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# Pressure and Temperature Determination

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Suggest the pressure and temperature at which 1.0 mol of (a) Nh3, (b) Xe, (c) He will be in states that correspond to 1.0 mol of H2 at 1.0 atm and 25 degrees Celsius. NH3: T = 3.64 x 10^3 K, p= 8.7 atm, Xe: T=2.60K, p=4.5 atm, He: T=46.7K, p=0.18 atm.

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https://brainmass.com/chemistry/physical-chemistry/pressure-and-temperature-determination-147442

#### Solution Summary

This solution uses the principles of corresponding states to determine the temperature and pressure of NH3, Xe and He. All steps are shown and brief explanations.

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## Pressure, Temperature and Absolute Zero Calculations

Procedure

1. Take a gas piston from the Glassware shelf and place it on the workbench.

2. Take a balance from the Tools shelf and drop it directly onto the gas piston. Record the mass of the empty piston.
Mass of empty piston 111.420 g

3. Select one of the gases from the Chemicals shelf and fill the gas piston with 100 mL of the gas. Record the mass of the piston plus gas.
Chose CH4 Methane new mass is 111.486 g

4. Remove the gas piston from the balance.

5. Open the Data window and click on the gas piston. Click the Pushpin icon on the blue bar of the Data window to lock its display to the gas piston.

6. Take a thermometer and pressure gauge from the Tools shelf and drop them on the gas piston.

7. Take a heating plate from the Tools shelf and drop it on the gas piston.

8. Open the Properties window and click on the heating plate. In the Properties window turn the heating plate on and turn the dial to set the heat to around 200 watts.

9. Watch the temperature of the gas in the piston increase and the gas volume in the piston rise.

10. Once the temperature of the gas has reached nearly 200C, remove the piston from the heating plate.

11. The temperature will begin to fall and the gas volume displayed in the Data window will decrease. Record pairs of temperature and volume data every 10 degrees C or so, until the temperature has returned to room temperature.

Temperatures Gas Volume
190 157.32
180 153.91
170 150.39
160 146.78
150 143.21
140 139.89
130 136.66
120 133.90
110 129.43
100 126.18
90 123.49
80 120.19
70 116.63
60 113.53
50 110.15
40 106.47
30 103.08
21 100.00

NOTE: This is best accomplished by working in pairs, with one person calling out the data values and the other writing them down.

12. Next, take a constant temperature bath from the Tools shelf and place it on the workbench.

13. Using the Properties window, set the bath to dry ice.

14. Drag the bath and drop it onto the gas piston.

15. When the temperature of the gas falls to nearly -70C, Remove the gas piston from the constant temperature bath.

16. Record the temperature and volume of the gas in the piston at every 10C increment or so as it warms back up to room temperature.

Temperature Gas Volume
-70 68.91
-60 72.66
-50 75.85
-40 79.14
-30 82.65
-20 85.83
-10 89.46
0.02 92.85
10 96.25
21 100.00

Assignment

1. Record the formula of the gas you selected to run the experiment.
CH4 Methane

2. What is the constant pressure at which this experiment was run?

3. The molecular weight of the gas is shown in the Data window. Calculate the number of moles of gas from the measured masses of the empty piston and the piston plus gas.

4. Use a spreadsheet to construct a graph of the recorded data with the temperature, in degrees C, on the x-axis and the volume, in mL, on the y-axis.

5. Find the slope and intercept of the straight line fit to the data points. In Excel, the slope is given by the function SLOPE (y values, x values) and the intercept is given by the function INTERCEPT (y values, x values). Record these values.

6. Calculate the value for absolute zero, in degrees Celsius, from the equation developed in the background section of the lab manual:

T0 = -(intercept / slope)

7. The accepted value for absolute zero is -273.15C. Calculate the percent error of your results according to:

%error = |T(experimental) - T(accepted)| / |T(accepted)| * 100

8. In designing the experimental procedure, should you aim to use a large or small initial volume of air? Explain why.

9. In designing the experimental procedure, should you try to control the heating/cooling rate of the apparatus to be slow or fast? Explain why.

10. This experiment extrapolates the behavior of an ideal gas down to coldest possible range. In reality, the gas would condense into a liquid as it approaches absolute zero. Does this affect the conclusion reached regarding the value of absolute zero?

11. Amazingly enough, researchers have recently been able to cool a low-density gas of sodium to nano-Kelvin temperatures, and -273.15C is indeed the limit that is approached. At these low temperatures, the gas is dominated by quantum mechanical effects.

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