The temperature coefficient for a reaction in which food deteriorates is $2$. Then food deteriorates ...... times as rapidly at $25\,^oC$ as it does at $5\,^oC$.

Match the column $I$ with column $II$ :

$a$. Rate constant for first order reaction	$i$. $mol \ lit^{-1} \sec^{-1}$
$b$. Molarity	$ii$. $\frac{k \times 1000}{M}$
$c$. Rate constant for zero order reaction	$iii$. $second^{-1}$
$d$. Limiting molar conductivity	$iv$. $\frac{\text{moles of solute}}{\text{Volume of solution (lit)}}$

Under identical reaction conditions,for a reactant with an initial concentration of $1.386 \, M$,the time taken for the concentration to become half is $40 \, s$ for a first-order reaction and $20 \, s$ for a zero-order reaction. The ratio of the rate constant of the first-order reaction $(K_1)$ to the rate constant of the zero-order reaction $(K_0)$ is ......... $mol \, L^{-1}$.

Match the rate expressions in List-$I$ for the decomposition of $X$ with the corresponding profiles provided in List-$II$. $X_s$ and $k$ are constants having appropriate units.

Write the half-life $({t_{1/2}})$ equation and its unit for the following reactions:
$(i)$ Zero order reaction
$(ii)$ First order reaction

For a chemical reaction, half-life period $(t_{1/2})$ is $10 \ minutes$. How much reactant will be left after $20 \ minutes$ if one starts with $100 \ moles$ of reactant and the order of the reaction is $(i)$ zero, $(ii)$ one, and $(iii)$ two?