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Which equation correctly expresses the rate constant of a first order reaction in terms of initial concentration [R]0 and concentration [R] at time t?
Ak = ([R]0 - [R]) / t
Bk = (2.303/t) log([R]0/[R])
Ck = (t/2.303) log([R]/[R]0)
Dk = (1/t)([R]0 - [R])^2
Answer & Solution
Correct answer: B. k = (2.303/t) log([R]0/[R])
1. Integrating $-\dfrac{d[R]}{dt} = k[R]$ gives $\ln\dfrac{[R]_0}{[R]} = kt$.
2. Converting natural log to base 10: $k = \dfrac{2.303}{t}\log\dfrac{[R]_0}{[R]}$.
3. Option A is the zero order form; option B is the first order form.
_Source: NCERT Class 12 Chemistry Ch 3 "Chemical Kinetics", p.13_
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