GASES Pressure Gas Laws (Boyle, Charles, Avogadro) Stoichiometry Gas Mixtures (Dalton) Kinetic...
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Transcript of GASES Pressure Gas Laws (Boyle, Charles, Avogadro) Stoichiometry Gas Mixtures (Dalton) Kinetic...
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