Question

Question 1. This is a consecutive reaction irreversible first-rate reactions below <Suppose that $k_1$ $k_2$ A?B?C?.... And you are interested in isolating the largest possible amount of B. Given the values of k1 and k2, derive an equation for the time that the concentration of B goes through the maximum. Now consider two cases: (a) A reacts more rapidly than B and (b) A reacts less rapidly than B. For a given value of k2, in which case would you wait the longer time for B to go through its maximum? Hint: Start by writing out the differential equations for each step (i.?. $ \frac{d[A]}{dt} = -k_1[A]$ ). Then $\frac{d[B]}{dt}$ solve for [B]. 2nd hint: [B] is maximum when $ \frac{d[B]}{dt} = 0$ Question 2. Nth order derivation for half-life ($t_{1/2}$). The reaction A=B is nth order (where n= ½, 3/2, 2, 3, etc) and goes to completion to the right. Derive the expression for the half-life as a function of k, n and [Ao]. Question 3. Steady-state approximation problem Consider the following reaction mechanism: $k_1$ $k_3$ A + B $ \rightleftharpoons$ C ? D Hint: the reverse reaction for C ? A+ B should be $k_2$ (a) Derive the rate law using the steady state approximation to eliminate the concentration of [C]. (b) Assuming that $k_3<<k_2$, express the pre-exponential A and activation energy Ea for the apparent second-order rate constant in terms of A1, A2 and A3 and Ea1, Ea2 and Ea3 for the three steps.

          Question 1. This is a consecutive reaction irreversible first-rate reactions below
<Suppose that
$k_1$
$k_2$
A?B?C?....
And you are interested in isolating the largest possible amount of B. Given the values of k1 and
k2, derive an equation for the time that the concentration of B goes through the maximum.
Now consider two cases: (a) A reacts more rapidly than B and (b) A reacts less rapidly than B.
For a given value of k2, in which case would you wait the longer time for B to go through its
maximum?
Hint: Start by writing out the differential equations for each step (i.?. $
\frac{d[A]}{dt} = -k_1[A]$
). Then
$\frac{d[B]}{dt}$
solve for [B]. 2nd hint: [B] is maximum when $
\frac{d[B]}{dt} = 0$
Question 2. Nth order derivation for half-life ($t_{1/2}$).
The reaction A=B is nth order (where n= ½, 3/2, 2, 3, etc) and goes to completion to the right.
Derive the expression for the half-life as a function of k, n and [Ao].
Question 3. Steady-state approximation problem
Consider the following reaction mechanism:
$k_1$
$k_3$
A + B $
\rightleftharpoons$
C ? D
Hint: the reverse reaction for C ? A+ B should be $k_2$
(a) Derive the rate law using the steady state approximation to eliminate the concentration
of [C].
(b) Assuming that $k_3<<k_2$, express the pre-exponential A and activation energy Ea for the
apparent second-order rate constant in terms of A1, A2 and A3 and Ea1, Ea2 and Ea3 for the
three steps.

Question 1. This is a consecutive reaction irreversible first-rate reactions below
<Suppose that
k1
k2
A?B?C?....
And you are interested in isolating the largest possible amount of B. Given the values of k1 and
k2, derive an equation for the time that the concentration of B goes through the maximum.
Now consider two cases: (a) A reacts more rapidly than B and (b) A reacts less rapidly than B.
For a given value of k2, in which case would you wait the longer time for B to go through its
maximum?
Hint: Start by writing out the differential equations for each step (i.?. (d[A])/(dt) = -k1[A]
). Then
(d[B])/(dt)
solve for [B]. 2nd hint: [B] is maximum when (d[B])/(dt) = 0
Question 2. Nth order derivation for half-life (t1/2).
The reaction A=B is nth order (where n= ½, 3/2, 2, 3, etc) and goes to completion to the right.
Derive the expression for the half-life as a function of k, n and [Ao].
Question 3. Steady-state approximation problem
Consider the following reaction mechanism:
k1
k3
A + B ⇌
C ? D
Hint: the reverse reaction for C ? A+ B should be k2
(a) Derive the rate law using the steady state approximation to eliminate the concentration
of [C].
(b) Assuming that k3<<k2, express the pre-exponential A and activation energy Ea for the
apparent second-order rate constant in terms of A1, A2 and A3 and Ea1, Ea2 and Ea3 for the
three steps.

Added by Pam F.

Question

Please give Ace some feedback