Question

If for a first-order reaction, \([A]_0 = 1.0 \text{M}\) and \([A]_t = 0.25 \text{M}\) after 276 s, find the value of the rate constant (k).

• A. \(0.0021 \text{s}^{-1}\)
• B. \(0.0050 \text{s}^{-1}\)
• C. \(0.003 \text{s}^{-1}\)
• D. \(0.006 \text{s}^{-1}\)

Hint:

Use k = (2.303/t) log (A0/At).

Answer 1

The Correct Option is B

Step 1: Half-life route
A fall from $1.0$ M to $0.25$ M is two successive halvings, so $276 = 2 t_{1/2}$.

Step 2: Compute
$t_{1/2} = 138$ s, so $k = \frac{0.693}{138} = 0.0050\ \text{s}^{-1}$.

Step 3: Answer
Option (B).

Final Answer:
0.0050 per second. \[ \boxed{\text{(B)}\ 0.0050\ \text{s}^{-1}} \]