Chapter 10

Gases

Chapter 10 suggested problems
10th Ed.: 17, 27, 31, 33, 35, 37, 53, 59, 63, 67, 102, 105
11th Ed.: 19, 29, 33, 35, 37, 39, 55, 61, 65, 69, 107, 112

Class Notes

  1. General gas properties

    1. Fluid, no fixed volume or shape, take the shape and volume of the container

    2. Molecular level - particles are relatively far apart and generally do not interact - reason for compressibility

    3. Temperature and pressure

      1. Temperature - a measure of how hot or cold something is; there is a direct correlation between temperature and kinetic energy

        1. K.E. = 3/2 kT (k = 1.38 x 10-23 J K-1)

        2. 1/2 mv2 = 3/2 kT

        3. mv2 = 3 kT

        4. v = (3 kT / m)1/2

      2. Pressure => P = F/A => P = (# of collisions) x (KE of collisions) / area over which collisions occur

        1. lbs/in2

        2. atm (14.7 psi)

        3. bar (14.5 psi)

        4. Torr (T)

        5. mm Hg

        6. in Hg

        7. Pascals (Pa)

        8. 1 atm = 14.7 psi = 760 T = 760 mm Hg = 101,325 Pa

      3. STP - standard temperature and pressure - 1 atm and 273 K

  2. The Ideal Gas Law (Universal Gas Law)

    1. Ideal gases vs. real gases - no volume or interactions; real gases are most like ideal gases at low P and high T

    2. The synthesis of work by Boyle, Charles, Gay-Lussac, and Avogadro

      1. Boyle's Law: P1V1 = P2V2

      2. Charles's Law: V1/T1 = V2/T2

      3. Gay-Lussac's Law: P1/T1 = P2/T2

      4. Avogadro's Law: V1/n1 = V2/n2

    3. PV = nRT

      1. P = pressure (atm)

      2. V = volume (L)

      3. n = number of moles (mol)

      4. T = temperature (K)

      5. R = gas constant = 0.0821 L atm / mol K

    4. Examples

      1. If 1.00 mole of a gas occupies a volume of 1.00 L at 298 K, what is the pressure inside the container? (24.46 atm)

      2. A 5.00 L container holds a gas at 810 T and 62 oC. How many moles of gas are present? (0.194 moles)

      3. If you blow exactly 2.00 moles of air into a balloon at a pressure of 780 mm Hg and at a temperature of 35 oC, what volume must the balloon hold to keep from bursting? (49.3 L; volumes: 11" balloon - 11.4 L, 18" balloon - 50.0 L)

      4. 6.75 moles of an unknown gas occupy a volume of 13.3 L at a pressure of 17.6 atm. What is the temperature of the gas? (422.4 K)

    5. Determination of molar masses - can use the Ideal Gas Law to find the molar mass of unknown substances

      1. n = number of moles = mass of substance / molar mass

      2. PV = gRT / MW

      3. examples

        1. 44.9 g of an unknown gas exert a pressure of 2.55 atm within a 10.2 L container at 325 K. Is the unknown gas nitrogen dioxide or sulfur dioxide? (mw = 46.06 g/mol; mw for NO2 = 46.01 g/mol, mw for SO2 = 64.06 g/mol)

        2. A damaged unmarked cylinder of compressed gas in found. You suspect that the gas is either argon, nitrogen, helium, or carbon dioxide. A 5.00 L mylar bag is filled with the gas to a pressure of 1900 T at 298 K. When weighed, the mass of the gas is 20.42 g. What is it? (mw = 39.97 g, Ar)

    6. Stoichiometry

      1. An 18" balloon has a volume of 50.0 L. How many grams of water must be decomposed via electrolysis to fill the balloon with hydrogen to a pressure of 1.05 atm at 298 K?
        PV/RT = n = 2.146 moles hydrogen
        2.146 moles hydrogen is generated by the decomposition of 38.7 grams of water

      2. The reaction of 75.0 g of iron (III) sulfide with excess hydrochloric acid will produce what volume of gas at 755 T and 293 K?
        75.0 g iron (III) sulfide is equivalent to 1.082 moles hydrogen disulfide; (26.2 L)

  3. Ideal gases and real gases

    1. Ideal gas law and its assumptions

    2. The properties of real (non-ideal) gases may be calculated using the van der Waals equation

      1. (P + an2/V2)(V-nb) = nRT

      2. a and b are unique for each gas

      3. a: corrects for attractive interactions, which may cause gas pressure to be less than ideal

      4. b: corrects for the actual volume of the gas particles

        1. http://chemed.chem.purdue.edu/genchem/topicreview/bp/ch4/deviation5.html

        2. http://www.ac.wwu.edu/~vawter/PhysicsNet/Topics/Thermal/vdWaalEquatOfState.html

  4. Comparative calculations

    1. For any gas under any set of conditions PV = nRT

    2. for any gas in which the conditions change

      1. start: P1V1 = n1RT1

      2. finish: P2V2 = n2RT2

      3. Since R is constant in both cases

        1. R = (P1V1) / (n1T1)

        2. R = (P2V2) / (n2T2)

        3. (P1V1) / (n1T1) = (P2V2) / (n2T2)

      4. This is Boyle's Law, Charles's Law, Gay-Lussac's Law, and Avogadro's Law all rolled into one. If you remember this relationship you don't need to remember all of the others.

    3. Examples

      1. 7.5 moles of a gas at 2.25 atm of pressure occupy a volume of 2.00 L. If the gas is compressed to a volume of 1.00 L what is the new pressure of the gas? (4.50 atm)

      2. A sample of gas at 373 K exerts a pressure of 1500 T. If the temperature drops to 273 K, what will the new pressure be? (1.44 atm)

      3. 10.0 moles of helium at 298 K occupy a volume of 20.5 L at a pressure of 11.93 atm. If the temperature of the gas increases to 328 K, how must the container volume change for the pressure to remain the same? (22.56 L)

      4. A 3.6 mole sample of gas in a sealed vessel has a pressure of 4.25 atm. If the number of moles of gas is increased to 4.9 moles, what will the new pressure be? (5.78 atm)

      5. 10.0 moles of a gas at 26.0 atm and 303 K occupy a volume of 9.57 L. If the number of moles of gas is suddenly changed to 15.0 moles while the temperature increases to 373 K and the volume decreases to 5.00 L, what will the new pressure in the container be? (91.89 atm)

  5. Dalton's Law of Partial Pressures

    1. If more than one substance is present in gaseous form, the total pressure is the sum of pressures of all of the gases present

    2. The pressure each gas contributes to the total pressure is called it's partial pressure

    3. PT = P1 + P2 + P3 + . . . .

    4. Examples

      1. A sealed flask contains nitrogen at a pressure of 500 T and oxygen at a pressure of 250 T. What is the total pressure in the flask? (750 T)

      2. A 10.0 L flask contains 1.0 mole of carbon dioxide, 2.0 moles of methane, and 4.0 moles of water vapor. If the temperature inside the flask is 303 K, what is the total pressure? (2.49 atm + 4.98 atm + 9.95 atm = 17.4 atm)

    5. Mole fraction - the ratio of the gas pressure of a single component divided by the total pressure (P1 / PT), or, the ratio of the number of moles of a single component divided by the total number of moles (n1 / nT)

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