# How to Analyze Ideal Gas Data

Instructor: Matthew Bergstresser
The ideal gas law involves temperature, pressure, volume of a gas and the ideal gas constant. In this lesson, we will look at pressure, temperature, and volume of a gas and plot these data.

## Ideal Gas

The word ''ideal'' means different things to different people. An ideal morning to some might be sitting outside with a cup of coffee watching the birds. Another person's ideal morning might be staying in bed! The point is, an ideal situation has a set of parameters that must be met. The same concept applies to an ideal gas. An ideal gas is one whose individual particles' volumes are negligible. They don't exert forces on each other, and they don't stick together when they collide. Let's look at some data involving an experiment with an ideal gas and make a graph of the data.

## Collecting Volume and Temperature Data

A student set up an experiment whereby they collected volume, pressure and temperature data for a gas in a cylinder-piston system. The piston can move up and down allowing the gas to expand. A wireless thermometer is inside the cylinder to relay temperature data. The piston has volume marks on it to indicate the volume of the gas inside the cylinder. The cylinder itself is a heating device allowing the user to increase or decrease the temperature of the gas. Since the piston can move with the increase or decrease in volume, the pressure will remain a constant 1 atmosphere. The student used 2.39 grams of nitrogen gas, which corresponds to 0.0853 mole of nitrogen in the cylinder. The amount of gas remains constant because the cylinder-piston setup is sealed.

The data collected from the experiment is listed in the table below.

Volume and Temperature Data
Volume (liters) Pressure (atmospheres) Temperature (Kelvin)
2.75 1 273
2.82 1 285
2.90 1 290
3.00 1 300
4.20 1 328

Now we can plot this data on a pressure-volume versus temperature graph.

### Graphing the Data

The ideal gas law is PV = nRT where

• P stands for pressure in atmospheres (atm)
• V stands for volume in liters (L)
• n is the number of moles of gas
• R is the ideal gas constant (0.0821 L·/mole·K)
• T is the temperature in Kelvin (K)

We'll plot the pressure-volume data on the y-axis and the temperature data on the x-axis and see where this leads us.

We can see this plot gives us a linear relationship. The next step is to draw a best-fit line through the data that extends past the data points we plotted.

The best-fit line touches the temperature-axis at -273.15 Kelvin. This is a special temperature, which is known as absolute zero. Absolute zero is the temperature at which there is no molecular movement whatsoever, which is theoretically impossible to reach. At this temperature, the gas has no volume; gas is matter, and matter must take up space. This leaves us with the lowest temperature that can be reached, which is just above -273.15 Kelvin. Now let's see what we can glean from the slope of this line.

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