Solveeit Logo
Login

Question

Question: The rate of a first order reaction is \(1.5\times {{10}^{-2}}mol{{L}^{-1}}{{\min }^{-1}}\) at 0.5 M ...

The rate of a first order reaction is 1.5×10−2molL−1min⁡−11.5\times {{10}^{-2}}mol{{L}^{-1}}{{\min }^{-1}} at 0.5 M concentration of the reactant. The half-life of the reaction is:
A. 0.383 min
B. 23.1 min
C. 8.73 min
D. 7.53 min

Explanation

Solution

Order of reaction defines the relationship between the rate of a chemical reaction and the concentration of the species which takes part in that chemical reaction. In order to obtain the order of reaction we first have to know about rate expression.

Complete answer:
The order of reaction can also be defined as the power dependence of rate of the concentration of all reactants. In case of first order of reaction it depends upon the concentration of one species in the reaction. This defines that rate of first order reaction will be:
Rate=K[R]Rate=K[R]
Rate 1.5×10−2molL−1min⁡−11.5\times {{10}^{-2}}mol{{L}^{-1}}{{\min }^{-1}}given at 0.5M concentration
1.5×10−2molL−1min⁡−11.5\times {{10}^{-2}}mol{{L}^{-1}}{{\min }^{-1}}= K (0.5)
K = 3×10−2 min-13\times {{10}^{-2}}\ \text{mi}{{\text{n}}^{\text{-1}}}
Half-life is defined as the amount of time taken for half of a particular sample for react and it can also be explained on the basis on the time which it requires to reduce its initial value to half. The equation of half-life is given by:
t1/2=0.693K{{t}_{1/2}}=\dfrac{0.693}{K}
Value of K is 3×10−2 min-13\times {{10}^{-2}}\ \text{mi}{{\text{n}}^{\text{-1}}}, put this value in the equation of half-life time
t1/2=0.6930.03=23.1{{t}_{1/2}}=\dfrac{0.693}{0.03}=23.1 Minutes
Therefore we can conclude that half-life time will be 23.1 minutes.

So option B is the correct answer.

Note:
Half-life time is generally used in nuclear physics to describe what time period an unstable atom undergoes through the process of radioactive decay and we can also calculate how long an atom survives to be stable.