Question

Graph between Concentration and Time for a first order reaction.

Answer 1

Hint :To plot a graph between concentration and time one must know the relation between these two quantities. Also the relation varies with the type of reaction whether it is zero order, first order reaction and so on.

Complete Step By Step Answer:
The order of reaction is defined as the sum of the powers of the concentration of the reactants in the rate law expression. The rate law is an equation that links the initial or forward reaction rate with the concentrations of the reactants and rate coefficients. Reaction can be first order, second order etc.
In a first order reaction the reaction rate is linearly dependent on the concentration of only one reactant. That means that in a first order reaction the chemical reaction in which the rate varies based on the changes in the concentration of only one of the reactants. Thus the order of these reactions is equal to one. The mathematical representation of first order reaction is-
The differential rate law for first order reaction is
 $\ln [A]=-kt+\ln [A_{\circ }]$
 $[A]=[A_{\circ }]e^{-kt}$
This expression is an integrated form of the first order rate law, where
 $A$ is the concentration at time $t$ and the expression $[A_{\circ }]$ is the concentration at time zero and $k$ is the constant for first order reaction.
Graphical representation-
The concentration and time graph for first order reaction is

For the expression $\ln [A]=-kt+\ln [A_{\circ }]$ , this is plotted as-

Note :
With the help of the graph one can determine that the concentration of the reactant decreases exponentially with time which is a characteristic feature of the first order reaction. The rate of the reaction is proportional to the first power of the concentration of the reactants. Also the half life is independent of the initial and final concentration of the reactants for the first order reaction.