Planetary Atmospheres. (a) Calculate the density of the atmosphere at the surface of Mars (where the pressure is 650 Pa and the temperature is typically 253 K, with a CO2 atmosphere), Venus (with an average temperature of 730 K and pressure of 92 atm, with a CO2 atmosphere), and Saturn’s moon Titan (where the pressure is 1.5 atm and the temperature is – 178o C, with a N2 atmosphere). (b) Compare each of these densities with that of the earth’s atmosphere, which is 1.20 kg/m3. Consult Appendix D to determine molar masses.

Solution 5E Step 1: We have the density of a gas = PM/RT p pressure of gas M molar mass of gas R universal real gas constant 8.3145 J/mol.k T absolute temperature gas constant Step 2: For Mars: Given pressure P = 650 Pa Temperature T = 253 K Molar mass M = molar mass of CO 2 Molar mass of CO =mo2ar mass of carbon + (2 × molar mass of oxygen) =12.011 + (2 × 15.999) =44.029 g/mol 3 =44.009 × 10 kg/mol mars= 650 × 44.009 × 10 /8.3145 × 253 = 13.5 × 10 kg/m 3 Step 3: For Venus: Given pressure P = 92 atm Temperature T = 730 K Molar mass M = molar mass of CO 2 Molar mass of CO =molar mass of carbon + (2 × molar mass of oxygen) 2 =12.011 + (2 × 15.999) =44.029 g/mol 3 =44.009 × 10 kg/mol 6 3 venus= 9.322 × 10 × 44.009 × 10 /8.3145 × 730 K 3 3 = 67.59 × 10 kg/m