At $380 °\mathrm{C}$, the half-life period for the first order decomposition of ${\mathrm{H}}_2{\mathrm{O}}_2$ is $360 \min$. The energy of activation of the reaction is $200 \mathrm{kJ} {\mathrm{mol}}^{-1}$. Calculate the time required for $75\%$ decomposition at $450 °\mathrm{C}$.

For the elementary reaction $2 \mathrm{A}+{\mathrm{B}}_2⟶2\mathrm{AB}$. Calculate how much the rate of reaction will change if the volume of the vessel is reduced to one third of its original volume?

A first order reaction $75\%$ Completed in $72 \min$. How long time will it take for $87.5\%$ completion

A first order reaction has a rate constant $1.5\times {10}^{-3}{\sec }^{-1}$. How long will $5.0 \mathrm{g}$ of this reactant take to reduce to$1.25 \mathrm{g}$.

Report your answer in the nearest integer value.

A drug is known to be ineffective after it has decomposed $30\%$. The original concentration of a sample was $500$ units / $\mathrm{mL}$. when analyzed $20$ months later, the concentration was found to be $420$ units/$\mathrm{mL}$ . Assuming that decomposition is of I order, what will be the expiry time of the drug?

At $100°\mathrm{C}$ the gas reaction $\mathrm{A}⟶2 \mathrm{B}+\mathrm{C}$ was observed to be of first order. On starting with pure $\mathrm{A}$ it is found that at the end of $10$ minutes the total pressure of system is $176 \mathrm{mm}.\mathrm{Hg}$ and after a long time 270 $\mathrm{mmHg}$. From these data find initial pressure of $\mathrm{A}$.

The following data were obtained in experiment on inversion of cane sugar.

Show that the reaction is of first order. After what time would you expect a zero reading in polarimeter?

Decomposition of reaction $3 \mathrm{A}\left(\mathrm{g}\right)⟶2 \mathrm{B}\left(\mathrm{g}\right)+2\mathrm{C}\left(\mathrm{g}\right)$ follows first order kinetics. Starting with pure '$\mathrm{A}$' pressure developed after $20 \min$ and infinite time are $3.5$ and $4 \mathrm{atm}$ respectively.

What is time taken for $75\%$ decomposition of $\text{A}$?