Presentation on theme: "Chapter 5: Gases Pressure KMT Gas Laws Effusion and Diffusion"— Presentation transcript:
1 Chapter 5: Gases Pressure KMT Gas Laws Effusion and Diffusion Stoichiometry Real GasesGas Mixtures
2 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.
3 PRESSURE Pressure = Force/Area Devices to measure pressure: manometer and barometerPressure Units (see p 181)pascal = N/m2 = kg/(m s2) SI derived unit1 mm Hg = 1 torr1 std atm = 1 atm = 760 torr = 760 mm Hg = E+05 Pa
4 GAS LAWSThese 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).
5 Figure 5.15 Increased Pressure due to Decreased Volume
6 Figure 5.5 a&b Plotting Boyle's Data (Table 5.1)
7 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.
8 Figure 5.17 The Effects of Increasing the Temperature of a Sample of Gas at Constant Pressure
10 Figure 5.18 Increased Volume due to Increased Moles of Gas at Constant Temperature and Pressure
11 IDEAL GAS LAW PV = nRT Combine Boyle, Charles and Avogadro’s Laws Equation of state for ideal gas; hypothetical stateNote 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.
12 IDEAL GAS LAW R = Universal Gas Constant = PV/nT (L-atm)/(mol-K) = J/(mol-K)Note units of P = atm, V = L, T = K, n = #molSTP = Standard Temperature and Pressure means 1 atm AND KMolar volume of a gas = Volume of one mole of gas at STP = L (see T5.2)
13 OTHER Use P, T and d to find molar mass (M) of gas. Start with IGL: PV = nRT divide by VRT to getn/V = P/RT then multiply by M to getn (M)/V = d = MP/RT or M = dRT/PEqn 5.1
21 KINETIC MOLECULAR THEORY OF GASES (1) Gas molecules are far apart form each other and their volumes areThey 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.
22 Figure 5.19 Collisions with Walls and other Particles Cause Changes in Movement
23 Figure 5.20 A Plot of the Relative Number of O2 Molecules that Have a Given Velocity at STP
24 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.
25 KINETIC MOLECULAR THEORY (QUANT.) Average kinetic energy = [(3/2) RT] α TKE depends on T onlyi.e. KE does not depend on identity of gas (M)Root mean square velocityurms = √(3RT/M) where R = J/(K-mol)As T increases, urms [dec, stays the same, inc]As M increases, urms [dec, stays the same, inc]
26 Figure A Plot of the Relative Number of N2 Molecules that Have a Given Velocity at 3 Temperatures
27 Figure 5.23 Relative Molecular Speed Distribution of H2 and UF6
28 EFFUSION AND DIFFUSION Diffusion: Mixing of gasesDiffusion rate is a measure of gas mixing rateDiffusion distance traveled α (1/√M)EffusionPassage of gas through orifice into a vacuumGraham’s Law describesEffusion rate α urms α (1/√M) α (1/T)or Effusion time α M α (1/T)
29 Figure 5.22 The Effusion of a Gas Into an Evacuated Chamber
31 REAL GASES IDEAL: PV= nRT van der Waals Eqn of State PeffVeff = P’V’ = (Pobs + n2a/V2) (Vobs - nb) = nRT1st term corrects for non-zero attractive intermolecular forces2nd term corrects for non-zero molecular sizea and b values depend on the gas’s identity – loss of universality in gas law
32 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)
33 Figure 5.25 Plots of PV/nRT versus P for Several Gases (200K)
34 Table 5.3 Values of the van der Waals Constants for Some Common Gases