Which of the following statements about the rate of a chemical reaction are correct?
(A) The rate of reaction is always proportional to the concentration of reactants
(B) An exponential time course is followed by the first order reaction
(C) The unit of rate of reaction in the gaseous state is atm \( s^{-1} \)
(D) The concentration of reactant decreases exponentially with time for a zero order reaction
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (B) and (C) only
The rate of a reaction is the change in concentration (or, for gases, in partial pressure) of a reactant or product per unit time. How it depends on concentration is given by the rate law, rate = \( k[\mathrm{R}]^{n} \), where n is the order. The integrated rate laws give how [R] changes with time:
\( \displaystyle \text{zero order:}\quad [\mathrm{R}] = [\mathrm{R}]_0 - kt \)
\( \displaystyle \text{first order:}\quad [\mathrm{R}] = [\mathrm{R}]_0\, e^{-kt} \)
(A) The rate of reaction is always proportional to the concentration of reactants — Incorrect. The rate is proportional to the concentration raised to the order, which is found by experiment. It is directly proportional only for a first order reaction; for a zero order reaction it does not depend on concentration at all.
(B) An exponential time course is followed by the first order reaction — Correct. For a first order reaction \( [\mathrm{R}] = [\mathrm{R}]_0 e^{-kt} \): the concentration falls exponentially, by the same fraction in every equal interval of time.
(C) The unit of rate of reaction in the gaseous state is atm \(s^{-1}\) — Correct. For gases, concentration is replaced by partial pressure, so the rate is expressed as change in pressure per unit time, atm s−1.
(D) The concentration of reactant decreases exponentially with time for a zero order reaction — Incorrect. For a zero order reaction \( [\mathrm{R}] = [\mathrm{R}]_0 - kt \): the concentration falls linearly with time.