Test Prep for AP® Courses
13.3 The Ideal Gas Law
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 (x 10 m5 Pa) | Volume (m3) | 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.
13.4 Kinetic Theory: Atomic and Molecular Explanation of Pressure and Temperature
Two samples of ideal gas in separate containers have the same number of molecules and the same temperature, but the molecular mass of gas X is greater than that of gas Y. Which of the following correctly compares the average speed of the molecules of the gases and the average force the gases exert on their respective containers?
| Average Speed of Molecules | Average Force on Container | |
| (a) | Greater for gas X | Greater for gas X |
| (b) | Greater for gas X | The forces cannot be compared without knowing the volumes of the gases. |
| (c) | Greater for gas Y | Greater for gas Y |
| (d) | Greater for gas Y | The forces cannot be compared without knowing the volumes of the gases. |
How will the average kinetic energy of a gas molecule change if its temperature is increased from 20 ºC to 313 ºC?
- It will become sixteen times its original value.
- It will become four times its original value
- It will become double its original value
- It will remain unchanged.
This graph shows the Maxwell-Boltzmann distribution of molecular speeds in an ideal gas for two temperatures, T1 and T2. Which of the following statements is false?
- T1 is lower than T2.
- The rms speed at T1 is higher than that at T2.
- The peak of each graph shows the most probable speed at the corresponding temperature.
- None of the above.
Suppose you have gas in a cylinder with a movable piston which has an area of 0.40 m2. The pressure of the gas is 150 Pa when the height of the piston is 0.02 m. Find the force exerted by the gas on the piston. How does this force change if the piston is moved to a height of 0.03 m? Assume temperature remains constant.
What is the average kinetic energy of a nitrogen molecule (N2) if its rms speed is 560 m/s? At what temperature is this rms speed achieved?
What will be the ratio of kinetic energies and rms speeds of a nitrogen molecule and a helium atom at the same temperature?