The general expression for rate constant k for an nth order reaction
`k=1/((n-1)t)[1/([A]^(n-1))-1/([A]_(0)^(n-1))]` is

Options

A. valid for zero order reaction
B. not valid for first order reaction
C. not valid for zero order reaction
D. not valid for negative/fractional order reaction

Answer

To determine the validity of the expression for the rate constant \( k \) for an nth order reaction, we can analyze the expression step by step.

### Step-by-Step Solution:

1. **Understanding the Expression**:
The expression given for the rate constant \( k \) for an nth order reaction is:
\[ k = \frac{1}{(n-1)t} \left( \frac{1}{[A]^{(n-1)}} - \frac{1}{[A_0]^{(n-1)}} \right) \]
Here, \( [A] \) is the concentration at time \( t \), \( [A_0] \) is the initial concentration, and \( n \) is the order of the reaction.

2. **Checking for Zero Order Reaction**:
For a zero-order reaction, \( n = 0 \):
\[ k = \frac{1}{(0-1)t} \left( \frac{1}{[A]^{-1}} - \frac{1}{[A_0]^{-1}} \right) \]
Simplifying this gives:
\[ k = -\frac{1}{t} \left( [A] - [A_0] \right) \]
Rearranging leads to the equation:
\[ [A] = [A_0] - kt \]
This is a valid expression for a zero-order reaction.

3. **Checking for First Order Reaction**:
For a first-order reaction, \( n = 1 \):
\[ k = \frac{1}{(1-1)t} \left( \frac{1}{[A]^{0}} - \frac{1}{[A_0]^{0}} \right) \]
This simplifies to:
\[ k = \frac{1}{0} \left( 1 - 1 \right) \]
This results in an undefined expression (division by zero), indicating that the expression is not valid for first-order reactions.

4. **Checking for Fractional Order Reactions**:
If \( n \) is a negative fraction, the expression can still be evaluated:
\[ k = \frac{1}{(n-1)t} \left( \frac{1}{[A]^{(n-1)}} - \frac{1}{[A_0]^{(n-1)}} \right) \]
This will yield a valid expression, as \( n-1 \) will not equal zero, and thus the expression remains defined.

### Conclusion:
The expression for \( k \) is valid for zero-order reactions and for reactions with negative fractional orders. However, it is not valid for first-order reactions.