Lab 11

Lab #11

Pressure-Temperature Relationship in Gases

Gases are made up of molecules that are in constant motion and exert pressure when they collide with the walls of their container. The velocity and the number of collisions of these molecules is affected when the temperature of the gas increases or decreases. In this experiment, you will study the relationship between the temperature of a gas sample and the pressure it exerts. Using the apparatus shown in Figure 1, you will place an Erlenmeyer flask containing an air sample in water baths of varying temperature. Pressure will be monitored with a Gas Pressure Sensor and temperature will be monitored using a Temperature Probe. The volume of the gas sample and the number of molecules it contains will be kept constant. Pressure and temperature data pairs will be collected during the experiment and then analyzed. From the data and graph, you will determine what kind of mathematical relationship exists between the pressure and absolute temperature of a confined gas. You will also do the extension exercise and use your data to find a value for absolute zero on the Celsius temperature scale.

OBJECTIVES

In this experiment, you will

·    Study the relationship between the temperature of a gas sample and the pressure it exerts.

·    Determine from the data and graph, the mathematical relationship between the pressure and absolute temperature of a confined gas.

·    Find a value for absolute zero on the Celsius temperature scale.

Figure 1

MATERIALS

computer	125 mL Erlenmeyer flask
Vernier computer interface	hot plate
Logger Pro	four 1 liter beakers
Vernier Gas Pressure Sensor	glove or cloth
Vernier Temperature Probe	ice
plastic tubing with two connectors
rubber stopper assembly

PROCEDURE

1. Obtain and wear goggles.

2. Prepare a boiling-water bath. Put about 800 mL of distilled water into a l L beaker and place it on a hot plate. Turn the hot plate to a high setting.

3. Prepare an ice-water bath. Put about 700 mL of cold tap water into a second 1 L beaker and add ice.

4. Put about 800 mL of room-temperature water into a third 1 L beaker.

5. Put about 800 mL of hot tap water into a fourth 1 L beaker.

6. Prepare the Temperature Probe and Gas Pressure Sensor for data collection.

a.    Plug the Gas Pressure Sensor into CH1 and the Temperature Probe into CH2 of the computer interface.

b.    Obtain a rubber-stopper assembly with a piece of heavy-wall plastic tubing connected to one of its two valves. Attach the connector at the free end of the plastic tubing to the open stem of the Gas Pressure Sensor with a clockwise turn. Leave its two-way valve on the rubber stopper open (lined up with the valve stem as shown in Figure 2) until Step 9.

c.    Insert the rubber-stopper assembly into a 125 mL Erlenmeyer flask. Important: Twist the stopper into the neck of the flask to ensure a tight fit.

d.   Close the 2-way valve above the rubber stopper—do this by turning the valve handle so it is perpendicular with the valve stem itself (as shown in Figure 3). The air sample to be studied is now confined in the flask.

Figure 2

Figure 3

7. Prepare the computer for data collection by opening the file “07 Pressure-Temperature” from the Chemistry with Computers folder of Logger Pro.

8. Click to begin data collection.

9. Collect pressure vs. temperature data for your gas sample:

a.    Place the flask into the ice-water bath. Make sure the entire flask is covered (see
Figure 3). Stir.

b.    Place the temperature probe into the ice-water bath.

c.    When the pressure and temperature readings displayed in the meter stabilize, click . You have now saved the first pressure-temperature data pair.

10. Repeat the Step-9 procedure using the room-temperature bath.

11. Repeat the Step-9 procedure using the hot-water bath.

12. Once the water is boiling remove the flask from the hot plate. Turn off the hot plate. Use the gloves to hold the hot beaker. Place the temperature probe in the water bath, place the flask in the water bath and repeat the Step-9 procedure. Click . CAUTION: Do not burn yourself or the probe wires with the hot plate.

13. Click when you have finished collecting data.

14. Examine your graph of pressure vs. temperature (°C). In order to determine if the relationship between pressure and temperature is direct or inverse, you must use an absolute temperature scale; that is, a temperature scale whose 0° point corresponds to absolute zero. We will use the Kelvin absolute temperature scale. Instead of manually adding 273 to each of the Celsius temperatures to obtain Kelvin values, you can create a new data column for Kelvin temperature.

a.    Choose New Calculated Column from the Data menu.

b.    Enter “Temp Kelvin” as the Name, “T Kelvin” as the Short Name, and “K” as the Unit. Enter the correct formula for the column into the Equation edit box. Type in “273+”. Then select “Temperature” from the Variables list. In the Equation edit box, you should now see displayed: 273+“Temperature”. Click .

c.    Click on the horizontal axis label and select “Temp Kelvin” to be displayed on the horizontal axis.

15. Decide if your graph of pressure vs. temperature (K) represents a direct or inverse relationship:

a.    Click the Curve Fit button, . Procedure

b.    Choose your mathematical relationship from the list. If you think the relationship is linear (or direct), use Linear. If you think the relationship represents a power, use Power. Click .

c.    A best-fit curve will be displayed on the graph. If you made the correct choice, the curve should match up well with the points. If the curve does not match up well, try a different mathematical function and click again. When the curve has a good fit with the data points, then click .

d.   Autoscale both axes from zero by double-clicking in the center of the graph to view Graph Options. Click the Axis Options tab, and select Autoscale from 0 for both axes.

16. Print a copy of the graph of pressure vs. temperature (K). The regression line should still be displayed on the graph. Enter your name(s) and the number of copies you want to print.

PROCESSING THE DATA

1. In order to perform this experiment, what two experimental factors were kept constant?

2. Based on the data and graph that you obtained for this experiment, express in words the relationship between gas pressure and temperature.

3. Explain the relationship between gas pressure and temperature using the concepts of molecular velocity and collisions of molecules.

4. Write an equation to express the relationship between pressure and temperature (K). Use the symbols P, T, and k.

5. One way to determine if a relationship is inverse or direct is to find a proportionality constant, k, from the data. If this relationship is direct, k = P/T. If it is inverse, k = P•T. Based on your answer to Question 4, choose one of these formulas and calculate k for the four ordered pairs in your data table (divide or multiply the P and T values). Show the answer in the fourth column of the Data and Calculations table. How “constant” were your values? You can also Add a New Calculated Column (the directions are at the end of the lab) You will need to put in the formula for the relationship. You can either write your data in the table below or print out a data table with all four columns visible.

6. According to this experiment, what should happen to the pressure of a gas if the Kelvin temperature is doubled? Check this assumption by finding the pressure at –73°C (200 K) and at 127°C (400 K) on your graph of pressure versus temperature. How do these two pressure values compare?

DATA AND CALCULATIONS

Pressure	Temperature (°C)	Temperature (K)	Constant, k (P / T or P•T)

EXTENSION

The data that you have collected can also be used to determine the value for absolute zero on the Celsius temperature scale. Instead of plotting pressure versus Kelvin temperature like we did above, this time you will plot Celsius temperature on the y-axis and pressure on the x-axis. Since absolute zero is the temperature at which the pressure theoretically becomes equal to zero, the temperature where the regression line (the extension of the temperature-pressure curve) intercepts the y-axis should be the Celsius temperature value for absolute zero. You can use the data you collected in this experiment to determine a value for absolute zero.

1. Remove the curve fit box on the graph by clicking on its upper-left corner.

2. Click on the vertical-axis label and select “Temperature” to plot the Celsius temperature. In the same way, select “Pressure” to be displayed on the horizontal axis.

3. Rescale the temperature axis from a minimum of –300°C to a maximum of 200°C. This may be done by clicking on the minimum or maximum value displayed on the graph axis and editing them. The pressure axis should be scaled from 0 kPa to 150 kPa (or 0 atm to 1.5 atm).

4. Click the Linear Fit button, a best-fit linear regression curve will be shown for the four data points. The equation for the regression line will be displayed in a box on the graph, in the form y = mx + b. The numerical value for b is the y-intercept and represents the Celsius value for absolute zero.

5. Print the graph of temperature (°C) vs. pressure, with the regression line and its regression statistics still displayed. Enter your name(s) and the number of copies you want to print. Clearly label the position and value of absolute zero on the printed graph.

Problems

1. At 22.5 °C the volume of a balloon is 3.25 L, what would the volume be at 3.5 °C?

(Assuming pressure and # of mols are constant.)

2. The volume in a piston is 275 mL at 15.0 °C, if the volume of the piston decreases to 135 mL, what is the temperature in °C? (Assuming pressure and # of mols are constant.)

3. If the pressure in a rigid tank of gas is 1500. torr at 35.0 °C, what will the pressure be if the temperature decreases to 21.5 °C?

4. A can will rupture if the pressure exceeds1400 torr. If the pressure is1250. torr at 15.0 °C, at what temperature (in °C) will the can rupture?

5. What is the pressure of 1.25 mol of N₂ that occupies 25.0 L at 22.5 °C?

6. If you have 35.0 g of carbon dioxide at 15.0 °C and a pressure of 795 torr, what is the volume?

7. At what temperature (in °C) would 5.0 g of oxygen have a volume of 2275 mL and a pressure of 1.850 atm?

8. If a sample of He has a volume of 12.5 L at 25.0 °C with a pressure of 995 torr, how many g do you have?

9. A sample of carbon dioxide has a volume of 2.75 L at 22.0 °C and a pressure of 875 torr. What will the volume be if you change the temperature to 45.0 °C and the pressure to 1095 torr?

10. A sample of nitrogen occupies 750. mL at 24.0 °C at a pressure of 595 torr. At what temperature (in °C) would the pressure be 775 torr and the volume be 895 mL?

R = 62.4 torr L R = 0.0821 atm L

mol K mol K