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.
Having a positive slope
Passing through the origin
Having zero pressure at a certain negative temperature
Approaching zero pressure as temperature approaches infinity
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
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.
Indicate whether the gas exhibits properties of an ideal gas, and explain what characteristic of your graph provides the evidence.
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.
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:
where
is pressure,
is volume,
is temperature,
is number of molecules, and
is the Boltzmann constant
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
,
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:
where
is number of moles and
is the universal gas constant,
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?
