# Ideal Gas Law- finding gas density

• chantalprince
In summary, the conversation discusses finding the density of radon gas at 0 degrees C and 1 atmosphere using the equation PV=nRT and the concept of density as mass over volume. The conversation also touches on the importance of considering the number of molecules per unit volume and the mass of a single radon gas molecule in finding the answer. In the end, the person asking the question was able to successfully solve the problem and confirm the accuracy of their solution.
chantalprince

## Homework Statement

What is the density of radon gas at 0 degrees C and 1 atmosphere?

## Homework Equations

PV= nRT
0 C = 273 K

density = mass/volume g/m^3

## The Attempt at a Solution

I want density = g/m^3

Below are the units of PV = nRT. I thought that breaking it down would help me to see where the g's and the m^3 are- but so far its just confused me.

I have been trying to manipulate PV = nRT so that the units eventually give me g/m^3. I think I got something close, but then realized that all I have to plug in is T and P. This is what I tried: P/R = nT/V Units end up: g/m^3 = 1/m^3 I'm not sure if that works out...

Nothing is changing so I can't cancel anything and then set up a proportion equation- What the heck do I do??

chantalprince said:

## Homework Statement

What is the density of radon gas at 0 degrees C and 1 atmosphere?

## Homework Equations

PV= nRT
0 C = 273 K

density = mass/volume g/m^3

...

Nothing is changing so I can't cancel anything and then set up a proportion equation- What the heck do I do??
You won't find the answer with just PV=nRT. This is because mass of the gas molecules has no effect on P, V or T for an ideal gas.

Since density is mass/volume you need to relate mass to volume. What is the number of molecules per unit volume? What is the mass of a molecule of Radon gas?

AM

Thanks so much! I worked it out then referenced to the actual density of radon that I found online and it agrees

Thanks again AM.

## 1. What is the Ideal Gas Law and how is it used to find gas density?

The Ideal Gas Law is a mathematical equation that describes the relationship between the pressure, volume, temperature, and number of moles of an ideal gas. It can be written as PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is temperature. To find gas density using this law, we rearrange the equation to solve for density (d = nM/V), where M is the molar mass of the gas.

## 2. What is an ideal gas and how does it differ from a real gas?

An ideal gas is a hypothetical gas that follows the Ideal Gas Law at all temperatures and pressures. It has particles that have no volume and do not interact with each other. In reality, no gas is truly ideal, and real gases can deviate from the Ideal Gas Law at high pressures and low temperatures due to intermolecular forces and particle volume.

## 3. How does temperature affect gas density according to the Ideal Gas Law?

According to the Ideal Gas Law, temperature and density have an inverse relationship. As temperature increases, the density of a gas decreases, and vice versa. This is because at higher temperatures, the gas particles have more kinetic energy and move faster, resulting in more space between the particles and lower density.

## 4. Is the Ideal Gas Law applicable to all gases?

The Ideal Gas Law is most accurate for low pressure and high temperature conditions. For gases that deviate from ideal behavior, such as real gases, high pressure and low temperature conditions, or gases with strong intermolecular forces, the Ideal Gas Law may not accurately predict gas density. In these cases, other equations, such as the van der Waals equation, may be used.

## 5. How can I use the Ideal Gas Law to find gas density in a real-life scenario?

To find the gas density in a real-life scenario, you would need to know the pressure, volume, temperature, and molar mass of the gas. You can then rearrange the Ideal Gas Law equation to solve for density (d = nM/V) and plug in the known values. Make sure to use consistent units for all variables.

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