For a reaction $A→C+D$, the initial concentration of A is 0.010 M. After 100 sec, the cone. of A is 0.001 M. The rate constant has numerical value 9.0. The order of reaction is

Second Order

The correct answer is Option (3) → Second Order.

To determine the order of the reaction, we need to use the integrated rate law expressions for different orders of reactions and compare them to the data given. Here, we are provided with the initial concentration, the concentration after 100 seconds, and the value of the rate constant.

Let us try to solve this for thefirst-order reaction first, because that would be most suitable based on the information provided (especially since we are given the rate constant).

First-Order Reaction:

The integrated rate law for a first-order reaction is:

\(\ln \left( \frac{[A]_0}{[A]} \right) = k t\)

Where:

\([A]_0\) = initial concentration of A = 0.010 M

\([A]\) = concentration of A after time \(t\) = 0.001 M

\(k\) = rate constant = 9.0 s\(^{-1}\)

\(t\) = time = 100 s

Now, substituting the values:

\(\ln \left( \frac{0.010}{0.001} \right) = 9.0 \times 100\)

\(\ln(10) = 900\)

\(2.303 = 900\)

Clearly, this equation doesn't hold for first-order reaction, meaning this is not a first-order reaction.

Second-Order Reaction:

For a second-order reaction, the integrated rate law is:

\(\frac{1}{[A]} - \frac{1}{[A]_0} = k t\)

Substituting the values:

\(\frac{1}{0.001} - \frac{1}{0.010} = 9.0 \times 100\)

\(1000 - 100 = 900\)

\(900 = 900\)

This equation is satisfied, indicating that the reaction follows second-order kinetics.

Conclusion:

The order of the reaction is second order.

Thus, the correct answer is: Second Order.