Half life of a first order reaction is $900 \ \text{min}$ at $400 \ K$. Find its half life at $300 \ K$. Given: $\frac{E_a}{2.303 \ R} = 1.3056 \times 10^3 \ K$. (in $\text{min}$)

The number of collisions depend upon

For a reaction,the value of rate constant at $300 \ K$ is $6.0 \times 10^5 \ s^{-1}$. The value of Arrhenius factor $A$ at infinitely high temperature is

The rate constant of a reaction is $2 \times 10^{-3} \ min^{-1}$ at $300 \ K$. By increasing the temperature by $10 \ K$,its value becomes double. Calculate the energy of activation $(E_a)$ and the rate constant at $320 \ K$.

The number of molecules with energy greater than the threshold energy for a reaction increases five-fold by a rise of temperature from $27^{\circ} C$ to $42^{\circ} C$. Its energy of activation in $J \ mol^{-1}$ is.............. (Take $\ln 5 = 1.6094$; $R = 8.314 \ J \ mol^{-1} K^{-1}$)

Consider the following statements:
$(i)$ Increase in concentration of reactant increases the rate of a zero order reaction
$(ii)$ Rate constant $k$ is equal to $A$ if $E_a = 0$
$(iii)$ Rate constant $k$ is equal to $A$ if $E_a = \infty$
$(iv)$ $\log_e k$ vs $T$ is a straight line
$(v)$ $\log_e k$ vs $1/T$ is a straight line
Which of the following statements are correct?