Question

Given 90% of the first-order reaction is completed in 70 minutes. The velocity constant of the reaction is:
A. 0.0329 \[{\min ^{ - 1}}\]
B. 0.329\[{\min ^{ - 1}}\]
C. 3.29 \[{\min ^{ - 1}}\]
D. 0.0293\[{\min ^{ - 1}}\]

Answer 1

Hint- As to solve this question we need to find out the velocity constant of the reaction, \[k = \dfrac{{2.303}}{t}\log \left( {\dfrac{a}{{a - x}}} \right)\]. We know the time (T), a and x in the formula, simply find the required data.

Complete step-by-step answer:
As we know that 90% of the first-order reaction is completed in 70 minutes.
The velocity constant of the reaction is \[k = \dfrac{{2.303}}{t}\log \left( {\dfrac{a}{{a - x}}} \right)\]
Where t is time (70mins), a is to be considered as 100%
And x is to be considered as 90%
Placing required data in equation of velocity constant of the reaction is \[k = \dfrac{{2.303}}{t}\log \left( {\dfrac{a}{{a - x}}} \right)\]. We get,
\[
  k = \dfrac{{2.303}}{{70}}\log .\dfrac{{100}}{{100 - 90}} \\
  k = \dfrac{{2.303}}{{70}}\log 10 \\
  k = \dfrac{{2.303}}{{70}} = 0.0329{\min ^{ - 1}} \\
\]

Velocity constant of the reaction is \[0.0329{\min ^{ - 1}}\].

Note- The conditions in which the reaction takes place, the process by which it takes place, it's rate and its balance. According to the law of mass action, chemical reaction rates depend solely on concentrations of substances that affect the rate at a constant temperature. The substances affecting the reaction rate are usually one or more of the reactants, however sometimes products are included. In the balanced overall chemistry equation, catalysts can also influence reaction rates. The rate law is calculated experimentally and can be used to predict the relation between the reaction rate.