Question

The air on Venus is composed, roughly, of 95% CO2 and 5% N2 by mass. Furthermore, the surface pressure on Venus is 92,000 mb and the surface temperature is a whopping 467 C. (a) Assuming that the percentages of CO2 and N2 are constant in Venus' atmosphere, what is the specific gas constant (in mass units) for Venus? (b) What is the density of air at Venus' surface and how many molecules occupy 1 cm^3? (c) Compare these values to those at Earth's surface.

Answer 1

a) The specific gas constant (in mass units) for Venus

The effective molecular weight of Venus's atmosphere is

0.95*(12 + 32) + 0.05*(28) = 43.2

The universal gas is 8.314 J / mole- K

Change the moles to kg for Venus,

Then 1 mole is replaced by 43.2 g = 0.0432 kg,

8.314 J / mole- K/0.0432 kg = 192.5 J/ (kg K).

The gas constant becomes 192.5 J/ (kg K)

b) On the surface of Venus pressure 92,000 mb = 92 bar

For the Venus atmosphere, the temperature is 467⁰C + 273 = 730 K

The pressure of carbon dioxide

PCO2 = (0.95)(90 bar) = 85.5bar .

Molecular weight of CO₂ is 44.0 g/mol, or 0.0440 kg/mol

R = 0.08314L bar mol–1K–1

d = m/V

or d = PM/RT

Substituting all the value into the expression for the density, the

d = (85.5 bar)(44.0 g/mol)/0.08314L bar mol–1K–1 x730K

   = (61.98 g/L)

    = (61.98 g/L) x 1L/1000 cm3

d= 0.06198 g/cm3

The density of air at Venus' surface is 0.06198 g/cm3

1000 cm³ = 1L

1 cm³ = 1/1000L

1 mol air = 22.4 L air contains 6.02 x 10^23 molecules

1/1000 L air 6.02 x 10^23/(22.4 x 1000)

2.6875 x 10^19 molecules

c) Mass:                              Earth 5.972 37 x 10²⁴ kg      Venus 4.8675 x 10²⁴ kg

Air Pressure:                       101.325 kPa                            9200 kPa

The density of air                0.001225 g/cm3                  0.06198 g/cm3