# 13.3 The ideal gas law  (Page 6/11)

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## Test prep for ap courses

A fixed amount of ideal gas is kept in a container of fixed volume. The absolute pressure P , in pascals, of the gas is plotted as a function of its temperature T , in degrees Celsius. Which of the following are properties of a best fit curve to the data? Select two answers.

1. Having a positive slope
2. Passing through the origin
3. Having zero pressure at a certain negative temperature
4. Approaching zero pressure as temperature approaches infinity

(a), (c)

This figure shows a clear plastic container with a movable piston that contains a fixed amount of gas. A group of students is asked to determine whether the gas is ideal. The students design and conduct an experiment. They measure the three quantities recorded in the data table below.

Trial Absolute Gas Pressure (x10m 5 Pa) Volume (m 3 ) Temp. (K)
1 1.1 0.020 270
2 1.4 0.016 270
3 1.9 0.012 270
4 2.2 0.010 270
5 2.8 0.008 270
6 1.2 0.020 290
7 1.5 0.016 290
8 2.0 0.012 290
9 2.4 0.010 290
10 3.0 0.008 290
11 1.3 0.020 310
12 1.6 0.016 310
13 2.1 0.012 310
14 2.6 0.010 310
15 3.2 0.008 310
1. Select a set of data points from the table and plot those points on a graph to determine whether the gas exhibits properties of an ideal gas. Fill in blank columns in the table for any quantities you graph other than the given data. Label the axes and indicate the scale for each. Draw a best-fit line or curve through your data points.
2. Indicate whether the gas exhibits properties of an ideal gas, and explain what characteristic of your graph provides the evidence.
3. The students repeat their experiment with an identical container that contains half as much gas. They take data for the same values of volume and temperature as in the table. Would the new data result in a different conclusion about whether the gas is ideal? Justify your answer in terms of interactions between the molecules of the gas and the container walls.

## Section summary

• The ideal gas law relates the pressure and volume of a gas to the number of gas molecules and the temperature of the gas.
• The ideal gas law can be written in terms of the number of molecules of gas:
$\text{PV}=\text{NkT},$
where $P$ is pressure, $V$ is volume, $T$ is temperature, $N$ is number of molecules, and $k$ is the Boltzmann constant
$k=1\text{.}\text{38}×{\text{10}}^{–\text{23}}\phantom{\rule{0.25em}{0ex}}\text{J/K}.$
• A mole is the number of atoms in a 12-g sample of carbon-12.
• The number of molecules in a mole is called Avogadro’s number ${N}_{\text{A}}$ ,
${N}_{\text{A}}=6\text{.}\text{02}×{\text{10}}^{\text{23}}\phantom{\rule{0.25em}{0ex}}{\text{mol}}^{-1}.$
• A mole of any substance has a mass in grams equal to its molecular weight, which can be determined from the periodic table of elements.
• The ideal gas law can also be written and solved in terms of the number of moles of gas:
$\text{PV}=\text{nRT},$
where $n$ is number of moles and $R$ is the universal gas constant,
$R=8\text{.}\text{31}\phantom{\rule{0.25em}{0ex}}\text{J/mol}\cdot \text{K}.$
• The ideal gas law is generally valid at temperatures well above the boiling temperature.

## Conceptual questions

Find out the human population of Earth. Is there a mole of people inhabiting Earth? If the average mass of a person is 60 kg, calculate the mass of a mole of people. How does the mass of a mole of people compare with the mass of Earth?

Under what circumstances would you expect a gas to behave significantly differently than predicted by the ideal gas law?

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