Chemical Kinetics and Reaction Rates

Chemical Kinetics and Reaction Rates - Numerical Applications

Q. For a reaction with an activation energy of 50 kJ/mol, what is the rate constant at 350 K if the rate constant at 300 K is 0.1 s^-1?

A. 0.2 s^-1
B. 0.3 s^-1
C. 0.4 s^-1
D. 0.5 s^-1

Solution

Using the Arrhenius equation, k2 = k1 * e^[-Ea/R(1/T2 - 1/T1)]. Substituting values gives k2 ≈ 0.4 s^-1.

Correct Answer: C — 0.4 s^-1

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Q. For a zero-order reaction, if the initial concentration is 0.5 M and the rate constant is 0.1 M/s, how long will it take for the concentration to drop to 0.2 M?

A. 3 s
B. 5 s
C. 7 s
D. 10 s

Solution

For a zero-order reaction, [A] = [A]0 - kt. Thus, 0.2 M = 0.5 M - (0.1 M/s)t, leading to t = (0.5 - 0.2) / 0.1 = 3 s.

Correct Answer: B — 5 s

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Q. If the rate of a reaction doubles when the temperature increases from 300 K to 310 K, what is the approximate activation energy (Ea) in kJ/mol?

A. 20.8
B. 40.8
C. 60.8
D. 80.8

Solution

Using the Arrhenius equation and the two-point form, Ea can be estimated as Ea ≈ 2.303RT²(Δlnk/Δ(1/T)). With R = 8.314 J/(mol·K), Ea ≈ 40.8 kJ/mol.

Correct Answer: B — 40.8

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Q. If the rate of a reaction is 0.05 M/s when the concentration of reactant A is 0.1 M, what is the rate constant k for a first-order reaction?

A. 0.5 s^-1
B. 1.0 s^-1
C. 0.05 s^-1
D. 0.1 s^-1

Solution

For a first-order reaction, rate = k[A]. Thus, k = rate / [A] = 0.05 M/s / 0.1 M = 0.5 s^-1.

Correct Answer: A — 0.5 s^-1

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Q. If the rate of a reaction is proportional to the square of the concentration of reactant A, what is the rate law?

A. rate = k[A]
B. rate = k[A]^2
C. rate = k[A]^3
D. rate = k[A]^0

Solution

If the rate is proportional to the square of the concentration of A, the rate law is rate = k[A]^2.

Correct Answer: B — rate = k[A]^2

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Q. In a reaction with a rate constant of 0.03 s^-1, how long will it take for the concentration to decrease to 25% of its initial value?

A. 23.1 s
B. 46.2 s
C. 69.3 s
D. 92.4 s

Solution

For a first-order reaction, t = (ln([A]0/[A]) / k). Here, [A] = 0.25[A]0, so t = (ln(1/0.25) / 0.03) ≈ 46.2 s.

Correct Answer: B — 46.2 s

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Q. What is the order of a reaction if the rate law is given by rate = k[A]^2[B]?

A. 0
B. 1
C. 2
D. 3

Solution

The order of the reaction is the sum of the exponents in the rate law. Here, it is 2 (from [A]^2) + 1 (from [B]) = 3.

Correct Answer: C — 2

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Q. What is the rate constant (k) for a first-order reaction with a half-life of 10 minutes?

A. 0.0693 min^-1
B. 0.1 min^-1
C. 0.693 min^-1
D. 0.5 min^-1

Solution

For a first-order reaction, k = 0.693 / t1/2. Thus, k = 0.693 / 10 min = 0.0693 min^-1.

Correct Answer: A — 0.0693 min^-1

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Chemical Kinetics and Reaction Rates - Numerical Applications

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