This example problem demonstrates how to use reaction rates to determine the coefficients of a balanced chemical equation.

### Problem

The following reaction is observed:

2A + bB → cC + dD

As the reaction progressed, the concentrations changed by these rates

rate_{A} = 0.050 mol/L·s

rate_{B} = 0.150 mol/L·s

rate_{C} = 0.075 mol/L·s

rate_{D} = 0.025 mol/L·s

What are the values for the coefficients b, c, and d?

### Solution

Chemical reaction rates measure the change in concentration of the substance per unit time.

The coefficient of the chemical equation shows the whole number ratio of materials needed or products produced by the reaction. This means they also show the relative reaction rates.**Step 1: **Find b

rate_{B}/rate_{A} = b/coefficient of A

b = coefficient of A x rate_{B}/rate_{A}

b = 2 x 0.150/0.050

b = 2 x 3

b = 6

For every 2 moles of A, 6 moles of B are needed to complete the reaction**Step 2:** Find c

rate_{B}/rate_{A} = c/coefficient of A

c = coefficient of A x rate_{C}/rate_{A}

c = 2 x 0.075/0.050

c = 2 x 1.5

c = 3

For every 2 moles of A, 3 moles of C are produced**Step 3:** Find d

rate_{D}/rate_{A} = c/coefficient of A

d = coefficient of A x rate_{D}/rate_{A}

d = 2 x 0.025/0.050

d = 2 x 0.5

d = 1

For every 2 moles of A, 1 mole of D is produced

### Answer

The missing coefficients for the 2A + bB → cC + dD reaction are b=6, c=3, and d=1.

The balanced equation is 2A + 6B → 3C + D