Balancing Chemical Equations

Master the algebraic method for balancing equations systematically

The Algebraic Method for Balancing Equations

A systematic approach using variables and equations to balance any chemical reaction.

Why Use This Method?

While trial-and-error works for simple equations, the algebraic method provides a systematic approach that works for ANY equation, no matter how complex. It's especially useful for redox reactions and equations with many elements.

Step 1: Assign Variables to Each Compound

Give each compound in the equation a variable (a, b, c, d, etc.) representing its coefficient.

Example: H2 + O2 → H2O becomes aH2 + bO2 → cH2O

Step 2: Write an Equation for Each Element

For each element, count the atoms on each side (multiplied by the coefficient variable).

  • Hydrogen (H): Left side has 2a atoms, Right side has 2c atoms → 2a = 2c
  • Oxygen (O): Left side has 2b atoms, Right side has c atoms → 2b = c

Step 3: Solve the System of Equations

Express all variables in terms of one "free" variable.

  • From hydrogen: 2a = 2c → a = c
  • From oxygen: 2b = c → c = 2b
  • Substituting: a = 2b

Step 4: Choose the Free Variable

Set the free variable to the smallest integer that makes ALL coefficients whole numbers.

Let b = 1, then: a = 2(1) = 2, c = 2(1) = 2

Step 5: Write the Balanced Equation

Substitute the values back into the original equation.

2H2 + O2 → 2H2O
Verification Tip: Always check your answer by counting atoms on both sides!
Element Left Side Right Side Balanced?
H 2 × 2 = 4 2 × 2 = 4 Yes
O 1 × 2 = 2 2 × 1 = 2 Yes

Worked Examples

Follow along with these step-by-step solutions to master the algebraic method.

Guided Practice

Fill in the blanks to complete each step of the balancing process.

Instructions: These problems guide you through the algebraic method step by step. Fill in the missing values to practice the process.

Independent Practice

Balance these equations on your own. Click "Show Solution" to see the step-by-step process.

Instructions: Enter the coefficients for each compound. Use 1 if no coefficient is needed. Click "Check" to verify your answer.