Question

How is the slope of the straight line in the plot of log₁₀C vs time for a first order reaction related to the rate constant of the reaction?

Answer 1

For a first-order reaction, the slope of the straight line in the plot of log_⁡10 vs. time (t) is directly related to the rate constant k by the following relation:

`log_10[C] = log_10[C_0] - k/2.303 t`

This is in the form of a straight line

y = c − mt

Where:

y = log⁡₁₀[C],

c = log⁡₁₀[C0],

`m = k/2.303` is the positive constant,

So the slope = `-k/2.303`

So the rate constant is k = −2.303 × slope

This allows you to determine the rate constant k from the slope of the straight-line graph.