**Half-life period of a second-order reaction**

The half-life period of a reaction is defined as the time it takes for the concentration of a reactant to decrease by half. In a second-order reaction, the rate of the reaction is directly proportional to the square of the concentration of one or both of the reactants. The half-life period of a second-order reaction can be determined by considering the rate equation and understanding the relationship between concentration and time.

**Rate equation of a second-order reaction**

For a second-order reaction, the rate equation can be written as:

Rate = k[A]^2

where [A] represents the concentration of the reactant A and k is the rate constant. The rate constant k is specific to a particular reaction and is determined experimentally.

**Explanation of the options**

A: Independent of the concentration
The half-life period of a second-order reaction is not independent of the concentration. The rate of the reaction is directly proportional to the square of the concentration, as shown in the rate equation. Hence, the concentration does affect the half-life period.

B: Directly proportional to the initial concentration
The half-life period of a second-order reaction is not directly proportional to the initial concentration. The rate of the reaction depends on the concentration at any given time, not just the initial concentration. As the reaction proceeds and the concentration decreases, the rate of the reaction also changes.

C: Inversely proportional to concentration
The half-life period of a second-order reaction is not inversely proportional to the concentration. In a second-order reaction, the rate of the reaction is directly proportional to the square of the concentration, as shown in the rate equation. Therefore, as the concentration decreases, the rate of the reaction decreases, resulting in a longer half-life period.

D: Directly proportional to the concentration
The correct answer is D. The half-life period of a second-order reaction is directly proportional to the concentration. This can be understood by rearranging the rate equation:

Rate = k[A]^2

Rearranging for time, we get:

t = 1/(k[A]^2)

As the concentration increases, the denominator of the equation increases, resulting in a smaller value for time (t). Therefore, the half-life period is directly proportional to the concentration.

In conclusion, the half-life period of a second-order reaction is directly proportional to the concentration. As the concentration decreases, the half-life period increases, and vice versa.

Inversely proportional to initial concentration.....