2 Kinetic Molecular Theory (KMT) Gas particles are tiny (molecular size is negligible compared to total volume of gas)Gas particles are in constant, rapid, random motionParticles are small spheres with insignificant volumeParticles are far apartNo attractive forces between particlesGas will spread out to fill containerAll particle collisions are perfectly elastic (kinetic energy can be transferred between molecules but as long as temperature is constant, average kinetic energy remains the same)Average kinetic energy is proportional to temperature (at any temperature, molecules have the same average kinetic energy)
3 Pressure Pressure = force distributed over an area Pressure results when particles collide No particles = no collisions, no pressure (a vacuum) SI unit of pressure = pascal (Pa) (1 Newton/square meter) Other pressure units: atmosphere (atm), millimeters of mercury (mmHg), torricelli (torr), bar To convert: 1 atm = 760 mmHg = kPa = 760 torrAlso: 1000 Pa = 1 kPa, 1 bar = Pa Manometer = instrument used to measure pressure based on the height of a mercury column that the gas pressure can supportBarometer = device used to measure atmospheric pressure
4 TemperatureAbsolute temperature (temperature in Kelvin) is directly proportional to average kinetic energy of particles Recall Temp in Kelvin = T in Celsius + 273 Temp in Celsius = T in Kelvin -273 Absolute zero (0 Kelvin, -273 Celsius) = essentially no kinetic energy, no particle movement Standard Temperature and Pressure For many gas calculations “standard temperature and pressure” (STP) conditions are used as common reference conditions. Standard temperature and pressure is 1 atm (= 760 mmHg = kPa etc.) and 273 K (0 degrees Celsius).
5 Following Links gives practice problems Boyles LawCharles LawCombined Gas LawIdeal Gas Law
6 Boyle's LawWith a given amount of gas and temperature as the volume is changed the pressure will vary inversely by a constant amount.V =k/P ( V is volume, P is pressure, and k is the proportionality constant)So long as temperature remains constant at the same value the same amount of energy given to the system persists throughout its operation and therefore, theoretically, the value of k will remain constant.P1V1 = P2V2 ( P1 is the initial pressure, V1 is the initial volume, P2 is the new pressure for a new volumeexample:A sample of oxygen with a volume of 500 mL and 760 mmHg is compressed to 425 mL. What is the pressure exerted by the oxygen after it is compressed? P1 = 760 mmHg, V1 = 500 mL, V2 = 425 mL , and P2 = ? ( 760 mmHg )(500 mL ) = P2 ( 425 mL ) ( 760 mmHg )( 500 mL ) / ( 425 mL ) = P2 = 894 mmHg
8 Samples1. If some neon gas at 121 kPa were allowed to expand from 3.7 dm3 to 6.0 dm3 without changing the temperature, what pressure would the neon gas exert under these new conditions? 2. A quantity of gas under a pressure of 1.78 atm has a volume of 550 cm3. The pressure is increased to 2.50 atm, while the pressure remains constant. What is the new volume? 3. Under a pressure of 172 kPa, a gas has a volume of 564 cm3. The pressure is decreased, without changing the temperature, until the volume of the gas is equal to 8.00 x 102 cm3. What is the new pressure?
10 Charle's Lawgiven amount of gas at a constant pressure changes volume directly related to the change in temperature.V = kT ( V is volume, T is temperature and k is constant of proportionality )When one goes up, the other goes upV1 / T1 = V2 / T2 example:To make 300 mL of oxygen at 20.0 C change in volume to 250 mL, what must be done to the sample if its pressure and mass are held constant. V1 = 300 mL, T1 = = 293 K, V2 = 250 mL, and T2 = ? ( 300 mL ) / ( 293 K) = (250 mL) / T2 T2 = (293 K)(250 mL) / (300 mL) = 244 K = -29 C
12 1. What volume will a sample of hydrogen occupy at 28 1. What volume will a sample of hydrogen occupy at 28.0 oC if the gas occupies a volume of 2.23 dm3 at a temperature of 0.0 oC? Assume that the pressure remains constant. (remember to change to Kelvin).2. If a gas occupies 733 cm3 at 10.0 oC, at what temperature will it occupy 950 cm3? Assume that pressure remains constant.3. A gas occupies 560 cm3 at 285 K. To what temperature must the gas be lowered to, if it is to occupy 25.0 cm3? Assume a constant pressure.
14 Gay-Lussac's LawThe pressure of given amount of gas held at constant volume is directly proportional to the Kelvin temperature.P = kT ( P is pressure, T is temperature, and k is constant of proportionality )P1 / T1 = P2 / T2 example:A sample of Nitrogen gas contained in a 50 L rigid container has a pressure of 101 kPa at 25 C. If the container is heated to 150 C what is the pressure in the container? P1 = 101 kPa, T1 = = 298 K, T2 = = 423 K, and P2 = ? (101 kPa) / (298 K) = P2 / (423 K) (101 kPa)(423 K) / (298 K) = P2 = 143 kPa
15 Combined Gas LawThe volume of a given amount of gas is proportional to the ratio of its Kelvin temperature and its pressure.PV = kTP1V1/T1 = P2V2/T2Memorize just the combined, and you can reduce it to any of the other three by cancelling out the variable you don’t need!Or, if you need to use all variables because more than one condition changes, keep them all… example:What will be the final pressure of a sample of nitrogen with a volume of 950 L at 745 torr and 25.0 C if it is heated to 60.0 C and given a final volume of 1150 L? P1 = 745 torr, V1 =950 L, T1 = = K, V2 = 1150 L , T2 = = K, and P2 = ? (745 torr)(950 L) / (298.2 K) = P2 (1150 L) / (333.2 K) (745 torr)(950 L)(333.2 K) / [(298.2 K)(1150 L)] = P2 = 688 torr
16 Avogadro's PrincipleWhen measured at the same temperature and pressure, equal volume of gases contain equal number of moles.1 mol of gas at STP occupies approximately 22.4 Liters.
17 Ideal Gas LawPressure, Volume, temperature and the number of moles of gas are related by a proportionality constant.PV = nRT ( P is pressure in atm, V is volume in Liters, n is the number of moles, T is temperature in Kelvin, and R is the ideal gas constant L atm /(mol K) example:What volume in milliliters does a sample of nitrogen with a mass of g occupy at 21 C and 750 torr? Convert all units to Liters, atmospheres and Kelvin. .245 g N2 ( 1 mol N2 / 14.0 g N2) = mol N2 21 C = 294 K 750 torr ( 1 atm / 760 torr ) = atm V (0.987 atm) = ( mol N2)( L atm / (mol K))(294 K) V = ( mol)( L atm /(mol K))(294 K) / (0.987 atm) = .428 L
18 Dalton's Law of Partial Pressures The total pressure of a mixture of nonreacting gases is the sum of their individual partial pressure.Ptotal = Pa + Pb + Pc ... example:How many grams of oxygen are present at 25 C in a 5.00 L tank of oxygen-enriched air under a total pressure of 30.0 atm when the only other gas is nitrogen at a partial pressure of 15.0 atm? Ptotal = 30.0 atm, PN2 = 15.0 atm, PO2 = ? 30.0 atm = 15.0 atm + PO2, PO2 = 15.0 atm (15.0 atm)(5.00 L) = n ( L atm / (mol K))(298 K), solve for n. n = 3.07 mol O2 3.07 mol O2 ( 32.0 g O2 / 1 mol O2) = 98.2 g O2
20 Vapor PressureThe amount of pressure exerted above a liquid by particles escaping from the liquid into a gas phase. Vapor pressure of any substance is dependent on the temperature. The higher the temperature the greater the amount of energy in the molecules the easier it is for the particles to escape.
22 Real Gas ideal gas real gas obey PV=nRT: always only at very low pressuresmolecularvolume: zero small, but nonzeromolecular attractions: zero smallmolecular repulsions: zero small
23 distance between molecules is related to gas concentration: n/V = P/RT high gas concentration = closer molecules = stronger intermolecular interactions = deviations from ideal behaviorrepulsions make pressure higher than expected by decreasing free volumeattractions make pressure lower than expected by braking molecular collisionstug-of-war between these two effectsrepulsions win at very high pressureattractions win at moderate pressureneither attractions nor repulsions are important at low pressure
24 Grahm’s LawGraham's Law shows the relationship between the molar or molecular mass of a gas and the rate at which it will effuseDiffusion can also be considered with Graham's Law, such as perfuming diffusing through a room.
25 The ratio of the rates of effusion of two gases is equal to the square root of the inverse ratio of their molecular masses or densities. The effusion rate of a gas is inversely proportional to the square root of its molecular mass.Mathematically, this can be represented as:Rate1 / Rate2 = square root of (Mass2 / Mass 1)
26 If given densities, must convert to molar mass by way of 22.4L/mol