Slope of the graph between $\log \frac{[A]_0}{[A]_t}$ ($y$-axis) and time ($x$-axis) for a first-order reaction is equal to:

Isomerisation of gaseous cyclobutene to butadiene is a first order reaction. At $T \ K$,the rate constant of the reaction is $3.3 \times 10^{-4} \ s^{-1}$. What is the time required (in $min$) to complete $90 \%$ of this reaction at the same temperature? $(\log 2 = 0.3)$

Which equation represents the $1/4^{th}$ life for a first-order reaction?

In a first-order reaction $A \rightarrow B,$ if $k$ is the rate constant and the initial concentration of the reactant $A$ is $0.5 \ M,$ then the half-life is:

For a first-order reaction $A \to B$,what will be the slope of the graph of $t$ versus $\log(a - x)$?

For the first-order gaseous reaction $A_{(g)} \to 2B_{(g)} + C_{(g)}$,the expression for the rate constant $K$ in terms of initial pressure $P_0$ and total pressure $P_t$ at time $t$ is: