For a first-order reaction $SO_2Cl_2 \to SO_2 + Cl_2$ at $320\, ^\circ C$,the rate constant is $2.2 \times 10^{-5}\, s^{-1}$. What percentage $(\%)$ of $SO_2Cl_2$ will decompose upon heating for $90\, min$?

For a first-order reaction,the concentration decreases from $800 \ mol/dm^3$ to $50 \ mol/dm^3$ in $2 \times 10^4 \ s$. What is the rate constant of the reaction?

Sucrose hydrolyses in acid solution into glucose and fructose following first order rate law with a half-life of $3.33 \ h$ at $25^{\circ} C$. After $9 \ h$,the fraction of sucrose remaining is $f$. The value of $\log _{10} (\frac{1}{f})$ is ..... $\times 10^{-2}$. (Rounded off to the nearest integer) [Assume : $\ln 10 = 2.303, \ln 2 = 0.693$ ]

For the first-order reaction $N_2O_5 \to 2NO_2 + \frac{1}{2}O_2$,the half-life at $30 \ ^\circ C$ is $24 \ \text{hours}$. Starting with $10 \ g$ of $N_2O_5$,how many grams of $N_2O_5$ will remain after $96 \ \text{hours}$ (in $g$)?

For a first order reaction,the half-life period is $5 \ min$. What time will it take for $99.9 \%$ completion of the reaction (in $min$)?

The time required for $60 \%$ completion of a first order reaction is $50 \ min$. The time required for $93.6 \%$ completion of the same reaction will be (in $min$)