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Gases: Properties and Behaviour Gas Laws Partial Pressures Kinetic Theory and Ideal Gases Real Gases Diffusion and Effusion

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Features of gases Gases are always miscible Gases are compressible Gases exert pressure Gases are mostly nothing: less than 0.1 % of the volume is occupied by molecules (contrast 70 % for solids and liquids) The ideal gas law assumes molecules occupy zero percent

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Molecular interactions The strength of the interactions between molecules determines the state Strong attractions make for high melting point ionic solids Weaker interactions between molecules occur in liquids

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Molecular interactions in gases are negligible Gases are mostly empty space: molecules occupy <0.1 % volume 1,000 times less dense than solids and liquids Emptiness allows complete mixing

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The Ideal gas The ideal gas is defined as follows Interactions between molecules are nonexistent Volume occupied by molecules is zero

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Collisions There are two types of collision collision Between the molecules and the container Between molecules In the ideal gas these collisions are perfectly elastic (no energy loss) Collisions between billiard balls mirrors the collisions between the molecules of an ideal gas

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Origins of pressure Pressure is force per unit area F/A Force is mass x acceleration F = ma Molecules colliding with the walls of the container exchange momentum

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Origins of pressure Pressure if force per unit area F/A Force is mass x acceleration F = ma Molecules colliding with the walls of the container exchange momentum

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Units of pressure The S.I. unit of pressure is the pascal (Pa) 1 Pa = 1 N/m 2, where N is the S.I. unit of force 1 N = 1 kgm/s 2 The weight of the air exerts pressure – atmospheric pressure This pressure is about 100,000 Pa

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Older is better 101 kPa is an inconvenient way of measuring pressure Traditional units are still used in preference to the SI system Atmospheres, cm (or mm) of Hg and torr are the most common

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How do I measure the atmosphere? Let me count the ways 1 atmosphere = 760 mm Hg = 76 cm Hg 14.7 psi 760 torr 1.01 bar 29.9 in Hg

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Standard temperature and pressure (STP) Standard conditions allow direct comparison of properties of different substances Standard temperature is 273 K (0ºC) Standard pressure is 760 mm Hg At STP, 1 mole of any ideal gas occupies 22.414 L

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The barometer of pressure The weight of the air supports an equal weight of mercury (or other liquid) Mercury being dense, the column is only 76 cm compared to the height of the atmosphere 76 cm (760 mm) Hg = 1 atm

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Manometers measure pressure in a container (a) If the pressure inside the bulb is less than atmospheric, the atmosphere pushes down more. (b) If the pressure inside the bulb is above atmospheric, the column is pushed towards the open end.

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Measuring pressure with a ruler The pressure in the container is given by atmospheric pressure plus (minus) the difference in levels for pressures greater (lower) than atmospheric

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Gas Laws Physical properties of gases were among the first experiments performed in the “modern” scientific era, beginning in the 17th century All gases exhibit similar physical properties even if their chemical properties differ widely Properties can be summarized in a few simple laws Variables are pressure, volume, temperature and quantity. Keep one (or two) constant and vary the others

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The four variables Pressure (P) Volume (V) Temperature (T in Kelvin) Number of molecules (n in moles)

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Variables and constants In the elementary gas laws two of the four variables are kept constant Each law describes how one variable reacts to changes in another variable All the simple laws can be integrated into one combined gas law

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The first experimental gas law Pressure increases, volume decreases (T, n constant) Boyle’s law

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Mathematical form The volume of a fixed amount of an ideal gas varies inversely with pressure at constant temperature PV = constant P α 1/V

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Charles’ Law Pressure and amount constant As temperature increases, the volume increases

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Mathematical form The volume of a fixed amount of an ideal gas varies directly with absolute temperature at constant pressure V α T V/T = constant NOTE: Temperature must be in Kelvin (ºC + 273) At absolute zero there is no motion and the residual volume is that of the atoms – which is assumed to be zero

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Avogadro’s Law Pressure and temperature constant Increase the amount, the volume increases Summary of gas laws

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Mathematical form The volume of a fixed amount of an ideal gas varies directly with absolute temperature at constant pressure V α T V/T = constant NOTE: Temperature must be in Kelvin (ºC + 273) At absolute zero there is no motion and the residual volume is that of the atoms – which is assumed to be zero

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Mathematical form The volume of an ideal gas varies directly with its molar amount at constant T and P V α n V/n = constant The same volume of any gas contains the same number of moles at constant T,P The standard molar volume at 273 K and 1 atm is 22.414 L

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Comparison with reality The standard molar volume of 22.41 L can be compared with the experimental values of common real gases Agreement shows that these ideal gas laws can be widely applied for real gases

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Putting them together: the ideal gas law P 1 V 1 /T 1 = P 2 V 2 /T 2 PV = nRT R is the gas constant = 0.0821 L-atm/mol-K Note the units of R. This constant also appears in thermodynamic calculations, but with different units and numerical value (8.315 k/K-mol). Use the one appropriate to the calculation Units of pressure – atm Units of temperature – K Units of volume – L Standard temperature and pressure: T = 0 ºC and P = 1 atm

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The combined gas law Allows us to calculate change in one variable for changes in the three other variables

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Applications A system under an initial set of conditions represented by a changes to a new set of conditions b If we know three of the conditions, the fourth can be obtained

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The “simple” laws are derived from the combined law For any change of conditions where a variable does not change its value, a = b Example: if T and n are unchanged, Boyle’s law is regenerated:

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Getting some exercise An exercise ball is at a pressure of 1000 mm Hg and has a volume of 60 L When sat on, the volume is only 40 L. What is the new pressure? Check: P increases as V decreases

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Stoichiometry and gas reactions Solids: mass and molar mass Solutions: volume and molarity Gases: volume and ideal gas law Calculate volume of gas produced (product) or consumed (reactant) in a reaction at given conditions of P and T Also can calculate molar mass or density of a gas using ideal gas law

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Mixtures of gases: partial pressures Dalton’s law states that, in a mixture of gases, each gas behaves independently of the others and exerts the same pressure that it would by itself The total pressure exerted is the sum of the individual (partial) pressures of the components of the mixture P = P 1 + P 2 + P 3 +…

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Mole fraction The pressure exerted by component i = P i = n i (RT/V) Where ni is the number of moles of i The total pressure is then: P (total) = (n 1 + n 2 + n 3 + …)RT/V The mole fraction is the ratio of the moles of component I to the total number of moles ntotal

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Mole fraction and the ideal gas law But n = PV/RT

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Mole fractions and partial pressures The partial pressure exerted by any gas is equal to the mole fraction x the total pressure What is the partial pressure of each component if the total pressure is 600 mm Hg?

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Visual summary of the gas laws

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