CHEM 254 EXPERIMENT 2 Critical point determination for SF 6

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Dennis Strickland
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1 CHEM 254 EXPERIMENT 2 Critical point determination for SF 6 The equation of state of a gas defines the relationship between the pressure, temperature and volume of the gas. For ideal gases the equation of state is given as follows; P V m = R T (1) where P pressure, V m is the molar volume, R is the gas constant and T is the temperature. Real gases show deviations from the ideal behavior so when the real gases are considered interaction between the gas molecules and the volumes of the molecules must be included. When the equation of state (equation 1) is expressed with the virial coefficients as in equation (2) the behavior of real gases can be explained. P V m = R T + B (T) P + C (T) P 2 + (2) P V m = R T + B V m 1 + C V m 2 Most commonly used equation of state for real gases is the Van der Waal s equation written in terms of molar volume; (3) In this equation a and b are known as Van der Waals constants. These constants define the deviations from ideal gas behavior and they are characteristics of individual gases. Since there are intermolecular attractive forces between the molecules the constant a provides correction for these forces in real gases. So the term in the equation is concerned with the attraction forces where attraction behaves as an additional pressure and this pressure is called as cohesion pressure. The cohesion pressure of a real gas is considered to be caused by the collision interaction of the gas molecules. The constant b provides correction for the volume of the individual gas molecules and called as co-volume. The available free volume where the molecules move around is reduced by this co-volume. The radius of a gas molecule can be estimated by means of this constant b since it is related to the molecular volume. b= 4. N A. 4/3. π. r 3 (4) The constants of the Van der Waals equation of state can be used to calculate the Boyle Temperature in the equation (5). The temperature where the second virial coefficient B(T) is zero called as Boyle temperature. At this temperature, the properties of real gases are close to the properties of ideal gases.

2 Van der Waals constants can be experimentally determined from the measurement of the critical values of the gas. The temperature, pressure, and the volume at critical point are called the critical temperature, T c, critical pressure, P c, and critical volume, V c, of the gas. When the gas is compressed at a temperature below the critical temperature, Tc, the gas can be liquefied and there occurs a distinguishable phase boundary between the gas and liquid phases. However, at the critical temperature or above, the gas cannot be condensed and there no longer exists a phase boundary. The pressure corresponding to this temperature is called as critical pressure. In the figure below P-V m graph for CO 2 gas is given. The critical temperature can be determined from the graph which in this case corresponds to C and marked with a star. Figure 1: Experimental isotherms of CO 2 gas at several temperatures When these critical quantities are determined experimentally it is possible to calculate the constants a and b from the following equations; Purpose: In this experiment sulfur hexafluoride gas will be enclosed in a variable volume and the variation of pressure with the change in the volume is recorded at different temperatures. The critical point and the critical quantities of SF 6 gas will be determined. Constants of the Van der Waals equation, the Boyle temperature and the radius of the molecules will be calculated.

Apparatus and Chemicals Chemical: SF 6 Figure 2. Experimental set-up. Procedure 1. Set up the experiment as shown in Figure 2. 2. The P-V isotherms of SF 6 should be measured at the following temperatures: 37, 40, 43, 46, and 49 C.

3 Apparatus and Chemicals Chemical: SF 6 Figure 2. Experimental set-up. Procedure 1. Set up the experiment as shown in Figure The P-V isotherms of SF 6 should be measured at the following temperatures: 37, 40, 43, 46, and 49 C. 3. Adjust the temperature of the thermostat (water bath) to 30 C. 4. Carefully turn the handwheel anti-clockwise down to the lower stop, so that the mercury surface is certainly below the inner opening of the valves. 5. Remove all residues of gas from the pressure chamber. To achieve this, evacuate the chamber for at least 30 minutes, so that any gas which might have been dissolved in the mercury is removed. 6. Fill the apparatus with SF 6. When connecting the gas container, it is necessary to prevent any potentially disturbing remnant air from the chamber. Connect the gas container, open the inlet valve a little, and rinse out any remaining air. Close the inlet valve and again evacuate the pressure chamber. After pumping for about 2 minutes, close the outlet valve and open the inlet valve to allow gas to flow into the chamber. Close the inlet valve. Remove the gas container and vacuum pump. The apparatus is now ready for use.

4 7. The pressure of the gas can be controlled using a mercury column. Perform a pressure reading for every 0.2 ml of volume difference. Read and record the exact pressure shown by the manometer. 8. Repeat the experiment for the temperature values mentioned above, collect data at these temperatures and fill in the table When you finish the experiment the piston must be lowered fully (i.e. the wheel turned as far anticlockwise as possible) Note! The setup includes a glass tube filled with SF 6 gas. This tube is surrounded by a water jacket where the temperature can be varied using the thermostat in the water bath. This allows you to control the temperature of the gas in the experiment. After a temperature change, wait for few minutes before reading the temperature to allow temperature equilibrium between the water bath and the gas to take place. Turn the handwheel to compress the gas until the mercury column is visible in the measuring capillary. With suitable gases, and on increasing compression, an increasing liquefaction of the gas can be seen above the mercury meniscus. The corresponding pressure values can be determined more accurately by lightly tapping the manometer to reduce frictional effects. Treatment of Data 1) Plot P-V graph for different temperatures (show each isotherm on the same graph) then find T cr from the graph and its corresponding P cr. 2) Calculate V cr from equation (6). 3) Calculate Van der Waals constants a and b by using the equations (7) and (8). 4) By using theoretical values of T cr and P cr calculate theoretical values of V cr, a and b. Find percent error for the Van der Waals constants. 5) Calculate radius of SF 6 gas from equation (4) and find percent error for this value. 6) Calculate Boyle Temperature from equation (5) for both experimental and theoretical values of a and b, then find percent error.

5 Questions 1) Define critical point and triple point. 2) What are the factors that affect the magnitude of a and b in Van der Walls equation? What is the difference between the two phase diagrams below? 3) Discuss your graph in terms of physical conditions & processes that take place in different regions. 4) What is the importance of supercritical fluids?

6 Data Sheet Table 1. SF 6 : s Volume (cm 3 ) 37 C 40 C 43 C 46 C 49 C

Chapter 3 PROPERTIES OF PURE SUBSTANCES

Thermodynamics: An Engineering Approach Seventh Edition Yunus A. Cengel, Michael A. Boles McGraw-Hill, 2011 Chapter 3 PROPERTIES OF PURE SUBSTANCES Copyright The McGraw-Hill Companies, Inc. Permission