chapter 5: gases
DESCRIPTION
Chapter 5: Gases. PressureKMT Gas LawsEffusion and Diffusion StoichiometryReal Gases Gas 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. - PowerPoint PPT PresentationTRANSCRIPT
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