Question

Half life of a first order reaction is 3 hours. Calculate the value of \(\frac{[\mathrm{A}]_0}{[\mathrm{~A}]_{\mathrm{t}}}\) after 8 hours.

• A. 2.17
• B. 4.34
• C. 6.34
• D. 8.12

Hint:

Find the rate constant from the half life, then use the first order integrated rate law.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept
For a first order reaction \(k = \dfrac{0.693}{t_{1/2}}\) and \(k = \dfrac{2.303}{t}\log\dfrac{[A]_0}{[A]_t}\).

Step 2: Calculation
\(k = \dfrac{0.693}{3} = 0.231\text{ h}^{-1}\)
\(\log\dfrac{[A]_0}{[A]_t} = \dfrac{0.231\times 8}{2.303} = 0.802\)

Step 3: Result
\(\dfrac{[A]_0}{[A]_t} = 10^{0.802} \approx 6.34\).

Final Answer:
The ratio after 8 hours is about 6.34. \[ \boxed{\text{(C) }6.34} \]