The data in the table below were obtained for the reaction: 2 ClO_2(aq) + 2OH^-

Question

The data in the table below were obtained for the reaction: 2 ClO_2(aq) + 2OH^- (aq) rightarrow ClO^-_3 (aq) + ClO^-_2(aq) + H_2O (l) What is the order of the reaction with respect to ClO_2? A04 B) 1 C) 0 D) 2 E)3 What is the order of the reaction with respect to OH^-? A)0 B) 1 C)2 D)3 E)4 What is the overall order of the reaction? A)0 B) 1 C)4 D)3 E)2 What is the magnitude of the rate constant for the reaction? A)115 B) 1.15 times 10^4 C) 713 D)4.6 E) 230 For a first-order reaction, a plot of ______ versus _____ is linear. A)ln[A]_t, t b) 1/[A]_t, t C) ln [A]_t, 1/t D) [A]_t, t E) t, 1/[A]_t

Explanation / Answer

9) Reaction rate -rA = k*CA^a*CB^b  ( Here CA = [OH-] & CB = [ClO2] ) and a & b are reaction orders w.r.t OH- & ClO2)

=> 0.0248 = K*0.03^a*0.06^b -----------------------------1)

and

=> 0.00276 = k*0.03^a* 0.02^b -----------------------2)

=> Dividing 2 by 1

=>  0.00276/0.0248 = (0.02/0.06)^b

=> 0.11129 = (1/3)^b

Taking "ln" on both sides

=> b*ln(1/3) = ln(0.11129) => b =  = ln(0.11129)/ln(1/3) = 1.9985 = 2

10) Do the same as above using experiment no. 2 & 3

=> 0.00276/0.00828 = (0.03/0.09)^a

=> 0.3333 = (1/3)^a => a*ln(1/3) = ln(0.3333) => a = 1

11) Overall order = a+b =2+1 =3 ( Sum all exponents in a reaction rate equation i.e -rA = k*CA^a*CB^b)

12)  -rA = k*CA^a*CB^b

from experiment no.1 => 0.0248 =k*0.03^1*0.06^2

=> k = 0.024/0.000108 =222.222

13) for first order: -rA = k*CA

=> -dCA/dt = k*CA => CA = CAo*exp(-k*t)

=> lnCA = lnCAo -k*t => [A] vs t is linear

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