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GASES! AP Chapter 10

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Characteristics of Gases Substances that are gases at room temperature tend to be molecular substances with low molecular masses. Air is the most common gas – a combination of N 2 and O 2. Some liquids and solids can exist in the gaseous state; they’re called vapors (i.e. water vapor)

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Characteristics, continued Gases are compressible. They mix in all proportions because their component molecules are very far apart.

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Pressure In general terms, pressure uses the idea of force, a push that tends to move an object in a certain direction. Pressure (P) is the force (F) that acts on a given area, (A). _ F__ A P = Gases exert pressure on any surface with which they are in contact.

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Pressure, continued Atmospheric pressure – Earth’s atmosphere exerts pressure at the surface of the planet due to the gravitational force. Atmospheric pressure at sea level is about 100 kPa, or 1 atm, or 1 bar. Actual pressure depends on altitude and weather conditions.

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Pressure and Barometers Barometer – typically involves mercury. The atmospheric pressure on the surface of the mercury forces the mercury up the barometric vacuum tube, which measures the pressure in mm Hg. Created by Torricelli, which is why 760 torr is the same as 760 mm Hg. A Manometer can be used to measure the pressure of enclosed gases.

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Manometer

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Pressure Pressure is expressed in SI units – pascals (Pa) 1 Pa = 1N/m 2 = 1kg/m-s 2 1 bar = 10 5 Pa or 100 kPa or 1 atm Conversions: 1 atm = kPa = 760 mm Hg = 760 torr = 1 bar

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The Gas Laws!

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Boyle’s Law! Boyle’s Law: The volume of a fixed quantity of a gas at constant temperature is inversely proportional to the pressure. Simply put, as one gets smaller, the other gets larger. PV = constant

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Boyle’s Law

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Charles’ Law! Charles’ Law: The volume of a fixed amount of gas maintained at constant pressure is directly proportional to its absolute temperature (K). Simply, as one gets larger, the other gets larger, too. VTVT = constant

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Gay-Lussac’s Law! Gay-Lussac’s Law: The pressure of a fixed volume of gas is directly proportional to its absolute temperature (K). As temperature increases, the pressure increases. PTPT = constant

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Avogadro’s Hypothesis Equal volumes of gases at the same temperature and pressure contain equal numbers of molecules L of any gas at 0 ° C and 1 atm contain 6.02 x gas molecules (1 mol). Or put another way, 1 mol of any gas at the same temp and pressure is 22.4 L.

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Avogadro’s Law! Avogadro’s Law: The volume of a gas maintained at constant temperature and pressure is directly proportional to the number of moles of the gas. V = constant x n Therefore, doubling the number of moles of gas will cause the volume to double as long as T and P remain the same.

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Ideal Gas Equation PV = n RT R is a proportionality constant, or the gas constant. Always use K for temperature! Pressure is most often atm and volume most often L and n is moles. STP – standard temperature and pressure (0 ° C and 1 atm)

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Combined Gas Law P 1 V 1 P 2 V 2 T 1 T 2 =

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Gas Density and Molar Mass The ideal gas equation allows for the determination of gas density from the molar mass, pressure, and temperature of the gas. n P V RT = n M P M V RT = M is the molar mass. Therefore, the density ( d ) of the gas is: P M RT d =

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Gas Density The density of a gas depends on its pressure, molar mass and temperature. The higher the molar mass and pressure, the more dense the gas. The higher the temperature, the less dense the gas. A less dense gas will lie above a more dense gas in the absence of mixing. (i.e. CO 2 )

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Gas Mixtures and Partial Pressures Dalton’s Law of Partial Pressures – states that the total pressure of a mixture of gases equals the sum if the pressures that each would exert if they were alone. P t = P 1 + P 2 + P

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Partial Pressures All gases in the mixture are at the same temperature and occupy the same volume. Therefore, at constant temperature and constant volume the total pressure is determined by the number of moles of gas present, whether that total is just one gas or a mixture. P t = n t RT V

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Partial Pressures and Mole Fractions The partial pressure of a gas in a mixture is its mole fraction times the total pressure. The mole fraction of N 2 in air is 0.78 (78% of the molecules in air are N 2.) If the total barometric pressure is 760 torr, then the partial pressure of N 2 is: P N2 = (0.78) (760 torr) = 590 torr

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Collecting Gases over Water The number of moles of a gas collected from a chemical reaction can be determined, and sometimes, that gas is collected over water. Example: 2KClO 3 (s) → 2 KCl (s) + 3 O 2 (g) The O 2 is collected in a bottle that is initially filled with water and inverted in a pan of water.

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Collecting Gases over Water, continued The volume of gas collected is measured by raising or lowering the bottle as necessary until the water levels inside the bottle is the same as outside the bottle. When this condition is met, the pressure inside the bottle is equal to the atmospheric pressure outside. The total pressure inside is the sum of the pressure of the gas collected and the pressure of water vapor in equilibrium with liquid water. P total = P gas + P water Use Appendix B for pressures exerted by water vapors at various temps!

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Kinetic Molecular Theory The ideal gas law describes how gases behave but now why they behave like they do. The Kinetic Molecular Theory is a model that was developed to understand what happens to gases as experimental conditions change. Rudolf Clausius published a form of this known as the Kinetic Molecular Theory.

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Kinetic Molecular Theory 1.Gases consist of large numbers of molecules that are in continuous, random motion. 2.The volume of all the molecules of the gas is negligible compared to the total volume in which the gas is contained. 3.Attractive and repulsive forces between gas molecules are negligible.

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Kinetic Molecular Theory 4.The average kinetic energy of the molecules does not change with time, as long as temperature remains constant. Energy can be transferred between molecules during collisions, but the collisions are elastic. 5.The average kinetic energy of the molecules is proportional to absolute temperature. At any given temperature, the molecules of all the gas molecules have the same average kinetic energy.

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Molecular Effusion Effusion – the escape of gas through a tiny hole into a vacuum The rate of Effusion is inversely proportional to the square root of its molar mass (Graham’s Law.) In other words, the lighter the gas, (or the smaller the molar mass) the more rapidly it effuses.

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The effect of molecular mass on molecular speeds.

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Diffusion Diffusion is faster for lower mass molecules than for higher mass ones. Because of molecular collisions, the direction of the molecule from one point to another is always changing. The average distance traveled by a molecule between collisions is called the mean free path of the molecule.

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Real Gas Deviations Real gases do not behave ideally at high pressure. Real gases do not behave ideally at low temperatures. They behave most like an ideal gas at low pressure and high temperature. Real molecules have finite volumes, and the do attract one another.

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Van der Waals Equation The Van der Waals equation is an equation of state for gases that modifies the ideal gas equation to account for intrinsic molecular volume and intermolecular forces.

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