Products” + products.join(‘, ‘);
document.getElementById(‘intermediate3’).innerHTML = “Coefficients” + solvedCoefficients.join(‘, ‘);

// Update chart data
updateChart(reactants, products, solvedCoefficients);
}

function resetCalculator() {
document.getElementById(‘chemicalEquation’).value = “H2 + O2 = H2O”; // Sensible default
document.getElementById(‘chemicalEquationError’).textContent = “”;
document.getElementById(‘main-result’).textContent = “–“;
document.getElementById(‘intermediate1’).innerHTML = “Reactants–“;
document.getElementById(‘intermediate2’).innerHTML = “Products–“;
document.getElementById(‘intermediate3’).innerHTML = “Coefficients–“;
// Clear canvas
var ctx = document.getElementById(‘reactionChart’).getContext(‘2d’);
ctx.clearRect(0, 0, ctx.canvas.width, ctx.canvas.height);
document.querySelector(‘.chart-legend’).innerHTML = ”; // Clear legend
}

function copyResults() {
var mainResult = document.getElementById(‘main-result’).textContent;
var reactants = document.getElementById(‘intermediate1’).textContent.replace(‘Reactants’, ”).trim();
var products = document.getElementById(‘intermediate2’).textContent.replace(‘Products’, ”).trim();
var coefficients = document.getElementById(‘intermediate3’).textContent.replace(‘Coefficients’, ”).trim();

if (mainResult === “–“) {
alert(“No results to copy yet.”);
return;
}

var textToCopy = “Balanced Equation: ” + mainResult + “\n\n” +
“Reactants: ” + reactants + “\n” +
“Products: ” + products + “\n” +
“Coefficients: ” + coefficients + “\n\n” +
“Method: Algebraic balancing ensuring conservation of mass.”;

navigator.clipboard.writeText(textToCopy).then(function() {
// Optional: Show a confirmation message
var copyButton = event.target;
var originalText = copyButton.textContent;
copyButton.textContent = “Copied!”;
setTimeout(function() {
copyButton.textContent = originalText;
}, 1500);
}).catch(function(err) {
console.error(‘Failed to copy text: ‘, err);
alert(“Failed to copy results. Please copy manually.”);
});
}

// Charting Logic
var reactionChart;
var chartContext;

function initializeChart() {
var canvas = document.getElementById(‘reactionChart’);
chartContext = canvas.getContext(‘2d’);
// Clear previous chart if any
chartContext.clearRect(0, 0, canvas.width, canvas.height);
reactionChart = null; // Reset chart object
}

function updateChart(reactants, products, coefficients) {
if (!chartContext) {
initializeChart();
}
if (!chartContext) return; // If canvas not found

var canvas = document.getElementById(‘reactionChart’);
var legendContainer = document.querySelector(‘.chart-legend’);
legendContainer.innerHTML = ”; // Clear previous legend

var allSpecies = reactants.concat(products);
var speciesCoeffs = coefficients.slice(0, reactants.length).concat(coefficients.slice(reactants.length));

// Assign colors dynamically
var colors = [‘#007bff’, ‘#6c757d’, ‘#28a745’, ‘#dc3545’, ‘#ffc107’, ‘#17a2b8’, ‘#fd7e14’, ‘#6f42c1’];
var colorMap = {};
var colorIndex = 0;

allSpecies.forEach(function(species, index) {
if (!colorMap[species]) {
colorMap[species] = colors[colorIndex % colors.length];
colorIndex++;
}
// Add to legend
var legendItem = document.createElement(‘span’);
legendItem.innerHTML = ‘‘ + species + ‘ (coeff: ‘ + speciesCoeffs[index] + ‘)’;
legendContainer.appendChild(legendItem);
});

// Chart Data Preparation
var labels = [];
var reactantData = [];
var productData = [];

// Use coefficients as a proxy for relative amounts for visualization
for (var i = 0; i < reactants.length; i++) {
labels.push("Reactant " + (i + 1));
reactantData.push(coefficients[i]);
}
for (var i = 0; i < products.length; i++) {
labels.push("Product " + (i + 1));
productData.push(coefficients[reactants.length + i]);
}

// Ensure data arrays have the same length if one side is empty
var maxLength = Math.max(labels.length, 1); // Ensure at least one label if empty
while (reactantData.length < maxLength) reactantData.push(0);
while (productData.length < maxLength) productData.push(0);
while (labels.length < maxLength) labels.push("N/A");

// Destroy previous chart instance if it exists
if (reactionChart) {
reactionChart.destroy();
}

// Create new chart
reactionChart = new Chart(chartContext, {
type: 'bar', // Use bar chart for coefficients
data: {
labels: labels,
datasets: [{
label: 'Reactant Coefficients',
data: reactantData,
backgroundColor: reactants.map(function(r, idx) { return colorMap[r]; }),
borderColor: reactants.map(function(r, idx) { return colorMap[r]; }),
borderWidth: 1
}, {
label: 'Product Coefficients',
data: productData.map(function(d, idx) { return idx < reactants.length ? 0 : d; }), // Offset product data visually if needed, or handle differently
backgroundColor: products.map(function(p, idx) { return colorMap[p]; }),
borderColor: products.map(function(p, idx) { return colorMap[p]; }),
borderWidth: 1
}]
},
options: {
responsive: true,
maintainAspectRatio: false,
scales: {
y: {
beginAtZero: true,
title: {
display: true,
text: 'Stoichiometric Coefficient (Mole Ratio)'
}
},
x: {
title: {
display: true,
text: 'Chemical Species'
}
}
},
plugins: {
title: {
display: true,
text: 'Stoichiometric Coefficients of Reactants and Products'
},
legend: {
display: false // Use custom legend
}
}
}
});
}

// FAQ Toggle Function
function toggleFaq(element) {
var parent = element.parentElement;
parent.classList.toggle('open');
}

// Initial chart setup on load
document.addEventListener('DOMContentLoaded', function() {
initializeChart();
// Trigger initial balance for default equation
balanceEquation();
});

// Re-balance on input change (optional, can be resource intensive)
// document.getElementById('chemicalEquation').addEventListener('input', balanceEquation);

<!–

// Example of native Canvas drawing (simplified)
function updateChartNativeCanvas(reactants, products, coefficients) {
var canvas = document.getElementById(‘reactionChart’);
var ctx = canvas.getContext(‘2d’);
ctx.clearRect(0, 0, canvas.width, canvas.height);

var allSpecies = reactants.concat(products);
var speciesCoeffs = coefficients.slice(0, reactants.length).concat(coefficients.slice(reactants.length));

var colors = [‘#007bff’, ‘#6c757d’, ‘#28a745’, ‘#dc3545’, ‘#ffc107’, ‘#17a2b8’, ‘#fd7e14’, ‘#6f42c1’];
var colorMap = {};
var colorIndex = 0;
allSpecies.forEach(function(species, index) {
if (!colorMap[species]) {
colorMap[species] = colors[colorIndex % colors.length];
colorIndex++;
}
});

var barWidth = (canvas.width * 0.8) / allSpecies.length;
var startX = canvas.width * 0.1;
var chartHeight = canvas.height * 0.7;
var maxYValue = Math.max(…speciesCoeffs, 1); // Max coefficient for scaling

// Draw bars
speciesCoeffs.forEach(function(coeff, index) {
var x = startX + index * barWidth;
var barHeight = (coeff / maxYValue) * chartHeight;
var y = canvas.height – barHeight – 30; // 30px for labels/axis

ctx.fillStyle = colorMap[allSpecies[index]];
ctx.fillRect(x, y, barWidth * 0.8, barHeight); // 80% width for spacing

// Draw labels
ctx.fillStyle = ‘#333′;
ctx.font = ’10px Arial’;
ctx.textAlign = ‘center’;
ctx.fillText(allSpecies[index] + ‘(‘ + coeff + ‘)’, x + barWidth * 0.4, canvas.height – 10);
});

// Draw Y-axis and labels (simplified)
ctx.beginPath();
ctx.moveTo(startX – 10, canvas.height – 30);
ctx.lineTo(startX – 10, 30);
ctx.stroke();
ctx.fillText(‘Coeff’, startX – 20, 30);
ctx.fillText(‘0’, startX – 10, canvas.height – 30);
ctx.fillText(maxYValue, startX – 10, 30);
}

–>