The correct graphical representation of first-order reaction is:

(a)  (b)
(c) (d)

   

1. (a) and (b) 2. (b) and (c)
3. (c) and (d) 4. (a) and (d)

HINT: k=2.303tlogRoR

Explanation:

Step 1:

For the first-order reaction

k=2.303tlogRoR
logRoR=k2.303t            ......(1)

The first equation is the same as y=mx+c. Thus, straight-line graph is obtained. The slope is k2.303

The correct plot between log R0[R} vs t can be represented by (d)

Step 2:

The time taken for any fraction of the reaction to complete is independent of the initial concentration Let, us consider it for half of the reaction to complete.

t = 2.303klog aa-x
For half life    
t = t1/2; x=a2
t1/2=2.303klog aaa2
t1/2=2.303klog 2
 t1/2=0.693k

t1/2 is independent of initial concentration. Hence, the correct plot of t1/2, and [Ro] can be represented by (a)