GASES

• Pressure

• Gas Laws (Boyle, Charles, Avogadro)

• Stoichiometry

• Gas Mixtures (Dalton)

• Kinetic Molecular Theory of Gases

• Effusion and Diffusion

• Real Gases

GAS

• State of Matter

• Compressible since molecules are far apart.

• Takes the shape and volume of container.

• Forms homogeneous mixtures with other gases.

• Pressure is a gas property which tells us about the amount of gas present.

•PRESSURE

• Pressure = Force/Area

• Devices to measure pressure: manometer and barometer

• Pressure Units– pascal = N/m2 = kg/(m s2) SI derived unit– 1 mm Hg = 1 torr– 1 std atm = 1 atm = 760 torr = 760 mm Hg =

1.01325E+05 Pa = @100kPa

GAS LAWS

• These are empirical laws that present mathematical relationships between properites of gases (P, V, T, n) based on expt observations rather than derived from a theory of gases.

• Boyle’s Law relates V vs P: V α 1/P or PV = k at constant n and T (Fig 5.5, 5.6).

• Charles’ Law relates V vs T (K): V α T or V/T = b at constant n and P (Fig 5.8, 5.9).

• Avogadro’s Law relates V vs n: V α n or V/n = a at constant P and T.

Figure 5.5 a&b Plotting Boyle's Data (Table 5.1)

Figure 5.9 Plots of V versus T as Before, Except Here the Kelvin Scale is Used for Temperature 1

GAS LAWS (2)

• IDEAL GAS LAW (IGL) PV = nRT– Combine Boyle, Charles and Avogadro’s Laws– Equation of state for ideal gas; hypothetical

state– Note universality of equation; I.e. identity of

the gas is unknown– Limiting law (in the limit of high T and low

P~1 atm); this means that as T increases and P decreases, real gases start to behave ideally.

OTHER

• R = Universal Gas Constant = 0.0821 (L-atm)/(mol-K) = 8.3145 J/(mol-K)– Note units of P – atm, V – L, T – K, n = 3mol

• STP means 1 atm AND 273.15 K

• Molar volume of a gas = Volume of one mole of gas at STP = 22.42 L (see T5.2)

STOICHIOMETRY of GAS PHASE REACTIONS

• Use gas laws in stoichiometric problems

• Law of Combining Volumes (Gay-Lussac)

• Use the gas laws to find molar mass:– Use V, P , T and IGL to find n = #mol; then

apply stoich unit from Ch. 3.– Use n and m to find molar mass, M = m/n– Use P, T and density of gas, d, to find M

because M = dRT/P Eqn 5.1

MIXTURES of IDEAL GASES

• DALTON’S LAW– Law of Partial Pressures

– PTOTAL = P = ∑ Pi at constant T and V

– Pi = niRT/V = partial pressure of a gas

– xi = mole fraction = ni/nTOTAL = Pi/PTOTAL

Fig 5.12 The Partial Pressure of each Gas in a Gas Mixture in a Container

Depends on n = #mol of that Gas

MIXTURES of IDEAL GASES

• COLLECTING GASES OVER WATER– PTOTAL = P = Pg + Pw

Fig 5.13 The Production of O2 by Thermal Decomposition of KCIO3

KINETIC MOLECULAR THEORY OF GASES (1)

• GAS MOLECULES are FAR APART FROM EACH OTHER and THEIR VOLUMES ARE NEGLIGIBLE.

• THEY MOVE CONSTANTLY, RAPIDLY and RAMDONLY IN ALL DIRECTIONS AND AT VARIOUS SPEEDS.

• THERE ARE NO INTERMOLECULAR FORCES EXCEPT FOR COLLISIONS.

Figure 5.20 A Plot of the Relative Number of O2 Molecules

that Have a Given Velocity at STP

KINETIC MOLECULAR THEORY (2)

• MEASURED PRESSURE OF A GAS IS DUE TO COLLISIONS WITH WALL.

• COLLISIONS ARE ELASTIC.• THE AVERAGE KINETIC ENERGY OF A

MOLECULE IS PROPORTIONAL TO T (K).• EXPLAINS MACROSCOPIC PROPERTIES

LIKE P, T, V, v AND EMPIRICAL GAS LAWS.

KINETIC MOLECULAR THEORY (QUANT.)

• Average kinetic energy = [(3/2) RT] α – KE depends on T only– i.e. KE does not depend on identity of gas (M)

• Root mean square velocity – urms = √(3RT/M) where R = 8.314 J/(K-mol)

– As T increases, urms [dec, stays the same, inc]

– As M increases, urms [dec, stays the same, inc]

Figure 5.21 A Plot of the Relative Number of N2 Molecules that Have a Given Velocity at 3 Temperatures

Figure 5.23 Relative Molecular Speed Distribution of H2 and UF6

EFFUSION AND DIFFUSION

• Diffusion: Mixing of gases– Diffusion rate is a measure of gas mixing rate– Diffusion distance traveled α (1/√M)

• Effusion – Passage of gas through orifice into a vacuum– Graham’s Law describes – Effusion rate α urms α (1/√M) α (1/T) – or Effusion time α M α (1/T)

Figure 5.22 The Effusion of a Gas Into an Evacuated Chamber

REAL GASES

• IDEAL: PV= nRT• van der Waals Eqn of State

– PeffVeff = P’V’ = (Pobs + n2a/V2) (Vobs - nb) = nRT

– 1st term corrects for non-zero attractive intermolecular forces

– 2nd term corrects for non-zero molecular size– a and b values depend on the gas’s identity –

loss of universality in gas law

KMT OF GASES (1-revisited)

• GAS MOLECULES are FAR APART FROM EACH OTHER and THEIR VOLUMES ARE NOT NEGLIGIBLE. (b ≠ 0)

• THEY MOVE CONSTANTLY, RAPIDLY and RAMDONLY IN ALL DIRECTIONS AND AT VARIOUS SPEEDS.

• THERE ARE (NO) INTERMOLECULAR FORCES EXCEPT FOR COLLISIONS.

(a ≠ 0)

Figure 5.25 Plots of PV/nRT versus P for Several Gases (200K)

Table 5.3 Values of the van der Waals Constants for Some Common Gases