3) The following set of data was obtained by the method of initial rates for the reaction:
2 HgCl2(aq) + C2O42-(aq) 2 Cl-(aq) + 2 CO2(g) + Hg2Cl2(s)
What is the rate law for the reaction?
[HgCl2], M [C2O42-], M Rate, M/s
0.10 0.10 1.3 × 10-7
0.10 0.20 5.2 × 10-7
0.20 0.20 1.0 × 10-6
A) Rate = k[HgCl2][C2O42-]-1 B) Rate = k[HgCl2][C2O42-]2
C) Rate = k[HgCl2]2[C2O42-] D) Rate = k[HgCl2][C2O42-]-2
I'll do one and leave the other for you.
Label these rates as 1, 2, and 3.
Then they follow this scheme.
rate = k*[Hg2Cl2]x[C2O4^-2]y
You want to determine x and y, the exponents.
Look for rates where concn is the same for one of them and different for the other. 1 is ok for this; Hg2Cl2 is the same 0.1 M while oxalate changes from 0.1 to 0.2. Here is what I do.
Write rate for #2 and divide it by rate for #1.
rate 2 ...k[Hg2Cl2]^x[C2O4]^y
------ = -----------------------
rate 1....k[Hg2Cl2]^x[C2O4]^y
5.2E-7...k[0.1]^x[0.2]^y
------- = -------------------------
1.3E-7...k[0.1]^x[0.1]^y
ks cancel, 0.1^x cancels and we are left with
4.00 = 2^y
So 2 to the y power is 4.00 which means y must be 2; therefore, the reaction is second order with respect to oxalate.
(Sometimes the power is not obvious; if that is the problem, you do it this way.
4.00 = 2^y
log 4.00 = y*log 2
0.602 = y*0.301
y = 0.602/0.301 = 2.00 and I think you will need to do that to find x power for Hg2Cl2.
To determine the rate law for the reaction, we need to analyze the data and see how the rate changes with the concentrations of the reactants.
By comparing the first and second experiments, we can see that doubling the concentration of C2O42- results in a 4-fold increase in the rate:
0.10 M [C2O42-]: 1.3 × 10-7 M/s
0.20 M [C2O42-]: 5.2 × 10-7 M/s
This indicates that the rate is directly proportional to the concentration of C2O42-. Therefore, we can eliminate options C and D, which have powers of 2 and -2, respectively, for the concentration of C2O42-.
Next, we can compare the first and third experiments, in which the concentration of HgCl2 is doubled:
0.10 M [HgCl2]: 1.3 × 10-7 M/s
0.20 M [HgCl2]: 1.0 × 10-6 M/s
Doubling the concentration of HgCl2 results in an 8-fold increase in the rate. This indicates that the rate is directly proportional to the concentration of HgCl2.
Therefore, the rate law for the reaction is Rate = k[HgCl2][C2O42-], which matches option B.
So, the correct answer is B) Rate = k[HgCl2][C2O42-]2.
To determine the rate law for the reaction, we need to analyze the data and identify the relationship between the initial concentrations of the reactants and the corresponding reaction rates.
Looking at the data given:
[HgCl2], M [C2O42-], M Rate, M/s
0.10 0.10 1.3 × 10-7
0.10 0.20 5.2 × 10-7
0.20 0.20 1.0 × 10-6
Let's compare the effect of changing the initial concentration of HgCl2 while keeping the concentration of C2O42- constant at 0.10 M. We observe that the rate increases by a factor of 4 when the concentration of HgCl2 is doubled.
Now, let's compare the effect of changing the initial concentration of C2O42- while keeping the concentration of HgCl2 constant at 0.10 M. We observe that the rate increases by a factor of 5 when the concentration of C2O42- is doubled.
From these comparisons, we can conclude that the rate of the reaction is directly proportional to the concentration of HgCl2 and C2O42-, i.e., Rate ∝ [HgCl2] and Rate ∝ [C2O42-].
Since the rate law expresses the relationship between the rate and the concentrations of the reactants, we can write the rate law for this reaction as:
Rate = k[HgCl2][C2O42-]
Comparing this rate law with the given options:
A) Rate = k[HgCl2][C2O42-]^-1
B) Rate = k[HgCl2][C2O42-]^2
C) Rate = k[HgCl2]^2[C2O42-]
D) Rate = k[HgCl2][C2O42-]^-2
We see that the correct rate law for the reaction is option B) Rate = k[HgCl2][C2O42-]^2.