The activation energy of a reaction is zero. Its rate constant at 280 K is 1.6×10-6s-1, the rate constant at 300 K is

MHT CET · Chemistry · Chemical Kinetics

The activation energy of a reaction is zero. Its rate constant at 280 K is $1.6 \times 10^{- 6} s^{- 1},$ the rate constant at 300 K is

A $3.2 \times 10^{- 6} s^{- 1}$
B Zero
C $1.6 \times 10^{- 6} s^{- 1}$
D $1.6 \times 10^{- 5} s^{- 1}$

Verified Solution

Answer & Solution

Correct Answer

(C) $1.6 \times 10^{- 6} s^{- 1}$

Step-by-step Solution

Detailed explanation

Key Idea Arrhenius equations is given as:

l o g \frac{k_{2}}{k_{1}} = \frac{E_{a}}{2.303 R} [\frac{1}{T_{1}} - \frac{1}{T_{2}}]

Given,
Activation energy of a reaction,

E_{A} = 0

Rate constant,

k_{1} = 1.6 \times 10^{- 6} s^{- 1}

Temperature,

T_{1} = 280 K, T_{2} = 300 K

According to Arrhenius equation

l o g \frac{k_{2}}{1.6 \times 10^{- 6}} = \frac{0}{2.303 R} [\frac{1}{280} - \frac{1}{300}]

l o g \frac{k_{2}}{1.6 \times 10^{- 6}} = 0

\frac{k_{2}}{1.6 \times 10^{- 6}} =

antilog 0

\frac{k_{2}}{1.6 \times 10^{- 6}} = 1

∴ k_{2} = 1.6 \times 10^{- 6} s^{- 1}

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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