Step 1 : A +B <==> C + D
( k1 in fwd direction, k2 in rev direction)
Step 2: A + C ==> B+D
(k3 in fwd direction)
Match the expressions to complete the equations, making use of the Steady State Approximation.
A) 2(k1)(k3)[A]^2[B] / (k2)[D]
B) (k1)[A][B] / (k3)[A]
C) 2(k1)(k3)[A]^2[B] / (k2)[D] +(k3)[A]
D) (k1)[A][B] / (k2)[D] + (k3)[A]
E) 2(k1)[A][B]
F) (k1)[A][B] - (k2)[C][D] - (k3)[A][C]
G) (k1)[A][B] / (k2)(k3)[A][D]
H) None of the above
match with!! _______
1. -d[A]/dt (in all instances)
2. d[D]/dt (when k3 >> k1 =k2)
3. d[D]/dt (when k3 <<k1=k2)
4. d[C]/dt
5. =[C]
I think 4 is F and 5 is D.
The rate I got in the end was: k1k3[A]^2[B]/k2[D]+k3[A]
but I'm pretty sure this isn't right..
To match the expressions with the given equations and determine their rates, let's analyze the reactions and apply the Steady State Approximation.
Step 1: A + B ⇌ C + D (k1 in forward direction, k2 in reverse direction)
Step 2: A + C ⟶ B + D (k3 in forward direction)
Steady State Approximation assumes that the rate of change of intermediate species is negligibly small compared to the rates of the other reactions. Applying this approximation:
1. A) 2(k1)(k3)[A]^2[B] / (k2)[D]
This expression accounts for the forward reaction of Step 1 and forward reaction of Step 2.
2. B) (k1)[A][B] / (k3)[A]
This expression represents the backward reaction of Step 2.
3. C) 2(k1)(k3)[A]^2[B] / (k2)[D] +(k3)[A]
This expression combines the forward reaction of Step 1, forward reaction of Step 2, and also accounts for the accumulation of the intermediate species C.
4. D) (k1)[A][B] / (k2)[D] + (k3)[A]
This expression represents the forward reaction of Step 1, the reverse reaction of Step 1, and the forward reaction of Step 2.
5. E) 2(k1)[A][B]
This expression represents the forward reaction of Step 1.
6. F) (k1)[A][B] - (k2)[C][D] - (k3)[A]
This expression represents the net rate of change of intermediate species C and the overall reaction rate.
7. G) (k1)[A][B] / (k2)(k3)[A][D]
This expression represents the forward reaction of Step 1 and the reverse reaction of Step 1.
To determine the rates, we need to match the expressions with the appropriate equations:
1. -d[A]/dt (in all instances): Matches E
2. d[D]/dt (when k3 >> k1 = k2): Matches D
3. d[D]/dt (when k3 << k1 = k2): No matching expression. None of the provided expressions represent the rate when k3 << k1 = k2.
4. d[C]/dt: Matches F
5. =[C]: No matching expression. None of the provided expressions represent the concentration of C.
Based on the given choices, 4 corresponds to F and 5 corresponds to D, which are correct.
The expression you obtained, k1k3[A]^2[B]/k2[D]+k3[A], is equivalent to option C. However, that expression does not match the given equations or rates accurately.