Question

If time required for 90 % completion of a first order reaction is '\(t\)'. What is the time required for 99.9 % completion of reaction at same temperature?

• A. \(3t\)
• B. \(2t\)
• C. \(t\)
• D. \(\frac{3t}{2}\)

Hint:

For first order, \(t = \frac{2.303}{k}\log\frac{100}{100-x}\).

Answer 1

The Correct Option is A

Step 1: Count the tenfold drops
90 percent done means the reactant is down to 1/10. 99.9 percent done means it is down to 1/1000.

Step 2: Compare
First order time depends on $\log$ of the ratio, so going from a factor 10 to a factor 1000 triples the time: $3t$. Option (A).

Final Answer:
The time is three times $t$, option (A). \[ \boxed{3t} \]