Sections 13.3 - 13.4: Instantaneous Rate

The rate of reaction or reaction rate at a particular time is called the instantaneous rate.

Example: Consider the decomposition of nitrogen dioxide:

2 NO_{2 (g)} à 2 NO _(g) + O_{2 (g)}

The experimental data of NO₂ concentration as a function of time during the reaction is given in the following table:

Time, s	[NO2], mol.L^-1
0	2.00
2	1.35
4	1.06
6	0.87
8	0.75
10	0.66

Calculate the instantaneous rate of decomposition of NO₂ at 3 s.

The reaction rate is expressed in terms of reactants as:

To calculate the instantaneous rate, first, make a graph of [NO₂] vs. time.

At 3 s, draw a vertical line that intersects the curve. Draw the tangent line to the curve at the point of intersection. Now select two points at a reasonable distance from each other on the tangent line. Find the x- and y-values for each of these points.

The difference in x-values is x₂ – x₁ = 5 – 1 = 4 s

The difference in y-values is y₂ – y₁ = 0.85 – 1.46 = - 0.61 mol/L

Instantaneous rate = ½ x 0.15 mol.L^-1.s^-1 = 0.08 mol.L^-1.s^-1