In a first order reaction, the concentration of the reactant decreased from 1M to 0.25 M in 20 minutes. The rate constant of the reaction is

To determine the rate constant kk for a first-order reaction where the concentration of the reactant decreases from 1 M to 0.25 M in 20 minutes, we can use the integrated rate law for first-order reactions:

Where:

• [A0][A0] is the initial concentration (1 M),
• [A][A] is the concentration at time tt (0.25 M),
• tt is the time in seconds (20 minutes = 1200 seconds),
• kk is the rate constant.

First, we calculate the natural logarithm of the concentrations:

Now, substituting these values into the integrated rate law:

Rearranging gives:

Calculating kk:

Thus, the rate constant kk for the reaction is approximately 0.001155 s−10.001155s−1.

Here is the ans: