Question

The initial concentration of A in the first-order reaction 4A→4B+C is 0.933 mol L−1. Given that the rate constant is 0.310 s−1, what is the half-life of the reaction in seconds? Remember to use correct significant figures in your answer (round your answer to the nearest hundredth). Do not include units in your response.

Answer 1

Answer: The half-life of the reaction in 2.24 seconds.

Explanation:

We are given a reaction which follows first order kinetics.

The formula used to calculate the half -life of the reaction for first order kinetics follows:

$t_{1/2}=\frac{0.693}{k}$

where,

$t_{1/2}$ = half-life of the reaction

k = rate constant of the reaction = $0.310s^{-1}$

Putting values in above equation, we get:

$t_{1/2}=\frac{0.693}{0.310s^{-1}}\\\\t_{1/2}=2.235sec\approx 2.24sec$

The rule which is applied for multiplication and division problems is that the least number of significant figures in any number of a problem will determine the number of significant figures in the solution.

In the problem, the least precise significant figures are 3. Thus, the answer will also have 3 significant figures.

Hence, the half-life of the reaction in 2.24 seconds.