If the concentration of the reactant increases by '$x$' for a first-order reaction,then $K = $?

$PCl_{5(g)} \rightarrow PCl_{3(g)} + Cl_{2(g)}$
In the above first order reaction,the concentration of $PCl_{5}$ reduces from an initial concentration of $50 \ mol \ L^{-1}$ to $10 \ mol \ L^{-1}$ in $120 \ minutes$ at $300 \ K$. The rate constant for the reaction at $300 \ K$ is $X \times 10^{-2} \ min^{-1}$. The value of $X$ is $......$
$[$ Given $\log 5 = 0.6989 ]$

For a first-order reaction,the time taken for the concentration of the reactant to reach $3/4$ of its initial value is $t_{1/4}$. If the rate constant for the reaction is $K$,then $t_{1/4}$ can be expressed as: (in $/K$)

Identify True $(T)$ and False $(F)$ statements of the following for a first-order reaction $R \rightarrow P$.
Statement $I$: $k = \frac{1}{(t_1 - t_2)} \ln \frac{[R]_1}{[R]_2}$
Statement $II$: $k = -\frac{1}{(t_1 - t_2)} \ln \frac{[R]_2}{[R]_1}$

The half-life period of a first-order reaction is given by:

For a first order reaction, the half-life is $5 \text{ hour}$. What time is required to reduce $10 \text{ g}$ of reactant to $2.5 \text{ g}$ (in $\text{ hour}$)?