Question

Consider the data for the following reaction at 25 ^oC

                2 HgCl₂(aq) + C₂O₄^2-(aq) --------2 Cl^-(aq) + 2 CO₂ (g) + Hg₂Cl₂(s)    Where Rate = [C₂O₄^2-]/t

Determine the 'orders for each reactant.

Determine the rate constant for this reaction.

Determine the instantaneous rate of change for HgCl₂ when [HgCl₂] = O.l22 M and [C₂O₄^2- ] = 0.50 M.           

Experiment	[HgCl2] (M)	[C2O42-] (M)	Rate (M/s)
1	0.164	0.15	3.2 x 10-5
2	0.164	0.45	2.9 x 10-5
3	0.082	0.45	1.4 x 10-5
4	0.246	0.15	4.8 x 10-5

Answer 1

suppose the rate law expression is ,r = k [HgCl2]^a [C2O42-]^b
where a is the order of reaction with respect to HgCl2 and b is order of reaction with respect to C2O4(2-)

From experiments 1 and 2 we can see that when concentration of HgCl2 is same i.e. in both the experiments concentration of HgCl2 is 0.164 M ....and concentration of C2O4(2-) has been tripled from 0.15 M to 0.45 M, the rate of reaction remained unchanged, that means with respect to C2O4(2-) order of reaction is 0..

Also, from experiments 2 and 3 we can see that when concentraton of C2O4(2-) is kept same (0.45 M),and concentration of HgCl2 is halved (0.164/0.082 = 2) rate of reaction is reduced to half (2.9 x 10^-5/1.4 x 10^-5 = 2.07 almost 2) that means with respect to HgCl2 order of reaction is 1...

thus combining both these facts .. we can say that
rate law,expression ,r = k [HgCl2]
thus overall order of reaction is 1+0 = 1

now to find the rate constant k ...choose any one experiment..suppose experiment 1..
rate = 3.2 x 10^-5 M/s
[HgCl2] = 0.164 M
[C2O42-] = 0.15 M
putting these values ..in rate law expression..
3.2 x 10^-5 = k X 0.164

Solving for k,

k = 1.95 x 10^-4 s-1

Thus,

The orders with respect to [HgCl2] = 1, and with respect to [C2O4(2-)] = 0

The rate constant for this reaction k = 1.95 x 10^-4 s-1

The instantaneous rate of change for HgCl₂ when [HgCl₂] = 0.l22 M will be,

Rate = k[HgCl2]

        =  1.95 x 10^-4 x 0.122

        = 2.38 x 10^-5 M/s

Thus, the instantaneous rate will be 2.38 x 10^-5 M/s