Q.On the planet Mars, the average temperature is around $-53°C$ and the atmospheric pressure is 0.9 kPa. Calculate the number of moles of the molecules per unit volume on the planet Mars. Is this greater than that on Earth?

Step 1. Convert Mars' temperature: $T_{Mars}=-53°C+273=220\ \text{K}$, and its pressure is $P_{Mars}=0.9\ \text{kPa}=900\ \text{Pa}$.

Step 2. From the ideal gas law $PV=\mu RT$, the number of moles per unit volume is $\dfrac{\mu}{V}=\dfrac{P}{RT}$. For Mars: $\dfrac{\mu_{Mars}}{V}=\dfrac{900\ \text{Pa}}{(8.314\ \text{J mol}^{-1}\text{K}^{-1})(220\ \text{K})}=\dfrac{900}{1829.1}\approx0.492\ \text{mol/m}^3.$

Step 3. For Earth, taking standard atmospheric pressure $P_{Earth}=101.3\ \text{kPa}=1.013\times10^5\ \text{Pa}$ and room temperature $T_{Earth}=300\ \text{K}$: $\dfrac{\mu_{Earth}}{V}=\dfrac{1.013\times10^5}{(8.314)(300)}=\dfrac{1.013\times10^5}{2494.2}\approx40.6\ \text{mol/m}^3.$

Step 4. So Mars has FAR FEWER moles per unit volume than Earth (about 0.49 vs about 40, roughly 80 times less) -- consistent with Mars' extremely thin atmosphere.

Apply $\mu/V=P/RT$ separately for Mars (given P, T) and Earth (standard atmospheric P, room T), then compare.

• Forgetting to convert Mars' Celsius temperature to kelvin before substituting.
• Comparing Mars' pressure directly to Earth's without also accounting for the different temperatures -- both P and T matter in $\mu/V=P/RT$.