For a hypothetical reaction $A + B + C \rightarrow \text{Product}$,the rate is given by $r = -\frac{d[A]}{dt} = K[A]^{1/2}[B]^{1/3}[C]^{1/4}$. The order of the reaction is:

The unit of the rate constant for a second-order reaction is ......

The rate equation for the reaction $2A + B \longrightarrow \text{products}$ is $\text{rate} = k[A][B]^2$. If $k$ at $T \, K$ is $5.0 \times 10^{-6} \, mol^{-2} \, L^2 \, s^{-1}$,the initial rate of the reaction,when $[A] = 0.05 \, mol \, L^{-1}$ and $[B] = 0.1 \, mol \, L^{-1}$ is:

........ of a reaction cannot be determined experimentally.

State whether the following statements are true $(T)$ or false $(F)$.
$(a)$ In a pseudo first order reaction,the rate and rate constant are determined with respect to the reactant present in lower concentration.
$(b)$ The hydrolysis of an ester is carried out in the presence of an excess of water in an acidic medium.
$(c)$ The hydrolysis of an ester is a second order reaction.

The rate constant for the reaction,$2N_2O_5 \to 4NO_2 + O_2$ is $3.0 \times 10^{-4} \ s^{-1}$. If the reaction starts with $1.0 \ mol \ L^{-1}$ of $N_2O_5$,calculate the rate of formation of $NO_2$ at the moment when the concentration of $O_2$ is $0.1 \ mol \ L^{-1}$.