Gases

Pressure affects gases much more than in solids or liquids. Gases are compressible and, therefore, the pressure on a gas can be increased. Pressure of gases comes from the collision of the gas particles with any surface (including the earth's surface!) so the more of them you have, the more pressure. The faster the gas particles are moving (higher temperatures), the more often they will collide with a surface, and therefore, the higher the pressure. Because the motion of gas particles is so much greater than in liquids and solids, there are more collisions with the container than in solids or liquids. Pressure is measured via many different units. Converting between the different units for pressure is a necessary evil for chemistry students.

STP or standard temperature and pressure is useful because we can compare volumes of gases if we have a standard temperature and pressure for comparison. The standard temperature is 0 ºC or 273.15 K and standard pressure is exactly 1 atm (same as 760 mm Hg or 760 torr or 101,325 Pa or 14.7 psi or 29.92 in Hg).

1. Convert each pressure unit to atm.

(a) 921 torr (b) 4.8 x 104 Pa (c) 87.5 psi (d) 34.22 in Hg

1. A scuba diver with a lung capacity of 5.2 L inhales a lungful of air at a depth of 45 m and a pressure of 5.5 atm. If the diver were to ascend to the surface (where pressure = 1.0 atm) while holding her breath, to what volume would the air in her lungs expand?

2. A syringe containing 1.55 mL of oxygen gas is cooled from 95.3 °C to 0.0 °C. What is the final volume of oxygen gas?

3. A cylinder with a moveable piston contains 218 mL of nitrogen gas at a pressure of 1.32 atm and a temperature of 298 K. What must the final volume be for the pressure of the gas to be 1.55 atm at a temperature of 335 K?

4. Calculate the volume of each gas sample at STP:

(a) 21.2 mol N2O (b) 0.215 mol CO (c) 0.364 mol CO2 (d) 8.6 mol C2H6

5. A 0.48-mol sample of helium gas occupies a volume of 11.7 L. What is the volume of 0.72 mol of helium gas under the same conditions?

6. A coke can with a pressure of 2.4 atm is cooled rapidly from 100°C to 0°C. What will the new pressure be inside the can?

Dalton's Law of Partial Pressures states that the total pressure, Ptotal, of a mixture of gases is equal to the sum of the partial pressures of the gases making up the mixture. Notice the word "mixture", this law does not apply to cases where the gases react in a chemical reaction. The air we live in would apply to Dalton's Law. Because our air especially contains a lot of water here in the gulf south, the water vapor in the air is also a part of this gas mixture. We call this partial pressure of water vapor, the vapor pressure of water and, like all gases, that pressure is dependent on the same factors affecting gases like V, amount and especially T. Which season has more water vapor in the air: summer or winter?.

1. Rank the following gases from least dense to most dense at 1.00 atm and 298 K: SO2, HBr, CO2. Explain. (10.50)

2. (a) Calculate the density of sulfur hexafluoride gas at 707 torr and 21 °C. (b) Calculate the molar mass of a vapor that has a density of 7.135 g/L at 12 °C and 743 torr. (10.54)

The idea that gases existed as molecules of these elements had to wait for Gay-Lussac and Avogadro to sort some things out. First, Gay-Lussac observed that for many chemical reactions of gases: at constant temperature and pressure, the volumes of gaseous reactants and products can be expressed as ratios of small whole numbers. In other words, using the example above,

1L nitrogen + 3L hydrogen ---> 2L ammonia

The volumes can be measured in any unit (mL, cubic centimeters, etc) and this same relationship exists. Well, Dalton's idea of single atoms combining to make a product does not really hold up with these observations. Avogadro came up with the idea of molecules for these gases (even as elements) and that the volume relationship was the same as those coefficients we have been using:

N2 + 3H2 ---> 2NH3

So the only way the volumes can be the same as the coefficients is if: equal volumes of gases at the same temperature and pressure contain equal numbers of molecules. We know that the coefficients in chemical reactions can be interpreted in terms of the number of particles reacting and forming (or in moles) BUT now we know that those coefficients can also be VOLUMES for gases at a constant temperature and pressure. Experiments eventually showed that for all the elements that are gases near room temperature, except the noble gases, normally exist as diatomic molecules.

1. What is the pressure in a 20.0 L cylinder filled with 0.683 mol of nitrogen gas at a temperature of 325 K?

2. A sample of gas has a mass of 0.555 g. Its volume is 117 mL at a temperature of 85 °C and a pressure of 753 mm Hg. Find the molar mass of the gas.

3. What is the volume, in liters, of 0.250 mole of oxygen gas at 20.0°C and 0.974 atm of pressure?

4. A student collects 425 ml of oxygen at a temperature of 24.0°C and a pressure of 0.899 atm. How many moles of oxygen did the student collect?

5. How many moles of H2O are required to form 1.3 L of O2 at a temperature of 325 K and a pressure of 0.988 atm?

2H2O (l) --> 2H2 (g) + O2 (g)

6. (a) How many grams of oxygen gas are necessary for the complete combustion of 94.5g of toluene (C7H8)? (b) What volume of oxygen would be necessary for this same reaction at STP? (c) What volume of oxygen would be necessary for this same reaction at 50°C and 3 atm of pressure?

Nonideal Gases

The tenets of the kinetic molecular theory are not always representable with real gases. Molecules of gases do exhibit attractions and take up space. This is especially true at high pressures where molecules come into closer contact with one another. The figure above shows that ideal behavior for most gases is not observed above 10 atm of pressure. The effect of temperature on attractive forces is best observed at low pressures.

The figure below shows that, at pressures below about 400 atm, cooling increases the extent to which a gas deviates from ideal behavior. As the gas cools the average kinetic energy of the molecules decreases. This drop in kinetic energy means that molecules do not have sufficient energy to overcome attractive forces and are more likely to "stick to each other" rather than bounce off. As the temperature of a gas increases, from 200 K to 1000 K in the figure above, the negative deviation of PV/RT from the ideal value of 1 disappears.

The van der Waals equation that is used by scientists and engineers in the "real world" takes nonideal behavior into account. Two constants, a (measures how strongly gas molecules attract each other) and b (a measure of the finite volume occupied by the molecules) are to correct for the two reasons gases deviate from ideal behavior: molecular attractions and finite volume of molecules. The term n2a/V2 accounts for attractive forces. The equation adjusts the pressure upward by adding n2a/V2 because attractive forces between molecules tend to reduce the pressure. The term nb accounts for the small but finite volume occupied by gas molecules.

Chemistry is a subject that must be practiced everyday if possible. Take advantage of the practice outlined in the "extra practice" link above and in Mastering Chemistry to give you the practice you need to be successful. DO NOT PROCRASTINATE! Check announcements on Blackboard everyday. Keep a printed copy of the most recent course calendar (included in syllabus) next to your work area. Email me with questions!!

Email: moliver@bishop.edu
Location: Bishop State Community College, North Broad Street, Mobile, AL, United States
Phone: (251)405-4504