Rate of a first order reaction is $1.5 \times 10^{-2} \ mol \ L^{-1} \ minute^{-1}$ at $0.5 \ M$ concentration of reactant,calculate half life of reaction.

Time required to decompose $SO_{2}Cl_{2}$ to half of its initial amount is $60 \ minutes$. If the decomposition is a first order reaction,calculate the rate constant of the reaction.

Identify True $(T)$ and False $(F)$ statements of the following for a first order reaction $R \rightarrow P$.
$(i) \ t_{1/2} \propto [R]_0^0$
$(ii) \ t_{1/2} = \frac{0.693}{k}$

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 $90\, min$?

$A$ first-order reaction decomposes such that the time taken for $1/8$ and $1/10$ of the initial concentration to decompose are $t_{1/8}$ and $t_{1/10}$ respectively. Find the value of $\frac{t_{1/8}}{t_{1/10}} \times 10$. (Given: $\log_{10} 2 = 0.3$)

Reaction $A_{(g)} \rightarrow 2B_{(g)} + C_{(g)}$ is a first order reaction. It was started with pure $A$.

$t/min$	Pressure of system at time $t/mm \ Hg$
$10$	$160$
$\infty$	$240$

Which of the following option is incorrect?