# How do you calculate the average rate of a reaction?

Apr 27, 2014

You divide the change in concentration by the time interval.

#### Explanation:

Consider a reaction $\text{aA + bB → cC + dD}$

You measure the rate by determining the concentration of a component at various times.

The rate of reaction of $\text{A}$ is "-"(Δ"[A]")/(Δt)

We insert a minus sign to make the rate a positive number.

We do not need the minus sign if we are working with a product. For example, the rate of reaction of C is

rate of reaction of "C" = (Δ"[C]")/(Δt)

The overall rate of reaction should be the same whichever component we measure.

So, we divide the rate of each component by its coefficient in the chemical equation.

rate of reaction = −1/a(Δ"[A]")/(Δt) = −1/b(Δ"[B]")/(Δt) = 1/c(Δ"[C]")/(Δt) = 1/d(Δ"[D]")/(Δt)

EXAMPLE

Consider the reaction

$\text{A → B}$

• You measure the concentrations of $\text{A}$ and $\text{B}$ over a period of time and get this graph.

What is the average rate of the reaction over 500 s?

Solution

If you use $\text{A}$ to determine the rate, you determine the slope of the line in the graph below.

rate of reaction = -1/1(Δ"[A]")/(Δt) = -(0.05" mol/L" – 1.70" mol/L")/(500" s" -0" s") = -(1.65" mol/L")/(500" s") = "0.003 30 mol·L"^"-1""s"^"-1"

If you use $\text{B}$ to determine the rate, you determine the slope of the line in the graph below.

Rate of reaction = 1/1(Δ"[B]")/(Δt) = "1.65 mol/L – 0.00 mol/L"/"500 s -0 s" = "1.65 mol/L"/"500 s" = "0.003 30 mol·L"^"-1""s"^"-1"