Question

Consider three gases: Ar, SF6, and Cl2. If 50.0 grams of these gases are placed in each of three identical containers, which container will have the highest pressure? The volume and temperature of all three containers are the same.

Answer 1

The ideal gas law:

`pV=nRT \Rightarrow p=(nRT)/(V)`
p - pressure, n - number of moles, R - the gas constant, T - temperature, V - volume

The volume and temperature of all three containers are the same, so the pressure depends on the number of moles. The greater the number of moles, the higher the pressure.
The mass of gases is 50 g.


`Ar \\ M \approx 39.948 \ (g)/(mol) \\ n=(50 \ g)/(39.948 \ (g)/(mol)) \approx 1.25 \ mol \\ \\ SF_6 \\ M \approx 146.06 \ (g)/(mol) \\ n=(50 \ g)/(146.06 \ (g)/(mol)) \approx 0.34 \ mol \\ \\ Cl_2 \\ M=70.9 \ (g)/(mol) \\ n=(50 \ g)/(70.9 \ (g)/(mol)) \approx 0.71 \ mol`

The greatest number of moles is in the container with Ar, so there is the highest pressure.