# How can the rate of reaction be calculated from a graph?

Apr 16, 2014

WARNING. This is a long answer.

You calculate the rate of reaction from the slope of a graph of concentration vs. time.

Assume we have a reaction 2A → 3B.

By definition, rate = -1/2(Δ[A])/(Δt) = +1/3(Δ[B])/(Δt).

If you plot a graph of [A] vs. t and draw a line tangent to the graph, then rate = ½ × |slope| of the line (rate is always a positive number).

To find the instantaneous rate of reaction at a given time:

1. Plot a graph of concentration of reactant against time of reaction. It might look like this. 1. I assume that each tick on the time axis represents 10 s. Mark a point on the graph that corresponds to a given time (say, 40 s).

2. Draw a straight line (green) tangent to the curve at that point.

3. Pick two convenient points on the tangent line, for example, where it crosses the horizontal and vertical axes (I assume the concentration has units of g/L).

4. Note the coordinates of these points, say (0 s, 50 g/L) and (52 s, 0 g/L).

5. Calculate the change in concentration.
Δ[A] = [A_2] – [A_1] = (0.0 – 50.0) g/L = -50.0 g/L

6. Calculate the change in time
Δt = t_2 – t_1 = (82 – 0) s = 82 s

7. Calculate the slope.
slope = (Δ[A])/(Δt) = ([A_2] –[A_1])/(t_2 –t_1) = (-50.0" g·L⁻¹")/(82" s") = -0.610 g•L⁻¹s⁻¹

8. Calculate the rate.
rate = ½ × |slope| = ½ × |-0.610 g•L⁻¹s⁻¹| = 0.305 g•L⁻¹s⁻¹