A first order reaction, A → B, requires activation energy of 70 kJ mol –1 . When a 20% solution of A was kept at 25ºC for 20 minutes, 25% decomposition took place. What will be the percentage decomposition in the same time in 30% solution maintained at 40ºC? Assume that activation energy remains constant in this range of temperature.
Text Solution
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Sol. According to Arrhenius equation, k = Ae –Ea/RT by solving this equation w.r.t the range of T1 and T2 absolute temperature, we get at a following equation :
∴ Ea = 
log 10 
70.0 × 103 = 
log 10 
On solving we get
= 3.872
(Ratio of rate constant at two different temperatures)
....(1)
For first order reaction,
k1 = 
log 10 
k1 = 
log 10 
= 0.014386 min–1
From equation (1)
= 3.872
Thus, at 313 K
k2 = 0.05571 min–1
∴ 0.05571 = 
log 10 
∴ x = 67.17%
Thus, 67.17% decomposition take place at
40ºC (313 K)
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