Question

The half-life of a first-order reaction is 13 min. If the initial concentration of reactant is 0.085 M, how long would it take until the concentration decreases to 0.055 M

Answer 1

Answer: It will take 8.2 minutes until the concentration decreases to 0.055 M

Explanation:

The time after which 99.9% reactions gets completed is 40 minutes

Explanation:

Expression for rate law for first order kinetics is given by:

$t=\frac{2.303}{k}\log\frac{a}{a-x}$

where,

k = rate constant

t = age of sample

a = let initial amount of the reactant

a - x = amount left after decay process  

a) for completion of half life:

Half life is the amount of time taken by a radioactive material to decay to half of its original value.

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

$k=\frac{0.693}{13min}=0.053min^{-1}$

b)  Time taken for 0.085 M to decrease to 0.055 M

$t=\frac{2.303}{0.053}\log\frac{0.085}{0.055}$

$t=8.2min$

Thus it will take 8.2 minutes until the concentration decreases to 0.055 M

Answer 2

To the concentration decreases to 0.055M it will take 8.2 minutes.

To calculate the amount of atoms present after a half-life decomposition process, it is necessary to use the following formula:

                                       $N = N_{0}(\frac{1}{2})^\frac{t}{t_{1/2}} }$

Since the initial amount of moles is equal to 0.085M, the half-life is 13 minutes and the final amount of moles is equal to 0.055 M, we just have to put these values in the expression above:

                                          $0.055=0.085\times(\frac{1}{2})^{\frac{t}{13}$

                                               $t = -13$㏒$_{2}(\frac{11}{17})$

                                              $t = 8.2 minutes$

So, it will take 8.2 minutes until the concentration decreases to 0.055 M.

Learn more about half-life in: brainly.com/question/11663896