CHAPTER 5: GasesGasesWays to produce gases include…Some properties of gasesPressurePressure by barometerUnits of pressureConnection between P & V: Boyle’s LawBoyle’s LawRelationship between V&T:Charles’ LawRelationship between V and TCharles’ Law in Kelvin T scaleIdeal Gas LawExample problemIdeal gas law w/ molar massGases in chemical reactionsMixtures of gasesMixtures of gases, cont’dKinetic Theory of GasesOrigin of pressureOrigin of pressure, cont’dOrigin of pressure, cont’dMaxwell-Boltzmann distribution of molecular speeds in N2 at 3 tempsMeasurement of speed distributionsRoot mean square (RMS) speedDiffusionRates of effusion and gaseous diffusionReal gasesReliability of ideal gas lawCHAPTER 5: Gases•Chemistry of Gases•Pressure and Boyle’s Law•Temperature and Charles’ Law•The Ideal Gas Law•Chemical Calculations of Gases•Mixtures of Gases•Kinetic Theory of Gases•Real GasesCHEM 1310 A/B Fall 2006Gases• The states of matter:– Gas: fluid, occupies all available volume– Liquid: fluid, fixed volume– Solid: fixed volume, fixed shape– Others? …• Gases are the easiest to understand – can model them more precisely than liquids or solids using simple equationsCHEM 1310 A/B Fall 2006Ways to produce gases include…• Decomposition2 HgO (s) → 2 Hg (l) + O2 (g)CaCO3(s) + heat → CaO (s) + CO2(g)etc.• Acids reacting with carbonates or hydrogen carbonates to release CO2(chapter 4)NaHCO3(s) + HCl (aq) →NaCl (aq) + H2O (l) + CO2(g)• Acids react with metalZn (s) + 2 HCl (aq) → ZnCl2(aq) + H2(g)CHEM 1310 A/B Fall 2006Some properties of gases• Pressure (P) : how much force it exerts per unit area• Temperature (T) : how hot or cold (kinetic energy of gas molecules)• Volume (V) : space it takes up (the whole volume of the container it’s in)CHEM 1310 A/B Fall 2006Pressure• Often measured by a barometer• The height of a column of mercury is related to the air pressure…Standard atmospheric pressure gives a column of mercury 76 cm high• How does this work?CHEM 1310 A/B Fall 2006Pressure by barometer• Atmosphere pushes down on mercury in beaker, causes it to rise in column• Push of atmosphere exactly balanced by force due to weight of mercury (F=ma)• Mass of mercury is m = d A h, and a=g, so F = ma = dAhg• P = F/A = dghCHEM 1310 A/B Fall 2006Units of pressure• P = F / A = N / m2= kg m s-2/ m2= kg / ms2. SI unit “pascal” (Pa). 105Pa = 1 bar.• Atmospheric pressure is 76 cm of Hg (or 760 mm Hg). Density is 13.596 g cm-1(at 0oC) or 1.3596 x 104kg m-3• P = gdh = 9.80665 m/s2x 1.3596 x 104kg/m3x 0.7600 m = 1.0133 x 105kg / ms2 = 1.01325 x 105Pa = “1 atmosphere” = 1 atmCHEM 1310 A/B Fall 2006Connection between P & V: Boyle’s Law• Pressure and volume of a gas are related• Use a “J tube” to figure out how• In (a), pressure of atm exactly balances pressure of trapped gas Pgas= Patm• In (b), pressure of gas is pressure balanced by Patm + that due to extra mercury added (=gdh), Pgas= Patm+ gdh•Gas is compressed (takes less V) and at higher pressure if more Hg is addedCHEM 1310 A/B Fall 2006Boyle’s Law• Boyle did experiments to show that if the pressure doubled, the gas took up ½ as much room, etc. Pressure and volume are inversely relatedP1V1= P2V2(for fixed T and amt of gas)or more generally, PV = C (constant at fixed T and amount of gas), where C is independent of the particular gas chosen!• C = 22.4 L atm at 0oC and 1 mol of gas; 0oC, 1atm are “standard temperature and pressure” (STP). At STP, one mol of gas occupies 22.4LCHEM 1310 A/B Fall 2006Relationship between V&T:Charles’ Law• As T goes up (at constant pressure Patm), gas expandsV = V0+ α V0Tcel, Tcelin Celcius• All gases expand by the same relative amount when heated! (i.e., α is nearly the same for all gases!)• Celcius temperature scale: water freezes at 0oC, water boils at 100oC by definition! Easy.• On Celcius scale, α = 1/(273.15oC)… has a weird result when T=-273.15oC… “Absolute zero”. Can’t get below -273.15oC.• “Absolute temperature scale”T (Kelvin) = 273.15 + Tcel(Celcius)CHEM 1310 A/B Fall 2006Relationship between V and TCHEM 1310 A/B Fall 2006Charles’ Law in Kelvin T scale• If we substitute Tcel= T (Kelvin) – 273.15, we get V = a T, where a = V0/ 273.15• So now (V1/V2) = (T1/T2) (for a fixed pressure and amount of gas)• Lots of easy problems can be worked with this… for example, if T (in Kelvin!) is doubled, what happens to V?CHEM 1310 A/B Fall 2006Ideal Gas Law• Combines Charles’ Law and Boyle’s LawV α nT / PVolume is proportional to amount of gas and temperature, and inversely proportional to pressure. Call the constant of proportionality R (“universal gas constant”)PV = nRT R = 0.082058 L atm mol-1K-1= 8.3145 J mol-1K-1• Can do lots of easy problems relating P, V, n, T of a gas using this simple equationCHEM 1310 A/B Fall 2006Example problem• A gas cylinder weighs 1.5 kg empty and 2.0 kg when filled with CO2gas. If the cylinder has a volume of 1.0 L, what’s the pressure of the gas at 25oC?CHEM 1310 A/B Fall 2006Ideal gas law w/ molar mass• Could have done the last problem more directly by re-casting the ideal gas law• N = m (mass) / M (molar mass)• PV = (m/M) RT• Also, since density d=m/V, d= PM/RT• Can predict density from P, T, M• Can determine M (and not just empirical formula!) from d, P, TCHEM 1310 A/B Fall 2006Gases in chemical reactions• Can use ideal gas law to do stoichiometry problems now using P, T, V… instead of just masses• Example: We want to make 15.0 kg of the rocket fuel hydrazine, using the reaction 2 NH3(g) + NaOCl (aq) →N2H4(aq) + NaCl (aq) + H2O (l)• If our ammonia is at 10oC and 3.63 atm, how much of it (in L) do we need?CHEM 1310 A/B Fall 2006Mixtures of gases• Suppose 3 containers of equal volume V, each of which contained 1 mol of gas at 1 atm of pressureH2O2N2V, T, 1atm, 1mol V, T, 1atm, 1mol V, T, 1atm, 1mol• What happens if we take the O2and N2from the 2ndand 3rdcontainers and put them in the 1stcontainer at constant T (and of course constant CHEM 1310 A/B Fall 2006V)? What’s the total pressure?Mixtures of gases, cont’dCHEM 1310 A/B Fall 2006• Partial pressure: pressure exerted by each gas in a gas mixture• Total pressure = sum of partial pressures• Each gas obeys ideal gas law separately for the number of moles of that gas and the partial pressure• Ideal gas law also holds for