Final answer:
To find the time required for the initial concentration to decrease by 45% in a first-order reaction, we use the integrated rate law, rearrange it to solve for time, and substitute known values into the equation.
Step-by-step explanation:
To determine the amount of time required for the initial concentration to decrease by 45%, we need to use the integrated rate law for a first-order reaction. The appropriate equation is:
A = [A0]e-kt
Where:
- [A] is the final concentration of the reactant,
- [A0] is the initial concentration,
- k is the rate constant with units of s-1,
- e is the base of the natural logarithms, and
- t is the time.
For a decrease of 45%, the final concentration [A] would be 55% of the initial concentration [A0]. To find the time t, rearrange the equation:
ln([A]/[A0]) = -kt
Substitute the known values into this equation and solve for t to find the required time.