For a reaction,the activation energy $E_{a} = 0$ and the rate constant at $200 \ K$ is $1.6 \times 10^{6} \ s^{-1}$. The rate constant at $400 \ K$ will be (given $R = 8.314 \ J \ K^{-1} \ mol^{-1}$):

The reaction: $Cr_{2}O_{3} + 2 Al \rightarrow Al_{2}O_{3} + 2 Cr$ $\quad (\Delta_{r}G^{\Theta} = -421 \ kJ)$ is thermodynamically feasible as is apparent from the Gibbs energy value. Why does it not take place at room temperature?

The temperature-dependent equation for the rate constant is written as:

The plot of $\log k_f$ versus $1 / T$ for a reversible reaction $A_{(g)} \rightleftharpoons P_{(g)}$ is shown. Pre-exponential factors for the forward and backward reactions are $10^{15} \ s^{-1}$ and $10^{11} \ s^{-1}$,respectively. If the value of $\log K$ for the reaction at $500 \ K$ is $6$,the value of $|\log k_b|$ at $250 \ K$ is $\qquad$ $[K = \text{equilibrium constant of the reaction}, k_f = \text{rate constant of forward reaction}, k_b = \text{rate constant of backward reaction}]$

Find True $(T)$ and False $(F)$ statements in the following:
$1.$ Effective collision depends on rate.
$2.$ When the reactant converts into product,the bonds in the reactant break and new bonds form.
$3.$ The breaking of old bonds and the formation of new bonds take place simultaneously.

$A$ chemical reaction was carried out at $300 \, K$ and $280 \, K$. The rate constants were found to be $K_1$ and $K_2$ respectively. The energy of activation is $1.157 \times 10^4 \, cal \, mol^{-1}$ and $R = 1.987 \, cal \, K^{-1} \, mol^{-1}$. Then: