Question

Titan, the largest satellite of Saturn, has a thick nitrogen atmosphere. At its surface, the pressure is 1.5 Earth-atmospheres and the temperature is 94 K.
A) What is the surface temperature in ?
B) Calculate the surface density in Titan's atmosphere in molecules per cubic meter.
C) Calculate the density of Earth's atmosphere at 22 .

Answer 1

Pressure \((p)=1.5\) Earth \(-\) atmosphere Temperature \((T)=94 \mathrm{~K}\) Universal gas constant \((R)=0.0820\) L.atm \(/ \mathrm{K} \cdot \mathrm{mol}\)

(a) Surface temperature in \({ }^{0} \mathrm{C}\) is, \(\begin{aligned}{ }^{0} \mathrm{C} &=\text { Temperature in kelvin }-273 \\ &=94-273 \\ &=-179{ }^{\circ} \mathrm{C} \end{aligned}\)

(b) Use the ideal gas equation to calculate the density in Titan's atmosphere in molecules per cubic meter. \(\begin{aligned} p V &=n k T \\ \frac{n}{V} &=\frac{p}{k T} \\ &=\frac{(1.5 \mathrm{~atm})\left(1.013 \times 10^{5} \mathrm{~Pa} / \mathrm{atm}\right)}{\left(1.38 \times 10^{-23} \mathrm{~J} / \mathrm{molecule} \mathrm{K}\right)(94 \mathrm{~K})} \end{aligned}\)

\(=1.2 \times 10^{26}\) molecules \(/ \mathrm{m}^{3}\)

(c) Again use the ideal gas equation to calculate the density of earth's atmosphere at \(22{ }^{\circ} \mathrm{C}\) \(\begin{aligned} p V &=n k T \\ \frac{n}{V} &=\frac{p}{k T} \\ &=\frac{(1.0 \mathrm{~atm})\left(1.013 \times 10^{5} \mathrm{~Pa} / \mathrm{atm}\right)}{\left(1.38 \times 10^{-23} \mathrm{~J} / \mathrm{molecule}\right)(273+22) \mathrm{K}} \\ &=2.5 \times 10^{25} \text { molecules } / \mathrm{m}^{3} \end{aligned}\)