Rate Equations & Mechanisms
Rate Equations Worksheet
1. Deduce Equations from Mechanisms
Write the overall equation and deduce the rate equation for the following reactions, given their mechanisms.
a)
A + B → C (Slow)
C + A → D (Fast)
Overall Equation: 2A + B → D
Rate Equation: Rate = k [A] [B]
b)
A + B → C (Fast)
C + A → D (Slow)
Overall Equation: 2A + B → D
Rate Equation: Rate = k [A]2 [B]
c)
X + Z → G (Slow)
G + Y → F + Z (Fast)
Overall Equation: X + Y → F
(Note: Z is a catalyst as it is used and regenerated; G is an intermediate).
Rate Equation: Rate = k [X] [Z]
d)
X + Z → G (Fast)
G + Y → F + Z (Slow)
Overall Equation: X + Y → F
Rate Equation: Rate = k [X] [Z] [Y]
e)
2X → Y (Slow)
Y + Z → H + I (Fast)
Overall Equation: 2X + Z → H + I
Rate Equation: Rate = k [X]2
2. Suggest Mechanisms from Rate Data
Suggest a mechanism for the following reactions, given their equations and their rate equations.
a)
A + 2B → C + D
Rate = k [A] [B]
Step 1 (Slow)
A + B
→
AB
Step 2 (Fast)
AB + B
→
C + D
Note: Any intermediate letter can be used instead of ‘AB’.
b)
A + 2B → C + D
Rate = k [A] [B]2
Step 1 (Fast)
A + B
→
AB
Step 2 (Slow)
AB + B
→
C + D
c)
2E + 2F → G + 2H
Rate = k [E] [F]
Step 1 (Slow)
E + F
→
EF
Step 2 (Fast)
EF + F
→
EFF
Step 3 (Fast)
EFF + E
→
G + 2H
Note: There are many valid options here, as long as the first slow step involves one E and one F.
d)
2E + 2F → G + 2H
Rate = k [E]2 [F]
Step 1 (Fast)
E + F
→
EF
Step 2 (Slow)
EF + E
→
E2F
Step 3 (Fast)
E2F + F
→
G + 2H
e)
2E + 2F → G + 2H
Rate = k [E]2
Step 1 (Slow)
2E
→
E2
Step 2 (Fast)
2F
→
F2
Step 3 (Fast)
E2 + F2
→
G + 2H
Other options exist, for example:
Step 1 (Slow)
2E
→
E2
Step 2 (Fast)
E2 + F
→
E2F
Step 3 (Fast)
E2F + F
→
G + 2H
f)
X + Y → F
Rate = k [X]
Step 1 (Slow)
X
→
Intermediate
Step 2 (Fast)
Intermediate + Y
→
F
g)
X + Y → F
Rate = k [X] [Z]
Step 1 (Slow)
X + Z
→
XZ
Step 2 (Fast)
XZ + Y
→
F + Z
(Z acts as a catalyst).
h)
X + Y → F
Rate = k [X] [Y] [Z]
Step 1 (Fast)
X + Z
→
XZ
Step 2 (Slow)
XZ + Y
→
F + Z
3. Real World Mechanisms
Suggest a mechanism for the following real-world reactions, given their equation and their rate equations.
a)
NO2 + CO → NO + CO2
Rate = k [NO2]2
Step 1 (Slow)
2NO2
→
N2O4 (or NO + NO3)
Step 2 (Fast)
N2O4 + CO
→
NO + CO2 + NO2
b)
2NO + 2H2 → N2 + 2H2O
Rate = k [NO]2 [H2]
Step 1 (Fast)
2NO
→
N2O2
Step 2 (Slow)
N2O2 + H2
→
N2O + H2O
Step 3 (Fast)
N2O + H2
→
N2 + H2O
c)
CCl(CH3)3 + OH– → C(OH)(CH3)3 + Cl–
Rate = k [CCl(CH3)3]
Step 1 (Slow)
CCl(CH3)3
→
+C(CH3)3 + Cl–
Step 2 (Fast)
+C(CH3)3 + OH–
→
C(OH)(CH3)3
d)
CH3CH2Cl + OH– → CH3CH2OH + Cl–
Rate = k [CH3CH2Cl] [OH–]
It is a single step mechanism (SN2) so it is the same as the equation above.
CH3CH2Cl + OH–
→
CH3CH2OH + Cl–