HW1. Due: 02/08/2024. 1. The density of dry air at p = 1.0 bar and T =300 K is 1.161 kg/m³. Assuming it consists entirely of N₂ and O₂ and using the ideal gas law, determine the amount of each gas in moles in a volume of 1 m³ and their mole fractions. 2. (a) Calculate the amount of gas in moles per cubic meter of atmosphere at p = 1 atm and T = 298 K using the ideal gas equation. (b) The atmospheric content of CO₂ is about 360 ppmv (parts per million by volume). Assuming a pressure of 1.00 atm, estimate the amount of CO₂ in a 10.0 km layer of the atmosphere at the surface of the earth. The radius of the earth is 6370 km. (The actual amount of CO₂ in the atmosphere is about 6.0 x 1015 mol.) 3. The van der Waals parameter b is a measure of the volume excluded due to the finite size of the molecules. Estimate the size of a single molecule from the data given below. STATES OF MATTER AND THE VAN DER WAALS EQUATION Table 1.1 Van der Waals constants a and b and critical constants T.. p, and V for selected gases Gas a/bar L² mol b/L mol TJK p/bar V/L mol 308.3 405.5 150.9 304.1 132.9 416.9 513.9 Acetylene (C₂H₂) Ammonia (NH₁) Argon (Ar) Carbon dioxide (CO₂) Carbon monoxide (CO) Chlorine (Cl₂) Ethanol (C,H,OH) Helium (He) Hydrogen (H₂) Hydrogen chloride (HCI) Methane (CH₂) Nitric oxide (NO) Nitrogen (N₂) Oxygen (O₂) Propane (C,Hs) Sulfur dioxide (SO₂) Sulfur hexafluoride (SF) Water (H₂O) 4.516 4.225 1.355 3.658 1.472 6.343 12.56 0.0346 0.245 3.700 2.300 1.46 1.370 1.382 9.385 6.865 7.857 5.537 0.0522 0.0371 0.0320 0.0429 0.0395 0.0542 0.0871 0.0238 0.0265 0.0406 0.0430 0.0289 0.0387 0.0319 0.0904 0.0568 0.0879 0.0305 5.19 32.97 324.7 190.5 180 126.2 154.59 369.82 430.8 318.69 647.14 61.39 113.5 49.55 73.75 34.99 79.91 61.32 2.22 12.93 83.1 46.04 64.8 33.9 50.43 42.50 78.84 37.7 220.6 0.113 0.072 0.075 0.094 0.093 0.123 0.167 0.057 0.065 0.081 0.099 0.058 0.090 0.073 0.203 0.122 0.199 0.056 19 Source: An extensive listing of van der Waals constants can be found in D.R. Lide (ed.), CRC Handbook of Chemistry and Physics, 75th edition. 1994, CRC Press: Ann Arbor, MI.
HW1. Due: 02/08/2024. 1. The density of dry air at p = 1.0 bar and T =300 K is 1.161 kg/m³. Assuming it consists entirely of N₂ and O₂ and using the ideal gas law, determine the amount of each gas in moles in a volume of 1 m³ and their mole fractions. 2. (a) Calculate the amount of gas in moles per cubic meter of atmosphere at p = 1 atm and T = 298 K using the ideal gas equation. (b) The atmospheric content of CO₂ is about 360 ppmv (parts per million by volume). Assuming a pressure of 1.00 atm, estimate the amount of CO₂ in a 10.0 km layer of the atmosphere at the surface of the earth. The radius of the earth is 6370 km. (The actual amount of CO₂ in the atmosphere is about 6.0 x 1015 mol.) 3. The van der Waals parameter b is a measure of the volume excluded due to the finite size of the molecules. Estimate the size of a single molecule from the data given below. STATES OF MATTER AND THE VAN DER WAALS EQUATION Table 1.1 Van der Waals constants a and b and critical constants T.. p, and V for selected gases Gas a/bar L² mol b/L mol TJK p/bar V/L mol 308.3 405.5 150.9 304.1 132.9 416.9 513.9 Acetylene (C₂H₂) Ammonia (NH₁) Argon (Ar) Carbon dioxide (CO₂) Carbon monoxide (CO) Chlorine (Cl₂) Ethanol (C,H,OH) Helium (He) Hydrogen (H₂) Hydrogen chloride (HCI) Methane (CH₂) Nitric oxide (NO) Nitrogen (N₂) Oxygen (O₂) Propane (C,Hs) Sulfur dioxide (SO₂) Sulfur hexafluoride (SF) Water (H₂O) 4.516 4.225 1.355 3.658 1.472 6.343 12.56 0.0346 0.245 3.700 2.300 1.46 1.370 1.382 9.385 6.865 7.857 5.537 0.0522 0.0371 0.0320 0.0429 0.0395 0.0542 0.0871 0.0238 0.0265 0.0406 0.0430 0.0289 0.0387 0.0319 0.0904 0.0568 0.0879 0.0305 5.19 32.97 324.7 190.5 180 126.2 154.59 369.82 430.8 318.69 647.14 61.39 113.5 49.55 73.75 34.99 79.91 61.32 2.22 12.93 83.1 46.04 64.8 33.9 50.43 42.50 78.84 37.7 220.6 0.113 0.072 0.075 0.094 0.093 0.123 0.167 0.057 0.065 0.081 0.099 0.058 0.090 0.073 0.203 0.122 0.199 0.056 19 Source: An extensive listing of van der Waals constants can be found in D.R. Lide (ed.), CRC Handbook of Chemistry and Physics, 75th edition. 1994, CRC Press: Ann Arbor, MI.
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Chapter1: Units, Trigonometry. And Vectors
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Transcribed Image Text:HW1. Due: 02/08/2024.
1. The density of dry air at p = 1.0 bar and T =300 K is 1.161 kg/m³. Assuming it consists entirely of
N₂ and O₂ and using the ideal gas law, determine the amount of each gas in moles in a volume of
1 m³ and their mole fractions.
2. (a) Calculate the amount of gas in moles per cubic meter of atmosphere at p = 1 atm and T = 298
K using the ideal gas equation.
(b) The atmospheric content of CO₂ is about 360 ppmv (parts per million by volume). Assuming a
pressure of 1.00 atm, estimate the amount of CO₂ in a 10.0 km layer of the atmosphere at the
surface of the earth. The radius of the earth is 6370 km. (The actual amount of CO₂ in the
atmosphere is about 6.0 x 1015 mol.)
3. The van der Waals parameter b is a measure of the volume excluded due to the finite size of the
molecules. Estimate the size of a single molecule from the data given below.
STATES OF MATTER AND THE VAN DER WAALS EQUATION
Table 1.1 Van der Waals constants a and b and critical constants T.. p, and V for selected gases
Gas
a/bar L² mol
b/L mol
TJK
p/bar
V/L mol
308.3
405.5
150.9
304.1
132.9
416.9
513.9
Acetylene (C₂H₂)
Ammonia (NH₁)
Argon (Ar)
Carbon dioxide (CO₂)
Carbon monoxide (CO)
Chlorine (Cl₂)
Ethanol (C,H,OH)
Helium (He)
Hydrogen (H₂)
Hydrogen chloride (HCI)
Methane (CH₂)
Nitric oxide (NO)
Nitrogen (N₂)
Oxygen (O₂)
Propane (C,Hs)
Sulfur dioxide (SO₂)
Sulfur hexafluoride (SF)
Water (H₂O)
4.516
4.225
1.355
3.658
1.472
6.343
12.56
0.0346
0.245
3.700
2.300
1.46
1.370
1.382
9.385
6.865
7.857
5.537
0.0522
0.0371
0.0320
0.0429
0.0395
0.0542
0.0871
0.0238
0.0265
0.0406
0.0430
0.0289
0.0387
0.0319
0.0904
0.0568
0.0879
0.0305
5.19
32.97
324.7
190.5
180
126.2
154.59
369.82
430.8
318.69
647.14
61.39
113.5
49.55
73.75
34.99
79.91
61.32
2.22
12.93
83.1
46.04
64.8
33.9
50.43
42.50
78.84
37.7
220.6
0.113
0.072
0.075
0.094
0.093
0.123
0.167
0.057
0.065
0.081
0.099
0.058
0.090
0.073
0.203
0.122
0.199
0.056
19
Source: An extensive listing of van der Waals constants can be found in D.R. Lide (ed.), CRC Handbook of Chemistry
and Physics, 75th edition. 1994, CRC Press: Ann Arbor, MI.
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