Consider the reaction:
C5H5Rh(CO)2(sol) + L(sol) → C5H5Rh(CO)L(sol) + CO(sol)
Use the Method of Initial Rates
The general rate law is Rate = k[C5H5Rh(CO)2]m[L]n
For all data sets, [L] is constant between experiments 1 and 2 and as the [C5H5Rh(CO)2] is doubled the initial rate also doubles, which means that m = 1.
Again for all data sets the [C5H5Rh(CO)2] is constant for experiments 2 and 3 and as the [L] doubles the initial rate also doubles, so n = 1.
This means the rate law is Rate = k[C5H5Rh(CO)2][L]
The rate constant is found by solving the rate law for k: k = Rate/[C5H5Rh(CO)2[L] for each experiment and then averaging.
The following data sets were measured experimentally:
(0) L = P(C4H9)3
Experiment # [C5H5Rh(CO)2] (M) [L] (M) Initial Rate (Ms–1) k (M–1s–1)
1 0.0040 0.053 7.0×10–3 33
2 0.0080 0.053 1.4×10–2 33
3 0.0080 0.027 7.0×10–3 32
kave = 33 M–1s–1
(1) L = P(OC4H9)3
Experiment # [C5H5Rh(CO)2] (M) [L] (M) Initial Rate (Ms–1) k (M–1s–1)
1 0.0012 0.660 3.0×10–3 3.8
2 0.0024 0.660 6.0×10–3 3.8
3 0.0024 0.330 3.0×10–3 3.8
kave = 3.8 M–1s–1
(2) L = P(C4H9)3
Experiment # [C5H5Rh(CO)2] (M) [L] (M) Initial Rate (Ms–1) k (M–1s–1)
1 0.0020 0.053 3.5×10–3 33
2 0.0010 0.053 1.7×10–3 32
3 0.0010 0.027 8.5×10–4 31
kave = 32 M–1s–1
(3) L = P(OC4H9)3
Experiment # [C5H5Rh(CO)2] (M) [L] (M) Initial Rate (Ms–1) k (M–1s–1)
1 0.00060 0.660 1.5×10–3 3.8
2 0.00030 0.660 7.5×10–4 3.8
3 0.00030 0.330 3.7×10–4 3.7
kave = 3.8 M–1s–1
(4) L = P(C4H9)3
Experiment # [C5H5Rh(CO)2] (M) [L] (M) Initial Rate (Ms–1) k (M–1s–1)
1 0.0080 0.053 1.4×10–2 33
2 0.016 0.053 2.8×10–2 33
3 0.016 0.027 1.4×10–2 32
kave = 33 M–1s–1
(5) L = P(OC4H9)3
Experiment # [C5H5Rh(CO)2] (M) [L] (M) Initial Rate (Ms–1) k (M–1s–1)
1 0.0024 0.660 6.0×10–3 3.8
2 0.0048 0.660 1.2×10–2 3.8
3 0.0048 0.330 6.0×10–3 3.8
kave = 3.8 M–1s–1
(6) L = P(C4H9)3
Experiment # [C5H5Rh(CO)2] (M) [L] (M) Initial Rate (Ms–1) k (M–1s–1)
1 0.0040 0.027 3.5×10–3 32
2 0.0080 0.027 7.0×10–3 32
3 0.0080 0.014 3.5×10–3 31
kave = 32 M–1s–1
(7) L = P(OC4H9)3
Experiment # [C5H5Rh(CO)2] (M) [L] (M) Initial Rate (Ms–1) k (M–1s–1)
1 0.0012 0.220 1.0×10–3 3.8
2 0.0024 0.220 2.0×10–3 3.8
3 0.0024 0.110 1.0×10–3 3.8
kave = 3.8 M–1s–1
(8) L = P(C4H9)3
Experiment # [C5H5Rh(CO)2] (M) [L] (M) Initial Rate (Ms–1) k (M–1s–1)
1 0.0040 0.018 2.3×10–3 32
2 0.0080 0.018 4.7×10–3 33
3 0.0080 0.0090 2.4×10–3 33
kave = 33 M–1s–1
(9) L = P(OC4H9)3
Experiment # [C5H5Rh(CO)2] (M) [L] (M) Initial Rate (Ms–1) k (M–1s–1)
1 0.0024 0.330 3.0×10–3 3.8
2 0.0048 0.330 6.0×10–3 3.8
3 0.0048 0.170 3.0×10–3 3.7
kave = 3.8 M–1s–1