APCH 211
TUT 2
Ndungu P
Steady State Mass Balance
1)
Imagine that 300 lb (1 lb = 453.59237 grams) of dry sewage is dumped
into a small lake, the volume of which is 300 million liters. How many
tonnes of oxygen are needed to completely degrade the sewage? Assume
the sewage has an elemental composition of C6H12O6.
2)
Imagine a one – car garage with a volume of 90 m3 and imagine that air in
the garage has a residence time of 3.3 hrs. At what rate does air leak into
and out of this garage? Convert your answer to mass/unit time
(ρ=1.3kg/m3)
3)
Methane enters and leaves the earths atmosphere at a rate of 500 million
tonnes per year. If it has a residence time of 10 years, how much methane
is present in the atmosphere, at any given time?
4)
Given that the flow of oxygen into and out of the Earth’s atmosphere is 3
x 1014 kg/year, what is the residence time of oxygen in the Earth’s
atmosphere? (Vol of atmosphere ~ 4.3 x 1021 L, Avg temp of atmosphere
= 15 °C)
5)
A sewage treatment plant is designed to process 9.3 x106 L of sewage
daily. What diameter (in feet) tank is required for the primary settling
process if the residence time is to be 7 hours? Assume the tank is
cylindrical and 2 m deep. (1.0 m = 3.28ft)
1)
Imagine that 300 lb of dry sewage is dumped into a
small lake, the volume of which is 300 million liters.
How many tonnes of oxygen are needed to
completely degrade the sewage? Assume the
sewage has an elemental composition of C6H12O6.
Solution:
C6H12O6 + 6O2 Æ 6CO2 + 6H2O
300lb ×
453.59237 g
= 136077.711g
1lb
136077.711g ×
1mol
= 755.3377mol Moles C6H12O6
180.1548g
755.3377mol ×
6molO 2
= 4532.026 Moles O2
1molC6 H12O6
4532.026mol ×
31.998g
= 145015.8g
mol
Mass O2
Ans = 0.145 tons
1
2)
Imagine a one – car garage with a volume of 90
m3 and imagine that air in the garage has a
residence time of 3.3 hrs. At what rate does air
leak into and out of this garage?
3
90m 3
= 27.27273 m
hr
3.3hrs
27.27273 m
3)
3
hr
×
1.3kg
= 35.45455 kg
hr
m3
Methane enters and leaves the earths atmosphere
at a rate of 500 million tonnes per year. If it has a
residence time of 10 years, how much methane is
present in the atmosphere, at any given time?
500x106 tons/yr x10yrs = 5x109 tons
4) Given that the flow of oxygen into and out of the Earth’s
atmosphere is 3 x 1014 kg/year, what is the residence
time of oxygen in the Earth
Earth’ss atmosphere?
Vol of O2 = 0.21 x 4.3 x 1021 L = 9.03 x 1020 L
1 mol of gas at 0 °C = 22.4 L
21% O2 in air
4.3 x1021 = Vol of atmos
mol O2 at 0 °C = 9.03 x 1020 L x 1mol/22.4 L
= 4.03125 x 1019 mol
4.03125 x 1019 mol x 273/288 = 3.82129 x 1019 mol
3.82129 x 1019 mol x 32g/mol
1.22274 x 1018 kg
1.22274 x 1018 kg/ 3 x 1014 kg/year
Ans =4075 years
5)
A sewage treatment plant is designed to process
9.3 x106 L of sewage daily. What diameter (in
feet) tank is required for the primary settling
process if the residence time is to be 7 hours?
Assume the tank is cylindrical and 2 m deep.
9.3 x106 L/day x day/24 hrs x 7hrs = 2712500 L
2712500 L x 1m3 /1000L = 2712.5 m3
Volume of a cylinder = length of the cylinder x Area of circular opening
Area = 2712.5 m3/ 2m = 1356.25 m2
Area = πr2=
r = √(1356.25 m2 / π )= 20.77758 m
=20.77758 x 3.28 ft/1m = 68.15046 ft
Ans = 68.1 ft
2