Question
Given below are two statements :
$R = 8.314\text{ }J{\text{ }K}^{- 1}{\text{ }mol}^{- 1}$ and $1cal = 4.2\text{ }J$
Statement I : When $Ea = 12.6kcal/mol$, the room temperature rate constant is doubled by a $10^{\circ}C$ increase in temperature ( 298 K to 308 K )
Statement II : For a first order reaction $A \rightarrow B$,
Here $\lbrack A\rbrack_{0}$ is the initial concentration of A and $t_{1/2}$ is half-life of reaction.
In the light of the above statements, choose the correct answer from the option given below :
Options
Solution
Sol. [Key Concept: Arrhenius $\ln\frac{k_{2}}{k_{1}} = \frac{E_{a}}{R}(\frac{10}{298 \times 308}) = 0.693$ so the rate doubles (Statement I true); but $t_{1/2} \propto \lbrack A\rbrack_{0}$ means a zero-order reaction, not first order, so Statement II is false.]
S-I : $ln\left( \frac{K_{2}}{{\text{ }K}_{1}} \right) = \frac{12.6 \times 10^{3}}{\left( \frac{8.314}{4.2} \right)}\left\lbrack \frac{10}{298 \times 308} \right\rbrack$
$${\Rightarrow ln\left( \frac{K_{2}}{{\text{ }K}_{1}} \right) = 0.693 }{\Rightarrow \frac{K_{2}}{{\text{ }K}_{1}} = 2 }$$S-II : For $1\ ^{\text{st}\text{~}}$ order
$\mathbf{t}_{\mathbf{1/2}} = \frac{ln2}{\text{ }K};t_{1/2} \propto \lbrack\text{ }A\rbrack^{0} =$ constant.
Statement-I is true but statement-II is false.
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