The following graph shows the relationship between $(a-x)^{-1}$ and time $t$ for a second-order reaction. If $\theta = \tan^{-1}(1/2)$ and $OA = 2 \ L \ mol^{-1}$,then the rate at the start of the reaction will be (in $mol \ L^{-1} \ min^{-1}$):

In the reaction $A \rightarrow B$,if the concentration of $A$ is doubled,then the reaction rate increases by $1.59$ times. What will be the order of the reaction?

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?

The rate law for the reaction $A + B \rightarrow \text{product}$ is $\text{rate} = k[A][B]$. When will the rate of reaction increase by a factor of $2$?

For the reaction $H_{2(g)} + Br_{2(g)} \rightarrow 2HBr_{(g)}$,the experimental data suggests the rate law is $\text{Rate} = K[H_2][Br_2]^{1/2}$. Find the order of the reaction and its molecularity.

Consider the reaction $2 \ A + 2 \ B \rightarrow C + 2 \ D$. If the concentration of $A$ is doubled at constant $B$,the rate increases by a factor of $4$. If the concentration of $B$ is doubled at constant $A$,the rate is doubled. What is the rate law?