For the reaction $3 \, A_{(g)} \xrightarrow{K} B_{(g)} + C_{(g)}$,$K$ is $10^{-14} \, L/mol \cdot min$. If $[A] = 0.5 \, M$,then the value of $-\frac{d[A]}{dt}$ (in $M/sec$) is:

For the reaction $2A + B \rightarrow \text{Product}$,the following mechanism is given. What is the order of the reaction?
$2A \rightleftharpoons A_2$ (fast)
$A_2 + B \rightarrow P$ (slow)

$A$ reaction involving different reactants can never be a/an......?

If the concentration of reactant $A$ is increased by $10$ times,the rate of reaction becomes $100$ times. What is the order of reaction if the rate law is,$\text{rate} = k[A]^{x}$?

Which will be the unit of rate constant for the reaction having Rate $= K[A]^{\frac{1}{2}} \cdot [B]^{\frac{3}{2}}$ ?

The rate law for the reaction $A + B \rightarrow \text{product}$ is given by $\text{rate} = k[A][B]$. Calculate $[A]$ if the rate of reaction and rate constant are $0.25 \ mol \ dm^{-3} \ s^{-1}$ and $6.25 \ mol^{-1} \ dm^3 \ s^{-1}$ respectively,and $[B] = 0.25 \ mol \ dm^{-3}$.