A plot of log (a-x) against time 't' is a straight line. This indicates that the reaction is of :

Options

A. zero order
B. first order
C. second order
D. third order

Answer

To determine the order of the reaction based on the plot of log(a - x) against time 't', we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Variables**:
- Let 'a' be the initial concentration of the reactant.
- Let 'x' be the amount of reactant that has reacted at time 't'.
- Therefore, (a - x) is the concentration of the reactant remaining at time 't'.

2. **Identify the Reaction Order**:
- For a **zero-order reaction**, the rate of reaction is constant and does not depend on the concentration of the reactant. The integrated rate law is:
\[ [A] = [A_0] - kt \]
where [A] is the concentration at time t, [A_0] is the initial concentration, and k is the rate constant. The plot of [A] vs. time would yield a straight line, but not log([A]) vs. time.

- For a **first-order reaction**, the integrated rate law is:
\[ \ln[A] = \ln[A_0] - kt \]
or rearranging gives:
\[ \log(a - x) = \log a - \frac{k}{2.303}t \]
This equation indicates that a plot of log(a - x) against time 't' will yield a straight line with a negative slope, confirming it is a first-order reaction.

- For a **second-order reaction**, the integrated rate law is:
\[ \frac{1}{[A]} = \frac{1}{[A_0]} + kt \]
This does not involve logarithmic terms, hence a plot of log(a - x) against time would not yield a straight line.

3. **Conclusion**:
- Since the plot of log(a - x) against time 't' is a straight line, we conclude that the reaction is of **first order**.

### Final Answer:
The reaction is of **first order**.