Question

expression of 1st order of reaction

Answer 1

k= (2.303/t)log[Ro]/[R]  for first order reactions. OR
kt= ln[Ro]/[R]

Answer 2

A first-order reaction is a reaction that proceeds at a rate that depends linearly on only one reactant concentration.

The Differential Representation

Differential rate laws are generally used to describe what is occurring on a molecular level during a reaction, whereas integrated rate laws are used for determining the reaction order and the value of the rate constant from experimental measurements. The differential equation describing first-order kinetics is given below:
Rate=−d[A]/dt=k[A]¹==k[A]

The "rate" is the reaction rate (in units of molar/time) and kk is the reaction rate coefficient (in units of 1/time). However, the units of kk vary for non-first-order reactions