An endothermic reaction with a high activation energy for the forward reaction is represented by the diagram:

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.

The following graph shows the variation of rate constant $(k)$ with temperature $(T)$. Which graph follows the Arrhenius equation?

Fill in the blanks:
$(1)$ The time required to complete $99.9\%$ of a first-order reaction is ............ times the ${t_{1/2}}$.
$(2)$ The reaction in which the rate is given by $-\frac{d[R]}{dt} = k$ has an order of reaction equal to ........
$(3)$ For the reaction $[R] = [R]_0 e^{-kt}$,the order is .......

Determine whether the following statements are True or False:
$(a)$ The rate of reaction can be decreased by decreasing the concentration of reactant.
$(b)$ Graphite quickly changes to Diamond.
$(c)$ The rate of corrosion of iron is fast.
$(d)$ The meaning of kinesis in Greek is movement.

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 $5\,^oC$.