If the rate constant of a first order reaction is $4.606 \times 10^{-3} \ s^{-1}$,then find the time required for $400 \ g$ of the reactant to reduce to $50 \ g$. (in $min$)

$A$ first-order reaction takes $69.3 \ min$ to complete $50\%$ of the reaction. How much time (in $min$) will it take to complete $80\%$ of the reaction?

$A$ first order reaction has a rate constant of $1.5 \times 10^{-3} \ s^{-1}$. How long will $5.0 \ g$ of this reactant take to reduce to $3.0 \ g$?

The reaction $X \rightarrow$ products is a first order reaction. In $40 \ min$,the concentration of $X$ changes from $1.0 \ M$ to $0.25 \ M$. What is the rate of reaction when $[X] = 0.1 \ M$? $(\log 4 = 0.60)$

In a first order reaction,the concentration of the reactant is reduced from $0.6 \ mol \ L^{-1}$ to $0.2 \ mol \ L^{-1}$ in $5 \ min$. What is the rate constant of the reaction (in $min^{-1}$)? $(\log 3 = 0.4771)$

$A_{(g)} \rightarrow B_{(g)} + C_{(g)}$ is a first order reaction.

Time	$t$	$\infty$
$P_{\text{system}}$	$P_t$	$P_{\infty}$

The reaction was started with reactant $A$ only. Which of the following expressions is correct for the rate constant $k$?