Engineering
Chemistry
Integrated Rate Law
Question

Match the graphs given in column I to the parameters and conditions.
{Given : ROR represents rate of reaction , [R] represents concnetration of reactant, t1/2 represents half life, [R]0 represents initial concentration of reactant }.
All other units have their usual meaning. Assume reactions to involve only one reactant unless otherwise stated. 

Column I Column II
(P) Graph of lnKeq vs 1T for exothermic reactions with = 0  and no entropy (ΔnCPm)Rxn change
(Q) Graph of ROR vs [R] for a first order reaction 
(R) Graph of t1/2 vs [R]0 for ether zero order, first order  or second order.
(S) Graph of [R] vs time for a zero order reaction.
  (T) Graph of rate of reaction vs [R] for a (–1) order reaction.
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Solution

(P) lnKP vs 1T   Exothermic reaction : ΔH° = – ve ,ΔS° = 0 
    ΔG° = – RT ln KP
    ΔH° – TΔS° = – RT ln KP
    ΔH° = – RT ln KP                
    ln KP = – ΔH°R×1T    

                
    As ΔH° = – ve    slope = +ve
(Q)  ROR = K [R]' first order reaction         
       
(S) R0 → R = Kt    zero order reaction
R = R0 – Kt
        
(T) Rate of reaction = K[R]–1
ROR × [R] = K