The rate constant for a first order reaction is given by the following equation:
$\ln k = 33.24 - \frac{2.0 \times 10^{4} \, K}{T}$
The activation energy for the reaction is given by $... \, kJ \, mol^{-1}$. (In nearest integer)
(Given: $R = 8.3 \, J \, K^{-1} \, mol^{-1}$)

The rate constants for the decomposition of acetaldehyde have been measured over the temperature range $700-1000 \ K$. The data has been analysed by plotting a $\ln \ k \ vs \ \frac{10^{3}}{T}$ graph,which gives a slope of $-18.5$. The value of activation energy for the reaction is $...... \ kJ \ mol^{-1}$. (Nearest integer) (Given: $R = 8.31 \ J \ K^{-1} \ mol^{-1}$)

For the reaction of $H_2$ with $I_2$,the rate constant is $2.5 \times 10^{-4} \ dm^3 \ mol^{-1} \ s^{-1}$ at $327 \ ^oC$ and $1.0 \ dm^3 \ mol^{-1} \ s^{-1}$ at $527 \ ^oC$. The activation energy for the reaction,in $kJ \ mol^{-1}$ is: $(R = 8.314 \ J \ K^{-1} \ mol^{-1})$

$A$ reaction has an activation energy of $209 \, kJ \, mol^{-1}$. The rate increases $10$-fold when the temperature is increased from $27^{\circ} C$ to $X^{\circ} C$. The temperature $X$ is closest to
[Gas constant,$R = 8.314 \, J \, mol^{-1} \, K^{-1}$ ]

$A_{(g)} + B_{(g)} \rightleftharpoons C_{(g)} + D_{(g)}$
The curves $M$ and $N$ represent the variation of energy with reaction coordinate for the reaction in absence and presence of catalyst.
Which value represents the activation energy $(E_a)$ for the backward reaction in the presence of catalyst?

In which of the following cases is the percentage increase in rate constant maximum?

$Case$	$E_a \ (kcal/mol)$	$Temp. \ Change \ (K)$
$I$	$40$	$200 - 210$
$II$	$80$	$200 - 210$
$III$	$40$	$300 - 310$
$IV$	$80$	$300 - 310$