Chapter 5: Gases

Pressure KMTGas Laws Effusion and DiffusionStoichiometry Real GasesGas Mixtures

Properties of a 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 (see p 181)– 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 (based on expts rather than derived from theory) that define mathematical relationships between any two gas properties (P, V, T, n).

• For example: If T and n are held constant, what happens to V if you increase P?

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

Figure 5.15 Increased Pressure due to Decreased Volume

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

GAS LAWS (2)

• If P and n are held constant, what happens to V if you increase T?

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

• If P and T are held constant, what happens to V if n increases?

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

Figure 5.17 The Effects of Increasing the Temperature of a

Sample of Gas at Constant Pressure

Figure 5.9 Plots of V versus T (Charles’ Law)

Figure 5.18 Increased Volume due to Increased Moles of Gas at

Constant Temperature and Pressure

IDEAL GAS LAW

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 not needed.• 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.

IDEAL GAS LAW

• R = Universal Gas Constant = PV/nT

• 0.0821 (L-atm)/(mol-K) = 8.3145 J/(mol-K)– Note units of P = atm, V = L, T = K, n = #mol

• STP = Standard Temperature and Pressure 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)

OTHER

• Use P, T and d to find molar mass (M) of gas.– Start with IGL: PV = nRT divide by VRT to

get– n/V = P/RT then multiply by M to get – n (M)/V = d = MP/RT or M = dRT/P– Eqn 5.1

Problems

• 19, 21, 34, 36, 42, 56, 62

STOICHIOMETRY of GAS PHASE REACTIONS

• Use IGL to find # mol gas in stoichiometric problems

• Law of Combining Volumes (Gay-Lussac)

• Problems: 54, 58

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

Problems

• 67, 72, 76

KINETIC MOLECULAR THEORY OF GASES (1)

• Gas molecules are far apart form each other and their volumes are

• They move constantly, rapidly and randomly in all directions and at various speeds.

• There are no intermolecular forces between gas molecules except when they collide. Collisions are elastic.

Figure 5.19 Collisions with Walls and other Particles Cause Changes in

Movement

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 T– 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

Problems

• 78, 80, 82, 88

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