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Gases have low densities: the density of air is ~ 0.0012 g/cm3. Remember, that the density of water is ~ 1 g/cm3. The low density is due to the fact that the gas molecules are widely spaced. A gas exerts pressure: gases exert a constant, uniform pressure on the walls of the container. This is a unique property of gases and is independent of outside influences such as gravitational forces. When the gas molecules collide with the walls of the container or with each other they do so without any loss in total kinetic E.
Gasses move rapidly in random straight lines and rarely bump into each other. Gas molecules behave as if they were independent particles: attractive forces between them are negligible Fig. 4-3, p.94
Gases can be compressed: that is, gases can be made to occupy a smaller volume. Gases expand to fill the container: the larger the space, i.e. the lower the force pushing down on a gas, the more the gas will expand. Fig. 4-1, p.92
Gases may be mixed together: The same gas or different gases may be mixed together.
Units of Pressure • The SI unit of measurement is the Pascal which is one newton/m2; P = Force/area. • 1 atm = 1.013 x 105 Pa = 101.3 kPa • 1 atm = 101.3 bar • 1 atm = 14.69 psi • 1 atm = 760 mm Hg= 760 torr Units of Temperature for gas calculations • Always expressed in Kelvin, K • Remember: Tk = Tc + 273
Boyle’s Law: The Volume-Pressure LawThe pressure of a gas is inversely proportional to the volume it occupies for a fixed quantity of gas at constant temperature. • P = k (1/V) • For any gas, PV = k, a constant, and it follows that P1V1 = P2V2. • If pressure increases, volume must decrease. And, if pressure decreases, volume must increase.
Charles’s Law: The Volume-Temperature LawThe volume of a fixed quantity of a gas at constant pressure is directly proportional to the absolute temperature • V = kT • For any gas, V/T = k, a constant, and it follows that V1/T1 = V2/T2. • Since V and T are directly proportional to each other, if one goes up the other must also go up, and if one goes down, the other must go down.
Avogadro’s Law: Volume and MolesEqual volumes of gases at the same temperature and pressure contain the same number of molecules. • The law follows that V is directly proportional to n, moles, or V1/n1 = V2/n2
The Ideal Gas Law • Charles’s Law, Boyle’s Law and Avogadro’s Law combine to yield the ideal gas law : PV = nRT R = universal gas constant = 0.08206 L atm/mol K Most gases behave like an ideal gas at low pressure (1 atm or lower) and high temperature (0 0C or higher)
The Combined Gas Law • When there is no change in the number of moles “n”, we can say that (P1V1)/T1 = nR = (P2V2)/T2 or (P1V1)/T1 = (P2V2)/T2 This is called the combined gas law. You do not have to remember this equation, because you can always use the idea gas equation instead.
Dalton’s Law of Partial Pressures For a mixture of gases in a container, the total pressure exerted is the sum of partial pressures of the gases present. The partial pressure of a gas is the pressure that the gas would exert if it were alone in the container. Ptotal = P1 + P2 + P3 Ptotal = ntotal(RT/V)
STP: Standard Temperature and Pressure! • It is defined as temperature equal to 0 degrees centigrade or (273 deg K) and a pressure of 1 atm: T = 0 ºC and P = 1 atm. Then we can use PV = nRT to find that one mole of any gas has a volume = 22.4 liters, the molar volume of any ideal gas V = nRT = (1.00 mol)(0.08206Latm/Kmol)(273K) = 22.4L P 1.00 atm
At STP, one mole of an ideal gas occupies exactly 22.4 L of volume
It Doesn’t Stop!!!!! Gay-Lussac’s Law: When gases react with each other, the reacting volumes are always in the ratio of small whole numbers, if temperature and pressure are constant. 1 liter O2 reacts with 2 liters H2 to form 2 liters water vapor 2 H2 + O2 2H2O Notice: With Gases, volumes can be used like moles! Thanks to Gay-Lussac’s Law, We don’t have to convert from liters to moles! We can (later) do stoichiometry based on Liters
Gay-Lussac’s Law: When gases react with each other, the reacting volumes are always in the ratio of small whole numbers, if temperature and pressure are constant. Fig. 13-1, p. 348
Stoichiometry with gases Two ways of doing stoichiometry with gases: 1. Do the stoichiometry at STP and convert to new conditions using P1V1/n1T1=P2V2/n2T2 You must remember that 1 mole = 22.4 liters at STP 2. Do the stoichiometry to get the moles and plug moles and knowns into the ideal gas equation. This is often faster.
Biggest problem with gas stoichiometry: Juggling too many numbers. When you have a comparison problem Make a table:
Examples • The pressure of a gas is measured to be 2.79 x 105 Pa. Represent this pressure in atm, torr, and psi. Ans. 2.75 atm; 2.10 x 103 torr; 40.4 psi • A steel tank of argon gas has a pressure of 34.6 atm. If all of the argon is transferred to a new tank with a volume 456L, the pressure is measured to be 2.94 atm. What is the volume of the original container? Assume constant temperature. Ans. 38.7 L • A sample of methane gas is collected at 285 K and cooled to 245 K. At 245 K the volume of the gas is 75.0 L. Calculate the volume of the methane gas at 285 K. Assume constant pressure. Ans. 87.2 L • Consider a gas with a volume of 9.25 L at 47 0C and 1 atm pressure. At what temperature does this gas have a volume of 3.50 L and 1 atm pressure? Ans. -152 0C (121K) • If 4.35 g of neon gas occupies a volume of 15.0 L at a particular temperature and pressure, what volume does 2.00 g of neon gas occupy under the same conditions? Ans. 6.90 L
Additional Examples • A 5.00 mol sample of oxygen gas has a pressure of 1.25 atm at 22 0C. What volume does this gas occupy? Ans. 96.8 L • Consider a sample of helium gas at 28 0C with a volume of 3.80 L at a pressure of 3.15 atm. The gas expands to 9.50 L and the gas is heated to 43 0C. Calculate the new pressure of the gas. Ans. 1.32 atm • Equal masses of oxygen and nitrogen gas present in a container. Which gas exerts the larger partial pressure? By what factor? Ans. N2 exerts a partial pressure that is 1.14 times as great as the partial pressure of O2. • A sample of hydrogen gas occupies a volume of 15.0 L at STP. What volume will this sample occupy at 22 0C and 2.50 atm. Ans. 6.48 L • When subjected to an electric current, water decomposes to hydrogen and oxygen gas: 2H2O (l) 2H2(g) + O2(g). If 25 g of water is decomposed, what volume of oxygen gas is produced at STP? Ans. 15.5 L
