Exam 1 CHEM-7330
In problems where plotting is required please attach any figures generated by spreadsheet
1a. The reaction nA ” B
obeys the second-order rate law: -d[A]/dt = k [A]2
Demonstrate that a plot of 1/[B] vs 1/t should result in a straight line (y = mx + b) with a slope
(m) equal to n/([A]02 k), and an intercept (b) of n/[A]0, where [A]0 = initial reactant
(Hint: use the law of conservation of mass.) (12 pts)
1b. The first-order reaction: NH2NO2(aq) ” N2O(g) + H2O(l)
occurs in solution by letting 50 mg of the reactant decompose for 70 min with T = 15 °C, at
which time 6.6 cm3 of N2O were collected in the gas phase under a pressure of 1 atm. How
much NH2NO2 remains unreacted after that time? (Hint: treat N2O as an ideal gas and assume
that all the generated nitrous oxide is in the gas phase).
i) Calculate the rate constant for the reaction.
ii) Find the time at which 40% of the reactant is consumed. (13 pts)
2a. Medicine CX decomposes in the human body via 3 different reactions; a zero-order, together
with a first-order and a second-order processes. The magnitude of k is 100 for the zero-order
reaction, 104 for the first-order process and 109 for the second-order transformation.
i) The reactions take place in the time scale of seconds when [CX]0 = 8 x 10-5 M; from the rate
constants with their appropriate units evaluate t1/2 for each reaction and rank them in terms of
ii) Which of the 3 processes is the slowest? (9 pts)
2b. The overall transformation 2NO2(g) ” 2NO(g) + O2(g)
occurs via a mechanism consisting of 2 elementary steps, the first of which is:
(1) NO2(g) ” NO(g) + O(g)
Two different reactions have been proposed as the possible 2nd elementary step of the
mechanism; O(g) + O(g) ” O2(g)
or: NO2(g) + O(g) ” NO(g) + O2(g)
Which of these reactions is the correct second elementary step and why? (3 pts)
2c. The elementary reaction I(g) + H2(g) ” H(g) + HI(g)
exhibits a DHrxn of 117.3 kJ mol-1, and k = 1014.1 e-140/RT , where Ea is in kJ mol-1. Using a
diagram of the activation process find the activation energy for the reverse reaction, R = 8.315 J
mol-1 K-1. (8 pts)
2d. The experimental rate law for 2H2(g) + 2NO(g) ” N2(g) + 2H2O(g)
was found to be: r = d[N2]/dt = k[NO]2 [H2]
The following mechanism has been proposed:
H2 + NO ” N + H2O rate constant = k1
N + N ” N2 rate constant = k2
Note the rate law derived from the correct mechanism must be identical to the experimental rate
law. i) Identify the intermediates.
ii) Using the steady-state approximation determine if the mechanism is correct.
3. The self-ionization equilibrium of NH3 is somewhat similar to that of water:
2NH3 D NH4+ + NH2- K = [NH4+] [NH2-] = 10-30
In liquid ammonia a rate constant of k = 3 x 1010 M-1 s-1 has been measured at -33 °C for the
elementary reaction: NH4+ + NH2- ® 2NH3
a) Evaluate the half-life for this elementary reaction at p(NH4+) = 15, where
p(NH4+) = -log[NH4+]. Note that p(NH4+) = 15 corresponds to “neutral” conditions in NH3, that
is when [NH4+] = [NH2-].
b) Make a plot of log(t1/2) vs p(NH4+) between 10 £ p(NH4+) £ 20, and justify the shape of the
(Hint: Remember the conditions for pseudofirst-order kinetics). (25 pts)
4. The thermolysis of propane (C3H8) has been proposed to take place according to the
1. C3H8 ® •CH3 + •C2H5
2. •CH3 + C3H8 ® CH4 + •C3H7
3. •C2H5 + C3H8 ® C2H6 + •C3H7
4. •C3H7 ® C2H4 + •CH3
5. 2•C3H7 ® C3H8 + C3H6
a) The main products are CH4, C2H6 and C2H4; a minor product is C3H6. What reasons can be
provided to support the idea that the proposed mechanism is that of a chain process? Justify your
b) Label the reactions in terms of the typical steps occurring in a chain process.
c) Identify the chain carriers.
d) Find the predicted rate laws for each of the main products. Are all the main products
generated with the same speed? Justify your answer remembering that the initial step is the
slowest. (25 pts)