Is 60% of a first order reaction was completed in 60 minutes 50% of the same reaction would be completed in?

If 75% of a first order reaction was completed in 60 minutes, 50% of the same reaction under the same conditions would be completed in ____________.

20 minutes
30 minutes
35 minutes
75 minutes

If 75% of a first order reaction was completed in 60 minutes, 50% of the same reaction under the same conditions would be completed in 30 minutes.

Concept: The Integrated Rate Equation

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A reaction is second order with respect to a reactant. How is the rate of rection affected if the concentration of the reactant is
(i) Doubled
(ii) Reduced to 1/2?

Let the reaction A → B is a 2nd order reaction w.r.t A and conc. of A is ‘a’ mol/L, then rate of reaction can be written as:

dxdt=k[A]2 =ka2

(i) When conc. [A] is doubled

i.e., [A’] = 2a mol/L
Then new rate of reaction

d'(x)dt=k[2a]2 = 4ka2 = 4dxdt

Thus rate of reaction will become four times where concentration is doubled.

(ii) Similarly, when conc. of A is reduced to 12 i.e., [A] is a/2 then new rate of reaction,

d'(x)dt = ka22 = 14ka2 = 14dxdt

The rate of reaction will become one-fourth of the initial rate of reaction.

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