Fill in the blanks:
$(1)$ If $t_{1/2} = \frac{0.693}{k}$,then the order of reaction is .......... .
$(2)$ For a zero order reaction,$t_{1/2}$ is proportional to .......... of the initial concentration.
$(3)$ In a first order reaction,the rate of reaction is proportional to the .......... exponent of the concentration of the reactant.

(N/A) $(1)$ The expression $t_{1/2} = \frac{0.693}{k}$ is characteristic of a first-order reaction.
$(2)$ For a zero-order reaction,$t_{1/2} = \frac{[R]_0}{2k}$,so $t_{1/2}$ is directly proportional to the initial concentration $[R]_0$.
$(3)$ For a first-order reaction,the rate law is $Rate = k[R]^1$,meaning the rate is proportional to the first $(1^{st})$ exponent of the concentration of the reactant.