(1) A graph of rate of a reaction and concentration : The differential rate law for first order reaction, `A to` Products is represented as,
Rate` = -(d[A])/(dt) = k[A]`
`therefore` Rate `= k xx [A]_(t)" "(y= mx)`
when the rate of a first order reaction is plotted against concentration, `[A]_(t)` , a straight line graph is obtained.
With the increase in the concentration `[A]_(t)`, rate R, increases. The slope of the line gives the value of rate constant k.
(2) A graph of concentration against time : When the concentration of the reactant is plotted against time t, a curve is obtained. The concentration `[A]_(t)` of the reactant decreases exponentially with time. The variation in the concentration can be represented as,`[A]_(t)= [A]_(0) e^(-kt)`
where [A], and [A] are initial and final concentrations the reactant and k is the rate constant. The time required to complete the first order reaction is infinity.
(3) A graph of half-life period and concentration :
The half -life period `t_(1//2)` of a first order reaction is given by `t_(1//2) = (0.693)/(k)`
where k is the rate constant .
For the given reaction at constant temperature , `t_(1//2)` is constant adn independent of the concentration of the reactant.
Hence when a graph of `t_(1//2)` is plotted against concentration, a stringht line parallel to the concentration axis (slope = zero) is obtained.
