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Chemical Kinetics and Nuclear Chemistry question

2021 · 1 Sep · Shift 2 · Q2

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Chemical Kinetics and Nuclear Chemistry
2021 · 1 Sep · Shift 2 · Q2

Chemical Kinetics and Nuclear Chemistry question

2021 · 1 Sep · Shift 2 · Q2

JEE MainChemistryChemical Kinetics and Nuclear ChemistryMCQ+4 / −1

Which one of the following given graphs represents the variation of rate constant (k) with temperature (T) for an endothermic reaction?

A
B
C
D

View written solutionFree

Correct answer: A

For a reaction, the temperature dependence of the rate constant is given by the Arrhenius equation:

$k = A e^{-E_a/(RT)}$

where:

$k$ = rate constant
$A$ = Arrhenius frequency factor
$E_a$ = activation energy
$R$ = gas constant
$T$ = absolute temperature

As temperature $T$ increases, the factor

$e^{-E_a/(RT)}$

increases, because $\dfrac{E_a}{RT}$ decreases.

Therefore, $k$ increases with temperature.

This increase is not linear. The Arrhenius relation shows that $k$ rises exponentially with $T$ , so the graph of $k$ vs $T$ is a curved increasing graph.
Whether the reaction is endothermic or exothermic does not directly determine the $k$ vs $T$ graph. The rate constant depends primarily on the activation energy through the Arrhenius equation. For ordinary reactions with positive activation energy, $k$ increases with $T$ .
Hence, the correct graph must be the one showing rate constant increasing with temperature in a curved manner.

Thus, the correct option is A.

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