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

• aleksbooker
In summary, the question asks how many atoms of mercury vapor occur per cubic meter in a room saturated with mercury vapor at 24 degrees Celsius. The ideal gas law can be used to find the molar density, which can then be multiplied by Avogadro's number to determine the number of atoms per cubic meter. The equation uses the vapor pressure at 24 degrees Celsius and converts liters to cubic meters.
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

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

Thanks, Chet!

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

## 1. What is the formula for calculating density of a vapor using only vapor pressure and temperature?

The formula for calculating density of a vapor using only vapor pressure and temperature is: density = (vapor pressure * molar mass) / (gas constant * temperature).

## 2. How do you determine the vapor pressure of a substance?

The vapor pressure of a substance can be determined by using a vapor pressure chart or by using the Antoine equation, which relates vapor pressure to temperature and other substance-specific constants.

## 3. Can you calculate the density of a vapor if the molar mass is not known?

No, the molar mass of the vapor is a necessary component in the formula for calculating density. It can be determined by using the ideal gas law, which relates the molar mass to other known variables such as pressure, volume, and temperature.

## 4. How does temperature affect the density of a vapor?

In general, as temperature increases, the density of a vapor decreases. This is because as the temperature increases, the molecules within the vapor have more energy and move farther apart, resulting in a lower density. However, this relationship can vary depending on the specific substance and its properties.

## 5. Is the density of a vapor affected by external factors such as pressure or volume?

Yes, the density of a vapor can be affected by external factors such as pressure or volume. According to the ideal gas law, an increase in pressure or decrease in volume will result in a higher density, while a decrease in pressure or increase in volume will result in a lower density. However, this relationship may not hold true for all substances and can vary depending on their properties.

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