Answer the following questions on the basis of the given curve for a first order reaction `A to P:`
(a) What is the relation between slope of this line and rate constant?
(b) Calculate the rate constant of the above reaction if the slope is `2xx10^(-4)s^(-1)`.
(c ) Derive the relationship between half-life of a first order reaction and its rate constant.

Explanation

(a) Slope of the straight line is given by slope `=(k)/(2.303)`
(b) `2xx10^(-4)s^(-1)=(k)/(2.303) or k=2.303xx2xx10^(-4)s^(-1) or k=4.606xx10^(-4)s^(-1)`
(c ) `t=(k)/(2.303)"log"([R]_(0))/([R])`
For half change `[R]=(1)/(2)[R]_(0)`
Substituting the values in the equation of first order, we have
`t_(1//2)=(2.303)/(k) log 2 or t_(1//2)=(2.303)/(k) xx 0.3010 or t_(1//2)=(0.693)/(k)`