**Time for Half Change**

In a first-order reaction, the rate of reaction is directly proportional to the concentration of the reactant. The time required for half change, also known as the half-life (t1/2), is the time it takes for the concentration of the reactant to decrease by half.

Let's assume the initial concentration of the reactant is A0, and after a certain time (t), the concentration becomes A. The equation for a first-order reaction is given by:

A = A0 * e^(-kt)

Where:
A = concentration of reactant at time t
A0 = initial concentration of reactant
k = rate constant of the reaction
t = time

For a first-order reaction, the half-life (t1/2) can be calculated using the equation:

t1/2 = (0.693/k)

Given that the time for half change is 25 minutes, we can use this information to find the rate constant (k).

**Calculating the Rate Constant (k)**

t1/2 = (0.693/k)
25 = (0.693/k)

Solving for k, we get:

k = 0.693/25
k = 0.0277 min^-1

**Calculating the Time for 99% of the Reaction**

Now that we have the rate constant (k), we can calculate the time required for 99% of the reaction to occur.

We know that the concentration of the reactant at any given time (t) is given by:

A = A0 * e^(-kt)

To find the time required for 99% of the reaction, we need to find the value of t when A = 0.01A0 (99% decrease in concentration).

0.01A0 = A0 * e^(-kt)

Taking the natural logarithm (ln) of both sides:

ln(0.01) = -kt

Solving for t, we get:

t = -ln(0.01)/k

Substituting the value of k we found earlier:

t = -ln(0.01)/0.0277
t = 166 minutes

Therefore, the time required for 99% of the reaction to occur is 166 minutes.