The thermal decomposition of a compound is of first order. If a sample of the compound decomposes $50\%$ in $120 \, minutes$,in what time will it undergo $90\%$ decomposition?

Decomposition of $A$ is a first order reaction at $T \ K$ and is given by $A_{(g)} \rightarrow B_{(g)} + C_{(g)}$. In a closed $1 \ L$ vessel, $1 \ bar$ of $A_{(g)}$ is allowed to decompose at $T \ K$. After $100 \ minutes$, the total pressure was $1.5 \ bar$. What is the rate constant (in $min^{-1}$) of the reaction? (Given: $\log 2 = 0.3$)

For a reaction,$X_{(g)} \to Y_{(g)} + Z_{(g)}$,the half-life period is $10 \ min$. In what period of time would the concentration of $X$ be reduced to $10 \%$ of its original concentration? $........... \ min$

$A$ first order reaction has the rate constant,$k = 4.6 \times 10^{-3} \ s^{-1}$. The number of correct statement/s from the following is/are
Given : $\log 3 = 0.48$
$A.$ Reaction completes in $1000 \ s$.
$B.$ The reaction has a half-life of $500 \ s$.
$C.$ The time required for $10 \ \%$ completion is $25$ times the time required for $90 \ \%$ completion.
$D.$ The degree of dissociation is equal to $(1 - e^{-kt})$.
$E.$ The rate and the rate constant have the same unit.

The rate constant for a first order reaction is $4.606 \times 10^{-3} \ s^{-1}$. The time required to reduce $2.0 \ g$ of the reactant to $0.2 \ g$ is......... $s$

Show that in a first order reaction,the time required for completion of $99.9 \%$ is $10$ times the half-life $(t_{1/2})$ of the reaction.