How do you calculate density of a vapor only vapor pressure and temp.

[aleksbooker]

Hello all,

The question given is:

Mercury and many of its compounds are dangerous poisons if breathed, swallowed or even absorbed through the skin. The liquid metal has a vapor pressure of 0.00169mmHg at 24 degrees Celsius. If the air in a small room is saturated with mercury vapor, how many atoms of mercury vapor occur per cubic meter?

I can't use Clausius-Clapeyron because I only have one pressure and one temperature to work with, and I can't use PV = nRT, because I don't know how many moles of mercury I have. If I arbitrarily increase the moles, I increase the volume just as quickly, which may not affect density, but either way I don't know the concentration of moles per liter. I even considered the pressure = force/area, but that's not relevant to volume.

I'm certain the fact that the air is saturated is somehow key, but I can't find anything in my textbook that seems to address this question. What am I missing?

Thanks,
Aleks

 

[Chestermiller]

Hi Aleks. Welcome to Physics Forums!

You can use the ideal gas law. You first need to find out how many moles of mercury there are in each cubic meter. From the ideal gas law, the molar density is $$\frac{n}{V}=\frac{P}{RT}$$. This has units of moles per cubic meter. You then multiply by Avagado's number to get the number of atoms per cubic meter. In this equation, P is the vapor pressure at 24 (room temperature) and you use T = 273+24.

Chet

 

[aleksbooker]

Thanks, Chet!

It took some fishing, but I figured it out. I didn't consider that liters could be converted into cubic meters.