Question

Consider the following reactions at 300 K.
A → B (uncatalysed reaction)
A →B (catalyst reaction)
The activation energy is lowered by 8.314 KJ mol–1 for the catalysed reaction. How many times the rate of this catalysed reaction greater than that of uncatalysed reaction ?
(1) 15 times
(2) 18 times
(3) 22 times
(4) 28 times

Answer 1

Answer on the Question #42344, Chemistry, Physical Chemistry

Question:

Consider the following reactions at 300 K.

A → B (uncatalysed reaction)

A → B (catalyst reaction)

The activation energy is lowered by 8.314 KJ mol⁻¹ for the catalysed reaction. How many times the rate of this catalysed reaction greater than that of uncatalysed reaction?

(1) 15 times

(2) 18 times

(3) 22 times

(4) 28 times

Solution:

Reaction rate is defined as a products income in the period of time and depends on the concentration of reagents in the way the following equation shows:

$$v = \frac {d [ P ]}{d t} = k _ {T} * [ A ] ^ {n}$$

Where [P] is products concentration, $k_{T}$ is rate constant at the temperature T and [A] is the concentration of reagent to the power n, which is called "reaction order".

According to the Arrhenius equation, the rate constant $k_{T}$ is the function of activation energy:

$$k _ {T} = A e ^ {- E _ {a} / (R T)}$$

Thus, lowering of activation energy by 8.314 kJ/mol will cause the lowering of rate constant $k_{T}$:

$$\frac {k _ {1}}{k _ {2}} = e ^ {(- E _ {a 1} + E _ {a 2}) / R T)} = e ^ {\left(\frac {8 3 1 4}{8 . 3 1 4 4 6 2 2 * 3 0 0}\right)} = 2 8. 0 3 \approx 2 8$$

That means, that the rate for catalysed reaction is 28 times greater than that of uncatalysed reaction.

Answer: (4) 28 times

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