Question

The time required for \(90\%\) completion of a certain first order reaction is \(1\) hour. Calculate the time required for \(99.9\%\) completion of the same reaction.

• A. \(2\) hours.
• B. \(1\) hour.
• C. \(3\) hours.
• D. \(0.5\) hour.

Hint:

t is proportional to log(A0/A). Compare log 10 and log 1000.

Answer 1

The Correct Option is C

Step 1: Shortcut:
At a fixed $k$, $t \propto \log(\text{initial}/\text{left})$.

Step 2: Ratio:
For 90%: $\log 10 = 1$. For 99.9%: $\log 1000 = 3$.

Step 3: Scale:
$t_{99.9}/t_{90} = 3/1$. So $t_{99.9} = 3\times 1 = 3$ h.

Final Answer:
Compare the logarithms: 3 against 1. \[ \boxed{C} \]