The rate constant for a first order reaction whose half life is 480 sec, is :

Options

A. `2.88 xx 10^(-3)sec^(-1)`
B. `1.44 xx 10^(-3)sec^(-1)`
C. `1.44 sec^(-1)`
D. `0.72 xx 10^(-3) sec^(-1)`

Answer

To determine the rate constant (k) for a first-order reaction given its half-life (t_half), we can use the formula that relates these two quantities. Here’s a step-by-step solution:

### Step 1: Understand the relationship between half-life and rate constant
For a first-order reaction, the half-life (t_half) is related to the rate constant (k) by the formula:
\[ t_{half} = \frac{0.693}{k} \]

### Step 2: Rearrange the formula to solve for k
To find the rate constant (k), we can rearrange the formula:
\[ k = \frac{0.693}{t_{half}} \]

### Step 3: Substitute the given half-life into the equation
We are given that the half-life (t_half) is 480 seconds. Now, we can substitute this value into the equation:
\[ k = \frac{0.693}{480 \, \text{sec}} \]

### Step 4: Calculate the value of k
Now, we perform the calculation:
\[ k = \frac{0.693}{480} \]
\[ k \approx 0.00144 \, \text{sec}^{-1} \]
or
\[ k \approx 1.44 \times 10^{-3} \, \text{sec}^{-1} \]

### Step 5: State the final answer
Thus, the rate constant (k) for the first-order reaction whose half-life is 480 seconds is:
\[ k \approx 1.44 \times 10^{-3} \, \text{sec}^{-1} \]