Questions & Answers

Question

Answers

a.) 10 min

b.) 20 min

c.) 30 min

d.) 40 min

Answer
Verified

We have for the first order reaction

$\ln \frac{{\left[ {{A_0}} \right]}}{{\left[ {{A_t}} \right]}} = kt$

Where $\left[ {{A_0}} \right]$ is the initial concentration

$\left[ {{A_t}} \right]$ is the final concentration

k is the rate constant and

t is the time taken for the reaction

Thus, by putting the values of certain variables, we can find the time taken for the reaction.

We know that for first order reaction, the half life time period can be given by –

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

Where k is the rate constant.

In the question, a half life period is given to us which is 10 min.

So, by filling the value of half life time, we can get value of rate constant (k) as-

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

k = $\frac{{0.693}}{{10}}$

k = 0.0693 ${\min ^{ - 1}}$

Further, for the first order reaction, we have the formula as-

$\ln \frac{{\left[ {{A_0}} \right]}}{{\left[ {{A_t}} \right]}} = kt$

Where $\left[ {{A_0}} \right]$ is the initial concentration

$\left[ {{A_t}} \right]$ is the final concentration

k is the rate constant and

t is the time taken fo$t = \frac{{\ln 4}}{{0.0693}}\min $r the reaction

As we have to find the time for the reaction. Thus, the equation can be modified as-

$\frac{{\ln \frac{{\left[ {{A_0}} \right]}}{{\left[ {{A_t}} \right]}}}}{k} = t$

So, from the question we have initial value of concentration = 0.08 M

The final value of the concentration = 0.02 M

And rate constant = 0.0693 ${\min ^{ - 1}}$

Thus, by putting the values; we have

$t = \frac{{\ln \frac{{\left[ {0.08M} \right]}}{{\left[ {0.02M} \right]}}}}{{0.0693}}\min $

$t = \frac{{1.38}}{{0.0693}}\min $

t = 19.91 min

So, the value is approximately 20 minutes.