By Chuck Roser, Retired Chemistry Instructor Show Next Generation Science Standards
ObjectivesThis experiment’s objectives are to (a) observe the relationship between the pressure and temperature of a constant number of moles of gas in a constant volume container, and (b) to experimentally determine an estimated value for absolute zero. IntroductionWhen a gas is heated, its molecules’ average speed and kinetic energy are increased. If the container has a constant volume, the molecules will strike its sides with greater frequency. This creates greater force on the container’s walls per unit area, increasing pressure in the container. It is one of the bases for the warning against heating an aerosol spray can. A graph may be plotted to show how the pressure of a fixed mass of gas varies as the temperature is changed. The temperature at which the pressure of an ideal gas would, in theory, reach zero can be determined by extrapolating the pressure vs. temperature graph to zero pressure. This temperature is referred to as absolute zero and is the zero point for the Kelvin temperature scale. An extrapolation to zero pressure is necessary because real gases condense to liquids and solidify before reaching absolute zero. The relationship between the pressure of an ideal gas and its Kelvin temperature is expressed in Gay-Lussac’s law: In this experiment, the pressure within the Absolute Zero Demonstrator apparatus is measured at several different temperatures. A graph of pressure vs. temperature is then prepared to establish the relationship between pressure and temperature and to estimate a value for absolute zero. The apparatus consists of a copper bulb having a fixed volume (copper expands and contracts only slightly with temperature), a pressure gauge, and a fixed mass of gas. Gas pressure is measured with the pressure gauge. Before a measurement is taken, the apparatus is allowed to equilibrate to ensure that the gas and bulb are at the same temperature. |
Reading No. | Type of Bath Used | Temperature (°C) | Temperature (°K) | Pressure (mm Hg) |
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Attach a graph of pressure vs. temperature in °C. This graph should have labeled axes with units as follows: scale the x-axis from –300 to 100° C (or a value negative enough to clearly show the x-intercept) and the y-axis from 0 to 1,000 mm Hg. Show the linear regression line through your data with the slope, y-intercept, and correlation factor.
Calculations and questions
- Regression analysis:
Linear regression statistics: slope: _________ y-intercept: _______ correlation factor (r): _____.
Equation of the regression line:Use the slope and a y value of zero to calculate a value for absolute zero:___________. Show your calculations.
- Calculate your relative percent error for the value of absolute zero based on an accepted value of –273° C.
- Are pressure and temperature directly or inversely related? Justify your answer based on your graph.
- Discuss any sources of error that occurred or any improvements that could be made in this experiment.
Instructor's notes
- Caution: Do not use open flames during the experiment. Ethanol and acetone are very flammable.
- Caution: Dry ice and liquid nitrogen should be handled very carefully (wear safety glasses and insulated thermal gloves) due to the risk of frostbite.
- Caution: Never put dry ice or liquid nitrogen in a closed container because each will build up pressure and explode the container.
- Sample data:
Reading No. Type of Bath Used Temperature (°C) Temperature (°K) Pressure (mm Hg) 1 Boiling water 100.0 373.1 945 2 Boiling water + room temp. water 53.0 326.1 840 3 Room temp. water 21.0 294.1 765 4 Ice water 0.0 273.1 720 5 Dry ice/ethanol (or acetone) –78.5 6 Liquid nitrogen –195.7 77.4 225 - It is easier to have 1 beaker available for each bath. Have the boiling-water, room temperature water, ice water, and dry ice/acetone baths already prepared. Have an extra-large beaker of boiling water available for making the boiling-water/room temperature water bath. Check the approximate amount of water needed to cover the bulb in the bath. Note: Be careful not to overfill the beakers or they will overflow when the bulb is immersed.
- Different pairs of students can read the pressure and temperature values for each data point. Note: A mercury thermometer cannot be used with the dry ice/acetone or liquid nitrogen baths since mercury freezes at –39° C. An alcohol thermometer will freeze in liquid nitrogen. The dry ice/acetone bath is assumed to be at the sublimation temperature of 1 atm and –78.5° C, and the liquid nitrogen at its boiling point of 1 atm and –195.7° C.
- A linear relationship between pressure and temperature can be demonstrated with the 4 water bath temperatures. A good value for absolute zero requires a low-temperature data point to reduce the range over which the extrapolation is done. The dry ice/acetone bath provides a good low-temperature data point; however, the liquid nitrogen value works better since it is closer to absolute zero.
- The device should be purged with helium if liquid nitrogen is used since the oxygen in air will condense at the temperature of liquid nitrogen, causing the pressure reading to be too low.
- Denatured ethanol and acetone can be obtained from a hardware store. Dry ice can be obtained from grocery or party stores. A Dewar flask and liquid nitrogen can sometimes be obtained from a local college.
- The dry ice is allowed to sublime at the end of the lab and the ethanol or acetone can be reused. The liquid nitrogen is allowed to evaporate.