Atmospheric Chemistry ATM 507
Fall 2014 – Assignment #5
Due Dec. 4, 2014
1. Aqueous equilibrium of water, carbon dioxide, and ammonia:
For the NH3/CO2/water equilibria presented in lecture calculate the pH of the solution for the
following 4 conditions:
a) T = 298 K, CO2 = 390 ppm, NH3 = 1 ppb
b) T = 298 K, CO2 = 390 ppm, NH3 = 10 ppb
c) T = 273 K, CO2 = 390 ppm, NH3 = 1 ppb
d) T = 273 K, CO2 = 390 ppm, NH3 = 10 ppb.
For part d) only, also calculate the molar concentrations of HCO3-, CO32-, and NH4+.
(You may use the methods for solving cubic equations, below; or approximation methods. If you
use the approximate methods, you need to justify the approximation at least once!)
2. Seinfeld and Pandis, problem 7.3.
3. Seinfeld and Pandis, problem 7.6.
For Condition A calculate the rates at pH = 3.5, 4.0, and 4.5, and produce a plot similar to Figure
7.19.
For Condition B calculate the rates at pH = 4.5, 5.0, 5.5 and 6.0, and produce a plot similar to Figure
7.19.
For manganese and iron catalyzed oxidation of S(IV), use the rate expressions given in lecture, and
as (7-102) in the book.
4. Jacob, problem 13.1 (attached).
5. Jacob, problem 13.3 (attached).
6. Jacob, problem 13.5 (attached).
7. Ammonium nitrate gas/aerosol equilibrium:
a) Calculate the concentration in µg m-3 of crystalline (solid) NH4NO3 in equilibrium with 3.4 µgm-3
of gaseous NH3 and 10.6 µg m-3 of gaseous HNO3 at 278 K, 1.00 atm, and a relative humidity
below the deliquescence point. The reaction is given by
NH3(g) + HNO3(g) ↔ NH4NO3(s)
[eq. 10.87 in text]
(See p. 16 in the book for conversions from ppb to µg m-3 and vice versa.)
The dissociation constant Kp(T) – in units of ppb2 at 1 atm total pressure – is given by
ln (Kp) = 84.6 - 24220/T - 6.1 ln (T/298).
[eq. 10.91 in text]
b) Repeat the calculation for 305 K. What does your answer tell you about the seasonality of
ammonium nitrate aerosol?
8. Gas/aerosol partitioning of pyrene:
Pyrene is a polycyclic aromatic hydrocarbon (or PAH), and will exist in gaseous and solid phases in
the atmosphere in equilibrium with the pre-existing particles in the air. (Some PAH’s are known
carcinogens, and are ubiquitous in the atmosphere.) The partition coefficient is defined in the
textbook (eq. 14.47 ) as
Kp =
c aer
;
M t cg
Where Kp is a temperature dependent partitioning coefficient (m3 µg-1), Mt is the total ambient
aerosol mass concentration (µg m-3), and caer and cg are the aerosol and gas-phase concentrations of
the species partitioned between the two phases (µg m-3).
An equation for the partition coefficient for pyrene in terms of its vapor pressure in Pascals is given
by
log10 Kp = -1.028 log10 (p0) - 5.92.
[A]
An equation for the vapor pressure of pyrene (again in Pascals) as a function of temperature is given
by
log10 (p0) = - 4760/T + 12.75.
[B]
a) Use equations A and B to derive an expression for the temperature dependence of the partition
coefficient of pyrene.
b) For a temperature of 20º C (293 K) find the value of Kp. Use this value to calculate the ratio of
caer/cg for pyrene at this temperature with a total aerosol mass loading of 10 µg m-3.
c) Use the value of Kp from part b) to calculate the ratio of caer/cg for pyrene at 20º C with a total
aerosol mass loading of 100 µg m-3.
d) For a temperature of 0º C (273 K) find the value of Kp. Use this value to calculate the ratio of
caer/cg for pyrene at this temperature with a total aerosol mass loading of 10 µg m-3.
(You will find more on this topic in Sections 14.5 and 14.6 of the textbook.)