10 PressureThe molecules in a gas are in constant motion. The purple balls represent gaseous atoms that collide with each other and the walls of the container. Gas molecules are in constant motion. "Pressure" is a measure of the collisions of the atoms with the container.
11 PressureForce per unit areaEquation: P = F/AF = force A = areaNext
13 Formulas For Surface Area Square: 6s²rectangle: 2ab + 2bc + 2acCylinder: 2πr²+ 2πrhsphere: 4πr²
14 Units of Measurement N/m2 Newton per square meter N/cm Newton per square centimeterPa PascalkPa kilopascalTorr TorrmmHg millimeters of mercurylb/in pound per square inch
15 Calculating Pressure Using P = F/A Suppose that a woman weighing 135 lb and wearing high-heeled shoes momentarily places all her weight on the heel of one foot. If the area of the heel is 0.50 in²., calculate the pressure exerted on the underlying surface.P = F/A= 135 lb/0.50 in²P = 270 lb/in²
16 Liquid PressureThe pressure depends height of liquid column and density of liquid.Ρ = dgh= density x acceleration due to gravity x height
17 Calculating Pressure Exerted by a Liquid Calculate the height of a mercury column, in feet, that is equal to a column of water that is 110 ft. high.Known valuesdwater = 1.0 g/cm dmercury = 13.6 g/cm g = 32 ft/s2Ρ = dghPwater = Pmercurydgh = dgh(1.0 g/cm3)(32ft/s2)(110 ft) = (13.6 g/cm3)(32 ft/s2)(h)h = 8.1 ft. Hg
18 BarometerBarometer is a device used to measure the pressure exerted by the atmosphere.Height of mercury varies with atmospheric conditions and with altitude.
22 Standard Atmosphere (atm) Pressure exerted by a mercury column of exactly 760 mm in heightthe density of Hg = g/cm3 (0oC)The acceleration due to gravity (g) is m/s2 exactly.1 atm =760 mmHg760 Torrlb/in2kPaCheck textbook for more values
23 Converting Pressure to an Equivalent Pressure A gas is at a pressure of 1.50 atm. Convert this pressure toKilopascals atm = kPa1.50 atm x kPa = 152 kPa1 atmmmHg1.50 atm x mmHg = 1140 mmHg
24 ManometersUsed to compare the gas pressure with the barometric pressure.Next
25 Types of Manometers Closed-end manometer The gas pressure is equal to the difference in height (Dh) of the mercury column in the two arms of the manometer
30 Gas pressure is greater than the barometric pressure. Pgas = Pbar + ∆P
31 Gas pressure is less than the barometric pressure. Pgas = Pbar + ∆P
32 Standard Temperature & Pressure (STP) Temperature = 0ºCPressure = 1 atm
33 Boyle’s Law Charles’ Law Gay-Lussac’s Law Combined Gas Law The Simple Gas LawsBoyle’s LawCharles’ LawGay-Lussac’s LawCombined Gas Law
34 Temperature & Gas Laws Three temperature scales Fahrenheit (ºF) Celsius (ºC)Kelvin K (no degree symbol)Always use K when performing calculations with the gas law equations.K = (ºC) Example: ºC = 20ºK = 293Next
35 Absolute Zero of Temperature Temperature at which the volume of a hypothetical gas becomes zeroºCNext
36 Absolute or Kelvin Scale Temperature scale that has ºC as its zero.Temperature interval of one Kelvin equals one degree celsius.1 K = 1 ºC
37 Boyle’s LawFor a fixed amount of gas at constant temperature, gas volume is inversely proportional to gas pressure.P1V1 = P2V2
42 Example . Charles’ LawA 4.50-L sample of gas is warmed at constant pressure from 300 K to350 K. What will its final volume be?Given:V1 = 4.50 LT1 = 300. KT2 = 350. KV2 = ?Equation: V1 = V2T T2or V1T2 = V2T1(4.50 L)(350. K) = V2 (300. K)V2 = 5.25 L
43 Gay-Lussac’s LawThe pressure of a sample of gas is directly proportional to the absolute temperature when volume remains constant.P1 = P2T T2or P1T2 = P2T1
44 On the next slide (43)The amount of gas and its volume are the same in either case, but if the gas in the ice bath (0 ºC) exerts a pressure of 1 atm, the gas in the boiling-water bath (100 ºC) exerts a pressure of 1.37 atm. The frequency and the force of the molecular collisions with the container walls are greater at the higher temperature.
46 Combined Gas LawPressure and volume are inversely proportional to each other and directly proportional to temperature.P1V1 = P2V2T T2or P1V1T2 = P2V2T1
47 Example. Combined Gas Law A sample of gas is pumped from a 12.0 L vessel at27ºC and 760 Torr pressure to a 3.5-L vessel at 52ºC. What is the final pressure?Given:P1 = 760 Torr P2 = ?V1 = 12.0 L V2 = 3.5 LT1 = 300 K T2 = 325 KEquation:P1V1 = P2V T T2or P1V1T2 = P2V2T1(760 Torr)(12.0 L)(325 K) =( P2)(3.5 L)(300 K)P2 = 2.8 x 10³ Torr
52 Avogadro’s Explanation of Gay-Lussac’s Law When the gases are measured at the same temperature and pressure, each of the identical flasks contains the same number of molecules. Notice how the combining ratio: 2 volumes H2 to 1 volume O2 to 2 volumes H2O leads to a result in which all the atoms present initially are accounted for in the product.
53 Avogadro’s Hypothesis Different gases compared at same temperature and pressurea. Equal equal number ofVolumes moleculesb. Equal number of – equalmoleculess volumes
54 Avogadro’s LawAt a fixed temperature and pressure, the volume of a gas is directly proportional to the amount of gas.V = c · nV = volume c = constant n= # of molesDoubling the number of moles will cause the volume to double if T and P are constant.
55 More STP Values For Gases 1 mol of a gas = 22.4 LNumber of molecules contained in 22.4 L of a gas is x 1023
58 Equation Includes all four gas variables: Volume Pressure Temperature Amount of gasNext
59 PV = nRTGas that obeys this equation if said to be an ideal gas (or perfect gas).No gas exactly follows the ideal gas law, although many gases come very close at low pressure and/or high temperatures.Ideal gas constant, R, isR = PVnT= 1 atm x 22.4 L1 mol x KR = L·atm/mol· K
60 Applications of the Ideal Gas Law Molar MassDensity
61 Molar Mass Determination n = number of molesMoles = mass of sample mMolar mass MIdeal Gas Equation: n = PVRTSubstituting: m = PVM RTM = mRTPV
62 Example: Molar MassThe density of carbon tetrachloride vapor at 714 torr and 125ºC is 4.43 g/L. What is its molar mass?M = dRTP= (4.43 g/L)( L-atm/mol-k)(398 K)(714 torr x 1 atm/760 torr)M = 154 g/mol
63 Gas Density (d) d = m/V so V = m/d Ideal Gas Equation: PV = nRT Substituting P m = mRTd M“m” cancels out d = PMRT
65 Example. Vapor DensityThe mean molar mass of the atmosphere at the surface of Titan, Saturn’s largest moon, is 28.6 g/mol. The surface temperature is 95 K, and the pressue is 1.6 Earth atm. Assuming ideal behavior, calcuate the density of Titan’s atmosphere.d = PMRT= (1.6)(1 atm)(28.6 g/mol)( L-atm/mol-K)(95 K)d = 5.9 g/L
66 Gases in Chemical Reactions Ideal Gas Law&Balanced Chemical Equation
67 Example. Reaction Stoichiometry How many moles of nitric acid can be prepared using 450 L of NO2 at a pressure of 5.00 atm and a temperature of 295 K?Step 1: Use Ideal Gas law equationn = PV (5.00 atm)(450 L)RT ( L-atm/mol-K)(295 K)n = 92.9 molNext ---- >
74 Mole Fraction of Compound in Mixture Fraction of all molecules in the mixture contributed by that component.Sum of all the mole fractions in a mixture is 1.Expression for mole fraction of a substance in terms of P and Vna = Pa = Vantot Ptot Vtot
76 Example: Gas Mixtures & Partial Pressure A gaseous mixture made from 6.00 g O2 and 9.00 g CH4 is placed in a 15.0 L vessel at 0ºC. What is the partial pressure of each gas, and what is the total pressure in the vessel?Step 1:nO2 = 6.00 g O2 x 1 mol O232 g O2= mol O2Next ---- >
77 Step 2: Calculate pressure exerted by each PO2 = nRT V nCH4 = 9.00 g CH4 x mol CH416.0 g CH4= mol CH4Step 2: Calculate pressure exerted by eachPO2 = nRTV= (0.188 mol O2)( L-atm/mol-K)(273 K)15.0 L= atm
83 Gas Collected Over Water A sample of KClO3 is partially decomposed, producing O2 gas that is collected over water. The volume of gas collected is L at 26ºC and 765 torr total pressure.2KClO3(s) > 2 KCl(s) + 3O2(g)Next ---- >
84 How many moles of O2 are collected? Step 1: Calculate pressure of O2 in mixturePO2 = Ptot – Pwater vapor= 765 torr – 25 torrPO2 = 740 torrNext ---- >
86 How many grams of KClO3 were decomposed? (9.92 x 10-3 mol O2) x 2 mol KClO3 x g KCLO33 mol O mol KClO3= g KClO3
87 c. When dry, what volume would the collected O2 gas occupy at the same temperature and pressure? Remove water vapor. P2 = 765 torrTemperature is the same.P1V1 = P2V2V2 = (740 torr)(0.250 L)(765 torr)V2 = L
89 Assumptions The molecules of gases are in rapid random motion. Their average velocities (speeds) are proportional to the absolute (Kelvin) temperature.At the same temperature, the average kinetic energies of the molecules of different gases are equal.Next
90 Relationship Between Temperature and Average Kinetic Energy Higher temperature means greater motion(KE)av = 3 RT2Obtained fromPV = RT = 2 (KE)avn
91 Apply to all gases whether alone or mixed with other gases PV = RT = 2 (KE)av = ½ mv²nApply to all gases whether alone or mixed with other gasesConstant Va. T changes – KE changesb. T increases – pressure increasesc. KE changes – speed of molecules changesConstant temperaturea. V increases, P decreasesb. KE doesn’t change – T didn’t changec. Speed of molecules doesn’t change-KE didn’t change
92 Root-Mean Square Speed (u 2) u 2 represents the average of the squares of theparticles velocities.The square root of u 2 is called the root mean square velocity.The unit of measurement is m/s.u 2 = 3RT Units: R = J K-1mol-1M or kgm2/s2 K-1mol-1Joule = kg·m2/s2Joule is a unit of measurement for energy.
93 ExampleHow is the root-mean square speed (rms) of F2 molecules in a gas sample changed byAn increase in temperature.An increase in volumeMixing with a sample of Ar at the same temperature
95 Example. Root-Mean Square Speed Calculate the root mean square speed for the atoms in a sample of helium gas at 25ºC.Given:T = 25ºC = 298 KKnown:R = J/K·molor kgm2/s2 / K·molMHe : Change g to kg4.00 g/mol = 4.00 x 10-3 kg/molEquation: u 2 = 3RTMu 2= 3 ( kgm2/s2 /K·mol)(298K)4.00 x 10-3 kg/molu = 1.36 x 103 m/s
96 EffusionThe escape of gas molecules from their container through a tiny orifice or pin hole.
98 DiffusionDiffusion is the moving or mixing of molecules of different substances as a result of random molecular motion.
99 Factors That Influence Effusion and Diffusion The greater the temperature the faster the ga will move or vise versa/If the mass increases, the kinetic energy will also increase if the speed remains constant.If the mass increases, the speed decreases if the kinetic energy remains constant.
100 Example. Rate of Effusion Calculate the ratio of the effusion rates of hydrogen gas (H2) and uranium hexafluoride (UF6), a gas used in the enrichment process fuel for nuclear reactors.Known:Molar MassesH2 = g/molUF6 = g/mol(Rate of effusion)² = MU compoundMH gas=2.016Rate of effusion = 13.21
101 Graham’s LawThe rate of effusion (or diffusion) of two different gases are inversely proportional to the square roots of their molar masses.(rate of effusion of A)2 = MB(rate of effusion of B)2 MA
102 Ratios of Ratesthe square root of two molar masses is also equal to the ratioMolecular speedsEffusion timesDistance traveled by moleculesAmount of gas effused
103 Based on Assumptions of Kinetic Molecular Theory Rates of diffusion of different gases are inversely proportional to the square roots of their densities.Rates of diffusion are inversely proportional to the square roots of their molar masses.
105 Ideal vs. Nonideal (Real) Gases High pressure- compressible, volume approaches zeroForce of collisions with container wall is greatNonidealHigh pressure – molecules are practically incompressibleForce of collision with container wall is less due to attractive force among the molecules.
106 Behavior of Gases Behave ideally at High temperatures Low pressures Behave nonideally atLow temperaturesHigh pressures
108 van der Waals EquationEquation corrects for volume and intermolecular forces(P + n²a/V²)(V-nb) = nRTn²a/V² = related to intermolecular forces of attractionn²a/V² is added to P = measured pressure is lower than expecteda & b have specific values for particular gasesV - nb = free volume within the gas
109 Intermolecular Force of Attraction Attractive forces of the orange molecules for the purple molecule cause the purple molecule to exert less force when it collides with the wall than it would if these attractive forces did not exist.
110 Source of Sketches/problems Chemistry, 7th ed. Brown, LeMay & Bursten, Prentice Hall