CEE111 First Midterm Review Sheet
Air quality engineering issues
 Acid deposition – economic and ecosystem damage
 Stratospheric ozone depletion - CFCs
 Hazardous air pollutants
 Biomass cookstoves
Hazardous wastes
 Corrosivity (high or low pH)
 Ignitability
 Reactivity
 Toxicity
Concentration
 %: percent, 1 parts species per 100 parts solution
 ‰: per mil, 1 parts species per 1000 parts solution
 ppm: parts per million, 1 parts species per 106 parts solution
 ppb: parts per billion, 1 parts species per 109 parts solution
 ppt: parts per trillion, 1 parts species per 1012 parts solution
𝐶𝑖 = 𝑀𝑊𝑖 [𝑖]
𝐶𝑖 = 𝜌𝑠 𝑋𝑖
[𝑖] molar concentration of i
𝑀𝑊𝑖 molar mass of i
𝐶𝑖 mass concentration of i
𝑋𝑖 mass fraction of i
𝜌𝑠 density of solution
𝐶𝑖 mass concentration of i
𝑃
1 𝑎𝑡𝑚
𝑚𝑜𝑙
𝐶𝑖
𝐶𝑎𝑖𝑟 =
=
= 41.6 3
𝑌𝑖 =
𝑅𝑇 0.08206 𝐿 𝑎𝑡𝑚 ∗ 293𝐾
𝑚
𝐶𝑎𝑖𝑟
𝐾 𝑚𝑜𝑙
Mass balance in − out + generation = accumulation
Qtotal = Q1 + Q2
Ctotal = C1 Q1 + C2 Q2
Accuracy describes the relationship between the average of several repeated determinations and the goal.
Precision describes the level of variability within several repeated determinations.
𝑆𝑡𝑜𝑐𝑘 𝑠𝑖𝑧𝑒
𝜏𝑟 =
𝑓𝑙𝑜𝑤 𝑟𝑎𝑡𝑒
kg
Density of water is greatest at 4°C, at 1000 𝑚3 . Density of water is higher in liquid than in solid.
Composition of dry air
N2 ~ 78.08%
O2 ~ 20.95%
Argon ~ 0.93 %
CO2 ~ 0.035 ppm
𝑃𝑖 =
𝑛𝑖
𝑅𝑇 𝑤ℎ𝑒𝑟𝑒 𝑃𝑖 𝑖𝑠 𝑡ℎ𝑒 𝑝𝑎𝑟𝑡𝑖𝑎𝑙 𝑝𝑟𝑒𝑠𝑠𝑢𝑟𝑒 𝑜𝑓 𝑔𝑎𝑠𝑒𝑜𝑢𝑠 𝑠𝑝𝑒𝑐𝑖𝑒𝑠 𝑖
𝑉
𝑛𝑖 𝑃𝑖
𝑌𝑖 = =
𝑛
𝑃
MW𝑑𝑟𝑦,𝑎𝑖𝑟 = (78.08% ∗ 28) + (20.95% ∗ 32) + (0.93 % ∗ 40) + (0.035% ∗ 44) = 𝟐𝟖. 𝟗𝟓
MW𝑤𝑒𝑡,𝑎𝑖𝑟 = 18𝑌𝐻2 𝑂 + MW𝑑𝑟𝑦,𝑎𝑖𝑟 ∗ (1 − 𝑌𝐻2 𝑂 )
𝑌𝑖,𝑚𝑜𝑖𝑠𝑡 = 𝑌𝑖,𝑑𝑟𝑦 ∗ (1 − 𝑌𝐻2 𝑂 )
𝐶𝑖 = 𝑀𝑊𝑖
Electroneutrality, ∑ 𝑧𝑖 𝐶𝑖 = 0
𝑛𝑖
𝑛
𝑃
= 𝑌𝑖 𝑀𝑊𝑖 = 𝑌𝑖 𝑀𝑊𝑖
𝑉
𝑉
𝑅𝑇
1
Ionic strength, I = 2 ∑ 𝑧𝑖2 𝐶𝑖
Hardness, the sum of the normalities of all multivalent cations. Main cations, 𝐶𝑎2+ 𝑀𝑔2+
𝐠
𝒎𝒐𝒍
Classification
Hardness (meq/L)
Soft
<1.5
Moderately hard
1.5~3
Hard
3~6
Very hard
>6
2−
Compute total harness (TH), compute Nc = [HCO−
3 ] + 2[CO3 ]
If Nc < TH
CH = Nc
NCH = TH-CH
If Nc > TH
CH = TH
NCH = 0
Hardness (mg/L as CaCO3)
<75
75~150
150~300
>300
2−
+
Alkalinity, A = [OH − ] + [HCO−
3 ] + 2[CO3 ] − [𝐻 ]
Organic compounds of environmental concern
Formaldehyde
CHC-12
Benzene
Perchloroethylene
2,3,7,8-TCDD (dioxin)
Benzo(a)pyrene
Toxic metals
Cadmium
Chromium
Lead
Mercury
𝑀𝐵
𝑉𝐴
𝑀𝐺
TDS =
= TS − SS
𝑉𝐷
𝑀𝐸
SS =
𝑉𝐷
𝑀𝐵 − 𝑀𝐶
TVS =
𝑉𝐴
𝑀𝐸 − 𝑀𝐹
VVS =
𝑉𝐷
aA + bB → cC + dD
TS =
𝑅𝑓 = 𝑘[𝐴]𝛼 [𝐵]𝛽 rate constant k, empirical coefficients α and β
𝑅𝑓 = −
Zero order
𝑑[𝐴]
𝑑𝑡
Second order
= −𝑘𝑜
𝑑[𝐴]
𝑑𝑡
1 𝑑[𝐴]
1 𝑑[𝐵] 1 𝑑[𝐶] 1 𝑑[𝐷]
=−
=
=
𝑎 𝑑𝑡
𝑏 𝑑𝑡
𝑐 𝑑𝑡
𝑑 𝑑𝑡
[𝐴] = [𝐴]𝑜 − 𝑘𝑡
= −2𝑘2 [𝐴]2
[𝐴] =
If α = a, β = b, elementary reaction
First order
𝑑[𝐴]
𝑑𝑡
= −𝑘1 [𝐴]
[𝐴] = [𝐴]𝑜 𝑒 −𝑘1 𝑡
[𝐴]𝑜
1+2𝑘2 𝑡[𝐴]𝑜
A system is at equilibrium:
1. does not vary in time
2. is internally uniform
3. has no net flows of mass, heat, or species within the system and its surroundings
4. net rate of chemical reactions equal to 0
𝑘𝑓 [𝐶]𝑐 [𝐷]𝑑
K=
=
𝑘𝑟 [𝐴]𝑎 [𝐵]𝑏
𝐻2 𝑂(𝑙) H + (aq) + OH − (aq) K 𝑤 = [𝐻 + ][𝑂𝐻 − ] = 10−14 K 𝑤 is a function of T
A(s) B+ (aq) + C− (aq) 𝐾𝑠𝑝 = [𝐵 + ][𝐶 − ]
Relative humidity (RH) = 100% ∗
𝑃𝐻2 𝑂
𝑃𝑜 𝐻2 𝑂 (𝑇)𝑠𝑎𝑡𝑢𝑟𝑎𝑡𝑖𝑜𝑛 𝑣𝑎𝑝𝑜𝑟 𝑝𝑟𝑒𝑠𝑠𝑢𝑟𝑒 𝑜𝑓 𝑤𝑎𝑡𝑒𝑟 𝑎𝑡 𝑇
The equilibrium partial pressure of species i is equal to vapor pressure equilibrium constant at T.
𝐶𝑤 , 𝑎𝑞𝑢𝑒𝑜𝑢𝑠 𝑝ℎ𝑎𝑠𝑒 𝑠𝑝𝑒𝑐𝑖𝑒𝑠 𝑐𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛 (𝑀) =
𝑃𝑔 , 𝑔𝑎𝑠 𝑝ℎ𝑎𝑠𝑒 𝑠𝑝𝑒𝑐𝑖𝑒𝑠 𝑝𝑎𝑟𝑡𝑖𝑎𝑙 𝑝𝑟𝑒𝑠𝑠𝑢𝑟𝑒 (𝑎𝑡𝑚)
𝐻𝑒𝑛𝑟𝑦 ′ 𝑠 𝑙𝑎𝑤 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 (𝑎𝑡𝑚 𝑀−1 )
Adsorption- surface uptake
Absorption- distributed uptake
Sorption- either one or both
Equilibrium sorption described by sorption isotherms
𝑙𝑖𝑛𝑒𝑎𝑟: 𝑞𝑒 = 𝐾𝑎𝑑𝑠 𝐶𝑒
𝑏𝐶𝑒
Langmuir: 𝑞𝑒 = 𝑞𝑚𝑎𝑥
1 + 𝑏𝐶𝑒
1
Freundlich: 𝑞𝑒 = 𝐾𝑓 𝐶𝑒𝑛
Equations you need for the dissociation of weak acic HA
water dissociation: K 𝑤 = [𝐻 + ][𝑂𝐻 − ]
material balance on A: 𝐶𝑡𝑜𝑡𝑎𝑙 = [𝐴− ] + [𝐻𝐴]
[𝐻 + ][𝐴− ]
[𝐻 + ][𝐴− ]
acid dissociation: K𝐴 =
=
[𝐻𝐴]
𝐶𝑡𝑜𝑡𝑎𝑙 − [𝐴− ]
𝐾𝐴 𝐶𝑡𝑜𝑡𝑎𝑙 − 𝐾𝐴 [𝐴− ] = [𝐻 + ][𝐴− ]
𝐾𝐴 𝐶𝑡𝑜𝑡𝑎𝑙
[𝐴− ] =
𝐾𝐴 + [𝐻 + ]
𝐾𝑤
𝐶𝑡𝑜𝑡𝑎𝑙 𝐾𝐴
electroneutrality: [𝐻 + ] = + +
[𝐻 ] 𝐾𝐴 + [𝐻 + ]
Carbonate system
𝐶𝑂2 (𝑔) carbon dioxide gas
𝐶𝑂2 (𝑎𝑞) dissolved carbon dioxide
𝐻2 𝐶𝑂3 (𝑎𝑞) carbonic acid
𝐻𝐶𝑂3− (𝑎𝑞) bicarbonate ion
𝐶𝑂32− (𝑎𝑞) carbonate ion
𝐶𝑎𝐶𝑂3 (𝑠) calcium carbonate
[𝐶𝑂2 (𝑎𝑞)] = 𝐾𝐻 𝑃𝐶𝑂2
𝐾𝐻 = 0.034
𝑀
𝑎𝑡𝑚
[𝐻2 𝐶𝑂3 ]
= 𝐾𝑚 = 1.58 ∗ 10−3
[𝐶𝑂2 (𝑎𝑞)]
[𝐻2 𝐶𝑂3 ∗] = [𝐶𝑂2 (𝑎𝑞)] + [𝐻2 𝐶𝑂3 ] = [𝐶𝑂2 (𝑎𝑞)](1 + 𝐾𝑚 )
𝐻2 𝐶𝑂3 → 𝐻 + + 𝐻𝐶𝑂3−
[𝐻 + ][𝐻𝐶𝑂3− ]
𝐾1 =
= 4.47 ∗ 10−7 𝑀
[𝐻2 𝐶𝑂3 ]
𝐻𝐶𝑂3− → 𝐻 + + 𝐶𝑂32−
𝐾2 =
[𝐻 + ][𝐶𝑂32− ]
= 4.68 ∗ 10−11 𝑀
[𝐻𝐶𝑂3− ]
𝐶𝑎𝐶𝑂3 → 𝐶𝑎2+ + 𝐶𝑂32−
𝐾𝑠𝑝 = [𝐶𝑎2+ ][𝐶𝑂32− ]
𝐶𝑐𝑎𝑟𝑏𝑜𝑛𝑎𝑡𝑒 = [𝐻2 𝐶𝑂3 ] + [𝐻𝐶𝑂3− ] + [𝐶𝑂32− ]
[𝐻 + ]2
[𝐻2 𝐶𝑂3 ∗]
𝛼𝐻2 𝐶𝑂3 ∗ =
=
𝐶𝑐𝑎𝑟𝑏𝑜𝑛𝑎𝑡𝑒 [𝐻 + ]2 + 𝐾1 [𝐻 + ] + 𝐾1 𝐾2
[𝐻𝐶𝑂3− ]
𝐾1 [𝐻 + ]
−
𝛼𝐻𝐶𝑂3 =
=
𝐶𝑐𝑎𝑟𝑏𝑜𝑛𝑎𝑡𝑒 [𝐻 + ]2 + 𝐾1 [𝐻 + ] + 𝐾1 𝐾2
𝛼𝐶𝑂32− =
[𝐶𝑂32− ]
𝐶𝑐𝑎𝑟𝑏𝑜𝑛𝑎𝑡𝑒
=
𝐾1 𝐾2
[𝐻 + ]2 + 𝐾1 [𝐻 + ] + 𝐾1 𝐾2
pH of water in a limestone aquifer
[𝐻𝐶𝑂3− ][𝐻 + ]
[𝐻2 𝐶𝑂3 ∗] =
𝐾1
[𝐻𝐶𝑂3− ]
[𝐻 + ][𝐶𝑂32− ]
=
𝐾2
[𝐻 + ][𝑂𝐻 − ] = 𝐾𝑤
[𝐶𝑎2+ ][𝐶𝑂32− ] = 𝐾𝑠𝑝
2[𝐶𝑎2+ ] + [𝐻 + ] = [𝑂𝐻 − ] + [𝐻𝐶𝑂3− ] + 2[𝐶𝑂32− ]
[𝐶𝑎2+ ] = [𝐻2 𝐶𝑂3 ∗] + [𝐻𝐶𝑂3− ] + [𝐶𝑂32− ]
2𝐾𝑠𝑝
+ [𝐻 + ]
[𝐶𝑂32− ]
[𝐻 + ][𝐶𝑂32− ]
𝐾𝑤
= + +
+ 2[𝐶𝑂32− ]
[𝐻 ]
𝐾2
[𝐶𝑂32− ] =
1
2
𝐾𝑠𝑝
[𝐻 + ]2 [𝐻 + ]
(
+
+ 1)
𝐾1 𝐾2
𝐾2
−
1
2
pH of pristine rainwater
[𝐻2 𝐶𝑂3 ∗] = (1 + 𝐾𝑚 )𝐾𝐻 𝑃𝐶𝑂2
𝐾1 [𝐻2 𝐶𝑂3 ∗]
[𝐻𝐶𝑂3− ] =
[𝐻 + ]
𝐾2 [𝐻𝐶𝑂3− ]
[𝐶𝑂32− ] =
[𝐻 + ]
+
−
[𝐻 ][𝑂𝐻 ] = 𝐾𝑤
+
[𝐻 ] = [𝑂𝐻 − ] + [𝐻𝐶𝑂3− ] + 2[𝐶𝑂32− ]
𝐾1 (1 + 𝐾𝑚 )𝐾𝐻 𝑃𝐶𝑂2
𝐾𝑤
[𝐻 + ] = + +
[𝐻 ]
[𝐻 + ]
𝐾1 𝐾2 (1 + 𝐾𝑚 )𝐾𝐻 𝑃𝐶𝑂2
+2
[𝐻 + ]2