Questions & Answers

Question

Answers

A. 230.3 minutes

B. 23.03 minutes

C. 46.06 minutes

D. 460.6 minutes

Answer

Verified

129.9k+ views

-In the given question we have to calculate the time required in which 99% of the reaction will complete

-It is given that the half-life is equal to 6.93 minutes.

-So, firstly we will calculate the rate constant for the first-order reaction:

${{\text{k}}_{1}}\text{ = }\dfrac{\text{0}\text{.693}}{{{\text{t}}_{1/2}}}=\text{ }\dfrac{\text{0}\text{.693}}{6.93}\text{= 0}\text{.1 /min}\text{.}$

-Now, we will find the time that is required for 99% completion of the reaction by applying the first-order reaction:

$\text{k = }\dfrac{2.303}{t}\text{ log}\left( \dfrac{{{\text{A}}_{0}}}{\text{A}} \right)$

-Here the ${{\text{A}}_{0}}$represents the initial concentration which is equal to 100 and A represents the final concentration which is $\left( \text{100-99} \right)$that is 1.

-So,

$\text{t = }\dfrac{\text{2}\text{.303}}{\text{k}}\log \left( \dfrac{\text{100}}{100-99} \right)\text{ = }\dfrac{2.303}{0.1}\log \left( \dfrac{\text{1}{{\text{0}}^{2}}}{1} \right)\text{ = 23}\text{.03 }\cdot \text{ 2log10}$

$\text{= 23}\text{.03 }\cdot \text{ 2 }\cdot \text{ 1 = 46}\text{.06 minutes}$.