The initial pressure of the system before decomposition for a first order gas phase reaction $A_{(g)} \rightarrow B_{(g)}+C_{(g)}$ was $\mathrm{P}_{\mathrm{i}}$. After lapse of time ' t ', total pressure of the system increased by ' x ' units and became $\mathrm{P}_{\mathrm{t}}$. The rate constant ' k ' for the reaction is given as:

A first order reaction is $50 \%$ complete in 30 minutes at 300 K and in 10 minutes at 320 K . The activation energy of the reaction ( $E_a$ ) is: $\left[R=8.314 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1} ; \log 2=0.3010 ; \log 3=0.4771\right]$

Which of the following factors is altered by the addition of a catalyst during a chemical reaction?

In the synthesis of $\mathrm{NH}_3$ from $\mathrm{H}_2$ and $\mathrm{N}_2$, if $6 \times 10^{-2}$ mole of hydrogen disappears in 10 minutes, the number of moles of $\mathrm{NH}_3$ formed in 0.3 minutes is: