# Chemical Reaction Engineering Questions and Answers – Reaction Kinetics Elements – Modelling the Rate Coefficient – 1

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This set of Chemical Reaction Engineering Multiple Choice Questions & Answers (MCQs) focuses on “Reaction Kinetics Elements – Modelling the Rate Coefficient – 1”.

1. The value of rate constant for a zero order reaction is obtained by the plot between ____
a) Concentration vs time
b) Concentration vs rate
c) Rate vs time
d) Concentration vs rate

Explanation: For a zero order reaction, $$\frac{-dC_A}{dt}$$ = k
Integrating the above equation between initial concentration CA0 and final concentration CA, (CA0 – CA)=kt
The slope of the graph of concentration vs time gives the rate constant for a zero order reaction.

2. Which of the following theories does not propose the temperature dependence of rate constant?
a) Arrhenius theory
b) Collision theory
c) Transition state theory
d) Bohr’s theory

Explanation: Bohr’s theory proposes the model of an atom. Arrhenius theory, Collision theory, Transition state theory propose the variation of rate constant with temperature.

3. Which among the following graphs represents a zero order reaction?
a) b) c) d) Explanation: For a zero order reaction, at time t=0, concentration=CA0. At time t=CA0/k, concentration=0. Hence, the graph is a straight line intercepting y- axis at CA0 and x- axis at CA0/k.
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4. For a first order reaction, the rate constant as a function of half life is given as ____
a) $$\frac{0.6931}{k}$$
b) 0.6931×k
c) 0.6931
d) $$\frac{k}{0.6931}$$

Explanation: Half life period is the time taken for one-half of the reactant to be consumed. For a first order reaction, ($$\frac{-dC}{dt}$$) = kCn. Integrating between initial concentration CA0 and final concentration $$\frac{C_{A0}}{2}$$, ln(2) = kt0.5
t0.5 = $$\frac{0.6931}{k}.$$

5. The rate constant is a ____
a) Linear function of frequency factor
b) Exponential function of frequency factor
c) Logarithmic function of frequency factor
d) Sinusoidal function of frequency factor

Explanation: By Arrhenius equation, k = $$Ae^{\frac{-E_a}{RT}}$$
K varies directly with respect to the frequency factor, A.

6. For any order n, the rate constant is expressed as ____
a) (-rA)
b) (-rA) × CAn
c) (-rA) × CA
d) $$\frac{-r_A}{C_A^n}$$

Explanation: For any order n, (-rA) = kCAn. Hence, k = $$\frac{-r_A}{C_A^n}.$$

7. For a reaction with negative order n, which one of the following is true about reaction rate constant?
a) k = (-rA)
b) k = 1
c) k = $$\frac{-r_A}{C_A^n}$$
d) k = (-rA) × CAn

Explanation: For n<0, (-rA) = kCAn
Hence, k = (-rA) × CAn

8. Which among the following is true for liquid phase reactions of order n?
a) ln($$\frac{-dC}{dt}$$) = lnk + n(lnC)
b) ln($$\frac{-dC}{dt}$$) = lnk + lnC
c) ln($$\frac{-dC}{dt}$$) = nlnk + lnC
d) ln($$\frac{-dC}{dt}$$) = lnk + $$\frac{lnC}{n}$$

Explanation: ($$\frac{-dC}{dt}$$) = kCn
Taking natural logarithm on both sides, ln($$\frac{-dC}{dt}$$) = lnk + n(lnC)

9. For a first order reaction, the rate constant is expressed in terms of initial concentration CAo and final concentration CA as ____
a) CA = CAo × k
b) CA = CAo × e-kt
c) CA = CAo × kt
d) CA = CAo × ekt

Explanation: ($$\frac{-dC}{dt}$$) = kCA
ln($$\frac{CAo}{CA}$$) = kt
CA = CAo × e-kt

10. If rate of a zero order reaction is 10 $$\frac{mol}{m^3×s}$$ and reaction time is 5s, then the value of rate constant is ____
a) 1 s-1
b) 2 s-1
c) 5 s-1
d) 10 s-1

Explanation: (-rA) = kCAn
10 = k (5)
Hence, k = 2 s-1.

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