Which of the following options correctly represents the relationship between $t_{7/8}$ and $t_{1/2}$ where $t_{7/8}$ represents the time required for the concentration to become $1/8$ of the original for a reaction of order $n$?

The rate law for the reaction $A + B \rightarrow P$ is given by $\text{rate} = k[A]^2[B]$. The rate constant of the reaction at $300 \text{ K}$ is $6.0 \text{ M}^{-2} \text{s}^{-1}$. Calculate the rate of the reaction when $[A] = 1 \text{ M}$ and $[B] = 0.2 \text{ M}$. (in $\text{ M s}^{-1}$)

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 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 $[B] = 0.25 \ mol \ dm^{-3}$.

$A$ complex reaction takes place in $2$ steps:
$(I)$ $NO_{2(g)} + F_{2(g)} \rightarrow NO_2F_{(g)} + F_{(g)}$ (slow)
$(II)$ $F_{(g)} + NO_{2(g)} \rightarrow NO_2F_{(g)}$ (fast)
Identify the reaction intermediate.

The rate law for the reaction below is given by the expression $Rate = k[A][B]$.
$A + B \to \text{Product}$
If the concentration of $B$ is increased from $0.1 \ M$ to $0.3 \ M$,keeping the concentration of $A$ constant at $0.1 \ M$,the rate constant $(k)$ will be: