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?

$A \rightarrow$ products ($1^{st}$ order reaction). Three sets of experiment were performed for a reaction under similar experimental conditions. Run $1 \Rightarrow 100 \ mL$ of $10 \ M$ solution of reactant $A$. Run $2 \Rightarrow 200 \ mL$ of $10 \ M$ solution of reactant $A$. Run $3 \Rightarrow 100 \ mL$ of $10 \ M$ solution of reactant $A + 100 \ mL$ of $H_2O$ added. The correct variation of rate of reaction is:

The decomposition of dimethyl ether leads to the formation of $CH_4$,$H_2$ and $CO$ and the reaction rate is given by
Rate $= k [CH_3OCH_3]^{3/2}$
The rate of reaction is followed by increase in pressure in a closed vessel,so the rate can also be expressed in terms of the partial pressure of dimethyl ether,i.e.
Rate $= k (p_{CH_3OCH_3})^{3/2}$
If the pressure is measured in $bar$ and time in $minutes$,then what are the units of rate and rate constants?

For a chemical reaction,$m A \rightarrow x B$,the rate law is $r = k[A]^{2}$. If the concentration of $A$ is doubled,the reaction rate will be,

For the reaction $2 NO_{(g)} + Cl_{2_{(g)}} \rightarrow 2NOCl_{(g)}$,when the concentration of $Cl_2$ is doubled,the rate of the reaction becomes twice the original rate. When the concentration of $NO$ is doubled,the rate becomes four times the original rate. What is the overall order of the reaction?

The rate law expression for the reaction $aA + bB \to P$ is $\text{rate} = K [A]^p [B]^q$. The order of the reaction is