Question

At 30$^\circ$C, the half-life for the decomposition of a compound is 100 seconds and the value of the half-life is independent of the initial concentration of the reactantThe time required for 30\% of the reactant to be consumed is _ _ _ seconds. (rounded off to one decimal place)

Hint:

For first order reactions, use $\ln\left(\frac{[A]_0}{[A]}\right)=kt$ directly when percentage remaining is given

Answer 1

Correct Answer: 51.4

Step 1: Order of the reaction.
A half-life that does not depend on concentration means first order, so $k = 0.693/100 = 0.00693$ per second.

Step 2: Fraction left.
If 30 percent reacts, 70 percent remains.

Step 3: Use the first order law.
\[ t = \frac{\ln(1/0.70)}{0.00693} \approx 51.4 \]

Step 4: Answer.
\[ \boxed{51.4 \text{ seconds}} \]