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Q. A first order reaction has the rate constant, k=4.6×103s1. The number of correct statement/s from the following is/are _______
Given: log3=0.48
A. Reaction completes in 1000s.
B. The reaction has a half-life of 500s.
C. The time required for 10% completion is 25 times the time required for 90% completion.
D. The degree of dissociation is equal to (1ekt)
E. The rate and the rate constant have the same unit.

JEE MainJEE Main 2023Equilibrium

Solution:

t10%=1Kln(aax)=1Kln(10090)
t10%=2.303K(log10log9)
t10%=2.093K×(0.04)
Similarly
t90%=1Kln(10010)
t90%=2.303K
t90%t10%=10.04=25
ekt=aax
axa=ekt
1xa=ekt
x=a(1ekt)
α=xa=(1ekt)