CHEM 331
Physical Chemistry
Fall 2014
Problem Set 1
(Historical Gas Laws)
1.
A McLeod Gauge is a device for measuring low gas pressures; down to about 10-6 Torr. It
was invented by Herbert McLeod in 1874. Read the Handout on the
theory of the operation of the McLeod Gauge. Suppose we have a
McLeod Gauge which has a bulb volume of 150 cm3 and attached
capillary tubes of 1.00 mm in diameter. When the Mercury comes to
equilibrium in the Gauge, it reaches a level 21.5 cm below the sealed end
of the bulb capillary and rises to 7.6 cm below the sealed end of the bulb
capillary in the side capillary. Calculate the pressure.
[Ans. 20.9 Pa]
2.
Charles’ Law is sometimes written in the form:
V = Vo (1 + )
where  is the Celsius temperature,  is a constant, and Vo is the volume of the sample at
0oC. The following values of  have been reported for Nitrogen at 0oC:
P [Torr]
749.7
599.6
333.1
98.6
103 [oC-1]
3.6717
3.6697
3.6665
3.6643
Using this data calculate the best value for the Absolute Zero of Temperature on the
Celsius scale.
[Ans. - 273.01 K; watch the sig figs. Must be this exactly.]
3.
The Ideal Gas Temperature scale, an absolute scale, uses the Kelvin as its unit of
measurement and employs Absolute Zero (0 Kelvin) and the Triple Point of Water (273.16
Kelvin) as its "fixed" points. I wish to construct another absolute scale which uses the
Altig as its unit of measurement and sets the Triple Point of Water to be 100.00 Altigs.
What is the boiling point of Water using this scale?
[Ans. 136.61 A]
4.
Consider an Ethanol thermometer whose fixed points are the Ice Point of Water, marked as
273.15K, and the Steam Point, marked as 373.15K. The thermometer has a volume Vo at
0oC and the expansion coefficient  for Ethanol is:
 = 1.0414 x 10-3 + (1.5672 x 10-6)  + (5.148 x 10-8) 
What will the thermometer read in a temperature bath that is 60oC?
5.
In 1901 the 3rd Conference on the International Committee on Weights and Measures
defined the Liter to be equal to the volume occupied by 1 kg of Water at its maximum
density, making it equal to 1.000028 dm3. In 1964 the 12th Conference restored the Liter's
original definition as equal to 1 dm3 exactly. Based on the currently accepted value of the
Universal Gas Constant R of 0.0820575 L atm/K mol, what would the value of R have
been during the period between the 3rd and 12th Conferences?
6.
Gas density data for Sulfur Dioxide at 273.15 K at different pressures is listed below.
P [atm]
0.25
0.50
1.00
 [g/L]
0.71878
1.44614
2.92655
(Take the pressure readings to be relatively exact.)
Use this data to determine the Molar Mass of Sulfur Dioxide. Compare this value with that
obtained on the basis of the atomic weights of the elements. Pay particular attention to
your significant figures.
[Ans. 64.059 g/mol]
7.
A bulb is charged with Hydrogen and Oxygen such that its total pressure reads 1.00 atm.
The mixture is sparked and the Water formed is removed. The bulb's pressure now reads
0.40 atm and the gas it contains is found to be entirely Hydrogen. What was the
composition of the gaseous mixture in the bulb before the reaction to form Water took
place.
[Ans. 80% Hydrogen and 20% Oxygen]
8.
A 1.600 L vessel at 25oC is charged with 1.60 mol of NH3. The vessel's temperature is
raised to 500K, whereupon its pressure reaches 4.85 MPa. At this temperature and pressure
the Ammonia will break-down according to:
NH3
½ N2 + 3/2 H2
What is the composition of the gaseous mixture in the vessel at 500 K?
[Ans. 1.33 mol NH3, 0.40 mol H2, 0.13 mol N2]
9.
The Coefficient of Thermal Expansion () is defined as:
 =
The Coefficient of Compressibilty () is defined as:
 = Compute the values of  and  for an Ideal Gas. Express the derivative:
in terms of  and .
[Ans.  = 1/T and  = 1/P]
10.
For an Ideal Gas, show that:
dP = P(n-1dn + T-1dT – V-1dV)
Suppose 1.0000 mole of Ideal Gas at 300.00K in a 30.000 L vessel has its temperature
increased by 1.00K and its volume increased by 0.050 L. Use the above result to estimate
the change in pressure, P. Calculate P exactly and compare it with your estimate.
[Ans. 0.001365 atm exactly vs. 0.001367 atm approx.]