Half-life periods for a reaction at initial concentrations of $0.1 \ M$ and $0.01 \ M$ are $5$ and $50$ minutes,respectively. The order of reaction is

For the first order decomposition reaction of $N_2O_5$,it is found that -
$(a)$ $2N_2O_5 \rightarrow 4NO_{2(g)} + O_{2(g)}$ ; $-\frac{d[N_2O_5]}{dt} = k[N_2O_5]$
$(b)$ $N_2O_5 \rightarrow 2NO_{2(g)} + 1/2 O_{2(g)}$ ; $-\frac{d[N_2O_5]}{dt} = k'[N_2O_5]$
Which of the following is true?

For the reaction,$PCl_5 \longrightarrow PCl_3 + Cl_2$,the rate and rate constant are $1.02 \times 10^{-4} \ mol \ L^{-1} \ s^{-1}$ and $3.4 \times 10^{-5} \ s^{-1}$ respectively at a given instant. The molar concentration of $PCl_5$ at that instant is

Rate law for the reaction,$C_2H_5I_{(g)} \rightarrow C_2H_{4_{(g)}} + HI_{(g)}$ is $r = k[C_2H_5I]$. What is the order and molecularity of this reaction?

Which one of the following statements regarding the order of a reaction is not correct?

For the reaction,$2N_2O_5 \to 4NO_2 + O_2$,the rate equation can be expressed in two ways $-\frac{d[N_2O_5]}{dt} = k[N_2O_5]$ and $+\frac{d[NO_2]}{dt} = k'[N_2O_5]$. $k$ and $k'$ are related as: