Gases Chapter 5 Lesson 3

Kinetic Molecular Theory of Gases Postulates of the KMT Related to Ideal Gases The particles are so small compared with the distances between them that the volume of the individual particles can be assumed to be zero The particles are in constant motion. Collisions of the particles with the walls of the container cause pressure. Assume that the particles exert no forces on each other The average kinetic energy of a collection of gas particles is assumed to be directly proportional to the Kelvin temperature of the gas

Kinetic Molecular Theory of Gases Explaining Observed Behavior with KMT P and V (T = constant) As V is decreased, P increases: V decrease causes a decrease in the surface area. Since P is force/area, the decrease in V causes the area to decrease, thus increasing the P

Kinetic Molecular Theory of Gases P and T (V = constant) As T increase, P increases The increase in T causes an increase in average kinetic energy. Molecules moving faster collide with the walls of the container more frequently, and with greater force.

Kinetic Molecular Theory of Gases V and T (P = constant) As T increases, V also increases Increased T creates more frequent, more forceful collisions. V must increase proportionally to increase the surface area, and maintain P

Kinetic Molecular Theory of Gases V and n (T and P constant) As n increases, V must increase Increasing the number of particles increases the number of collisions. This can be balanced by an increase in V to maintain constant P

Kinetic Molecular Theory of Gases Dalton’s Law of partial pressures P is independent of the type of gas molecule KMT states that particles are independent, and V is assumed to be zero. The identity of the molecule is therefore unimportant

Kinetic Molecular Theory of Gases Root Mean Square Velocity Velocity of a gas is dependent on mass and temperature Velocity of gases is determined as an average M = mass of one mole of gas particles in kg R = 8.3145 J/K•mol joule = kg•m2/s2 urms = 3RT M

Kinetic Molecular Theory of Gases Example: Calculate the root mean square velocity for the atoms in a sample of oxygen gas at 0°C. MO2 = 32g/mol 32g 1 kg = 0.032 kg 1000g T = 0 + 273 = 273K R = 8.3145 J/K•mol

Kinetic Molecular Theory of Gases Urms = 3(8.3145 kg•m2 •s-2•K-1 •mol-1)(273 K) = 461m•s-1 0.032 kg•mol-1 Answer 461m•s-1 or 461 m/s Recall 1 Joule = 1 J = 1 kg• m2/s2 = 1 kg• m2• s-2

Kinetic Molecular Theory of Gases Mean Free Path – distance between collisions Average distance a molecule travels between collisions 1 x 10 -7 m for O2 at STP

Effusion and Diffusion Movement of a gas through a small opening into an evacuated container (vacuum) Graham’s law of effusion Rate of effusion for gas 1 = √M2 Rate of effusion for gas 2 √M1

Effusion and Diffusion Example: How many times faster than He would NO2 gas effuse? MNO2 = 46.01 g/mol larger mass MHe = 4.003 g/mol effuses slower Rate He = 46.01 = He effuses 3.39 Rate NO2 4.003 times faster

Real Gases and van der Waals Equation (Johannes van der Waals, 1873) Volume Real gas molecules do have volume Volume available is not 100% of the container volume n= number of moles b = is an empirical constant, derived from experimental results

Real Gases and van der Waals Equation Ideal: P = nRT V Real: P = nRT V-nb V = Volume of the container nb = Volume correction

Real Gases and van der Waals Equation Pressure Molecules of real gases do experience attractive forces a = proportionality constant determined by observation of the gas Pobs = Pideal – a(n/V)2  Pressure correction

Real Gases and van der Waals Equation Combining to derive van der Waals equation Pobs = nRT - n2a V-nb V2 And then rearranging… (Pobs + n2a/V2)(V-nb) = nRT

Real Gases: Deviations from Ideality Real gases behave ideally at ordinary temperatures and pressures. At low temperatures and high pressures real gases do not behave ideally. The reasons for the deviations from ideality are: The molecules are very close to one another, thus their volume is important. The molecular interactions also become important. J. van der Waals, 1837-1923, Professor of Physics, Amsterdam. Nobel Prize 1910.

Real Gases: Deviations from Ideality van der Waals’ equation accounts for the behavior of real gases at low temperatures and high pressures. The van der Waals constants a and b take into account two things: a accounts for intermolecular attraction For nonpolar gases the attractive forces are London Forces For polar gases the attractive forces are dipole-dipole attractions or hydrogen bonds. b accounts for volume of gas molecules At large volumes a and b are relatively small and van der Waal’s equation reduces to ideal gas law at high temperatures and low pressures.

Real Gases: Deviations from Ideality Calculate the pressure exerted by 84.0 g of ammonia, NH3, in a 5.00 L container at 200. oC using the ideal gas law. PV = nRT P = nRT/V n = 84.0g * 1mol/17 g T = 200 + 273 P = (4.94mol)(0.08206 L atm mol-1 K-1)(473K) (5 L) P = 38.3 atm

Real Gases: Deviations from Ideality Calculate the pressure exerted by 84.0 g of ammonia, NH3, in a 5.00 L container at 200. oC using the van der Waal’s equation. The van der Waal's constants for ammonia are: a = 4.17 atm L2 mol-2 b =3.71x10-2 L mol-1 n = 84.0g * 1mol/17 g T = 200 + 273 P = (4.94mol)(0.08206 L atm mol-1 K-1)(473K) (4.94 mol)2*4.17 atm L2 mol-2 5 L – (4.94 mol*3.71E-2 L mol-1) (5 L)2 P = 39.81 atm – 4.07 atm = 35.74 (Using van der Waal’s Eq) P = 38.3 atm (Using IGL) 7% error

Chemistry in the Atmosphere Composition of the Troposphere The atmosphere is composed of 78% N2, 21% O2, 0.9%Ar, and 0.03% CO2 along with trace gases. The composition of the atmosphere varies as a function of distance from the earth’s surface. Heavier molecules tend to be near the surface due to gravity.

Chemistry in the Atmosphere Upper atmospheric chemistry is largely affected by ultraviolet, x ray, and cosmic radiation emanating from space. The ozone layer is especially reactive to ultraviolet radiation Manufacturing and other processes of our modern society affect the chemistry of our atmosphere. Air pollution is a direct result of such processes.