7/16/2012. Characteristics of Gases. Chapter Five: Pressure is equal to force/unit area. Manometer. Gas Law Variables. Pressure-Volume Relationship

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1 7/6/0 Chapter Five: GASES Characteristics of Gases Uniformly fills any container. Mixes completely with any other gas. Exerts pressure on its surroundings. When subjected to pressure, its volume decreases. Pressure is equal to force/unit area SI units Newton/meter Pascal (Pa) standard atmosphere atm atm 760 mm Hg 760 torr 0,35 Pa N kg m/s bar 0 5 Pa Example 5. A-C Atmospheric pressure is measured with a barometer. Manometer Mercury Evangelista is orricelli used to measure pressure because ( ) of its high density. By way of comparison, with orricellian the column of water required to measure Barometer a given pressure would be 3.5 times as high as a mercury column used for the same purpose. If a tube is completely filled with mercury and then inverted into a container of mercury open to the atmosphere, the mercury will rise 760 mm up the tube at standard atmospheric pressure conditions. A manometer is a device for measuring pressure of a gas in a container. he pressure of the gas is given by h (the difference in Hg levels) in units of torr. For A: Gas Pressure P atm h For B: Gas Pressure P atm + h Gas Law ariables is for olume is for emperature (in Kelvin!!!!!!!) P is for Pressure n is for moles R is the gas constant SP standard temperature (73 K) and standard pressure ( atm 0.3 kpa) Always use units in gas-law problems to keep track of required conversions. Pressure-olume Relationship As the weather balloon ascends, the volume increases because pressure decreases. Boyle s law states that the volume of a fixed quantity of gas, at constant temperature, is inversely proportional to its pressure. constant x /P OR P constant As we breathe in, the diaphragm moves down, and the ribs expand; therefore, the volume of the lungs increases. therefore P in lungs Atmospheric pressure then forces air into the lungs until pressure once again equals.

2 7/6/0 Boyle s Law Figure 5.5 a&b Plotting Boyle's Data from able 5. Pressure and olume are inversely related (constant and n) Boyle s Law P k P P Example 5. A-B emperature-olume Relationship Balloons shrink when cooled by liquid nitrogen. Hot air balloons expand when they are heated. Charles s law states that the volume of a fixed quantity of gas, at constant pressure, is directly proportional to its absolute temperature. constant x OR / constant Charles s Law We define absolute zero as 0 K 73.5 C olume and emperature are directly related (constant P and n) Charles s Law: b Example 5. C Plots of versus as Before, the Kelvin Scale is Used for emperature olume and number of moles are directly related (constant and P) Other Gas Laws emperature and pressure are directly related (constant and n) Avogadro s Law an n n Gay-Lussac s Law dp P P Example 5. D

3 7/6/0 he Combined Gas Law May be used when five of the six variable are the same. Don t mix units! P P Ideal Gas Law We can bring all of these laws together into one comprehensive law Used to calculate the amount of gas at any specified conditions of pressure, volume and temperature. P nr Ideal gas behavior is just that ideal. Remember real gases do not behave ideally, especially at high pressures and/or low temperatures. where R L kpa 8.3 K mol or L atm R K mol Further Applications of Ideal Gas Equation Molar volume one mole of any ideal gas at SP conditions will occupy.4 L By manipulating gas laws, one can also calculate molar mass (M) and density (d). When handling gases, gas laws are used to do stoichiometric calculations. Example 5.3 A-C Example 5.4 A-D Dalton s Law of Partial Pressures Since gas molecules are so far apart, we can assume they behave independently. Dalton observed that the total pressure of a mixture of gases equals the sum of the pressure that each would exert if present alone. Partial pressure is the pressure exerted by a particular component of a gas mixture. Dalton s law of partial pressures Ptotal 3 P + P + P +... Pn Partial Pressures and Mole Fractions Let n be the number of moles of gas exerting a partial pressure, P, then: P X P total Where X is the mole fraction (n /n total ) Note that the mole fraction is dimensionless number. he Production of Oxygen by hermal Decomposition of KCIO3 Collecting Gases over Water It is common to synthesize gases and collect them by displacing a volume of water. o calculate the amount of gas produced, we need to correct for the partial pressure of the water: P total P gas + P water he vapor pressure of water varies with temperature. Example 5.5 A-C 3

4 7/6/0 Kinetic Molecular heory he kinetic molecular theory was developed to explain gas behavior. It is a theory of moving molecules. Summary: Gases consist of a large number of molecules in constant random motion. he combined volume of all the molecules is negligible compared with the volume of the container. Intermolecular forces (forces between gas molecules) are negligible. Energy can be transferred between molecules during collisions, but the average kinetic energy is constant at constant temperature. he collisions are perfectly elastic. Kinetic Molecular heory Summary continued: he average kinetic energy (KE) of the gas molecules is proportional to the absolute temperature. Kinetic molecular theory gives us an understanding of pressure and temperature on the molecular level. he pressure of a gas results from the collisions with the walls of the container. he magnitude of the pressure is determined by how often and how hard the molecules strike. he absolute temperature of a gas is a measure of the KE. Some molecules will have varying amounts of KE (Some have more KE, some have less KE) As the temperature increases, the average KE of gas molecules increases. Figure 5.9 Collisions with Walls and other Particles Cause Changes in Movement A Plot of the Relative Number of N Molecules that Have a Given elocity at hree emperatures Root Mean Square elocity he expression dealing with the average velocity of gas particles is called the root mean square velocity, u rms (It derived in your textbook). Figure 5.3 Relative Molecular Speed Distribution of H and UF6 where R 8.3 J/K mol temp in K M molar mass in kg he average kinetic energy is related to its mass. he lighter species will move faster than a heavier species at the same temperature. he lower the molar mass, M, the higher the speed. Example 5.6 4

5 7/6/0 Graham s Law Diffusion is the tendency of molecules to move towards areas of lower concentration until the concentration is uniform throughout. Effusion is the escape of gas molecules through a tiny hole in an evacuated space. Graham s Law states that the rate of effusion and diffusion of a gas is inversely proportional to the square root of the gas s molar mass. Rate Rate A B molar mass molar mass B A or r r M M Diffusion and Mean Free Path Diffusion is faster for light gas molecules. Diffusion is slowed by collisions of gas molecules with one another. Consider someone opening a perfume bottle: it takes awhile to detect the odor, but the average speed of the molecules at 5 C is about 55 m/s (50 mi/hr). he average distance traveled by a gas molecule between collisions is call the mean free path. At sea level, the mean free path for air molecules is about 6 x 0-6 cm. Real Gases he assumptions in the kinetic molecular theory show where ideal gas behavior breaks down: Molecules of a gas do have finite volume. Molecules of a gas do attract each other. As pressure on a gas increases, the molecules are forced closer together and resemble an ideal gas less. he smaller the distance between gas molecules, the more likely that attractive forces will develop between molecules. As temperature increases, the gas molecules move faster and further apart. Higher temperatures mean more energy to break intermolecular forces. Lower temperature, and real gases behave less ideally. he van der Waals Equation We add two terms to the ideal gas equation to correct for the volume of molecules and molecular attractions: he correction terms generate the van der Waals equation: where a and b are empirical constants for different gases. o understand the effect of intermolecular forces on pressure, consider a molecule that is about to strike the wall of the container. A striking molecule that is attracted by neighboring molecules will have a lessened impact on a container wall. Notes 5.8 to end Molar olumes for arious Gases at 0 C and atm able 5.3 alues of the van der Waals Constants for Some Common Gases 5

6 7/6/0 Plots of P/nR ersus P for Several Gases (00 K) Plots of P/nR ersus P for Nitrogen Gas at hree emperatures he actual pressure in the container after the valve is opened is: Consider the following container of helium. Initially the valve is closed. he total pressure in the container after the valve is opened is: a) <5.0 atm b) 5.0 atm c) >5.0 atm.00 atm 9.00 L 3.00 atm 3.00 L Concentration for Some Smog Components vs. ime of Day able 5.4 Atmospheric Composition Near Sea Level (Dry Air)* 6