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

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

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

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

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

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

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

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

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

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

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

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

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

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

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.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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:

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

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

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 +…

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

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

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?

Visual summary of the gas laws

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