Question:

The temperature dependence of rate constant $(k)$ of a chemical reaction is written in terms of Arrhenius equation $k=A e^{-E_{\alpha} / R T}$. Activation energy $\left(E_{a}\right)$ of the reaction can be calculated by ploting

Updated On: Jul 27, 2022
  • $ \log \,k\,vs\,T $
  • $ \log \,k\,vs\,\frac{1}{T} $
  • $ k\,\,vs\,T $
  • $ k\,\,vs\,\,\,\frac{1}{\log T} $
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The Correct Option is B

Solution and Explanation

$k=A e^{-E_{a} / R T}$ $\log k=\log A-\frac{E_{a}}{2.303 R T}$ Comparing this equation with straight line $y=m x+ c$ $y=\log k$ and $x-\frac{1}{T}$ $\therefore E_{a}$ is calculated with the help of slope by plotting the curve between $\log k$ and $\frac{1}{T}$.
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Concepts Used:

Rate of a Chemical Reaction

The rate of a chemical reaction is defined as the change in concentration of any one of the reactants or products per unit time.

Consider the reaction A → B,

Rate of the reaction is given by,

Rate = −d[A]/ dt=+d[B]/ dt

Where, [A] → concentration of reactant A

[B] → concentration of product B

(-) A negative sign indicates a decrease in the concentration of A with time.

(+) A positive sign indicates an increase in the concentration of B with time.

Factors Determining the Rate of a Reaction:

There are certain factors that determine the rate of a reaction:

  1. Temperature
  2. Catalyst
  3. Reactant Concentration
  4. Chemical nature of Reactant
  5. Reactant Subdivision rate