Gases. Gas: fluid, occupies all available volume Liquid: fluid, fixed volume Solid: fixed volume, fixed shape Others?

Transcription

1 CHAPTER 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 Gases

2 Gases 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 equations

3 Ways to produce gases include Decomposition 2 HgO (s) 2 Hg (l) + O 2 (g) CaCO 3 (s) + heat CaO (s) + CO 2 (g) etc. Acids reacting with carbonates or hydrogen carbonates to release CO 2 (chapter 4) NaHCO 3 (s) + HCl (aq) NaCl (aq) + H 2 O (l) + CO 2 (g) Acids react with metal Zn (s) + 2 HCl (aq) ZnCl 2 (aq) + H 2 (g)

4 Some 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)

5 Pressure 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?

6 Pressure 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 = dgh

7 Units of pressure P = F / A = N / m 2 = kg m s -2 / m 2 = kg / ms 2. SI unit pascal (Pa) Pa = 1 bar. Atmospheric pressure is 76 cm of Hg (or 760 mm Hg). Density is g cm -1 (at 0 o C) or x 10 4 kg m -3 P = gdh = m/s 2 x x 10 4 kg/m 3 x m = x 10 5 kg / ms 2 = x 10 5 Pa = 1 atmosphere = 1 atm

8 Connection between P & V: 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 P gas = P atm In (b), pressure of gas is pressure balanced by Patm + that due to extra mercury added (=gdh), P gas = P atm + gdh Gas is compressed (takes less V) and at higher pressure if more Hg is added Boyle s Law

9 Boyle 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 related P 1 V 1 = P 2 V 2 (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 0 o C and 1 mol of gas; 0 o C, 1atm are standard temperature and pressure (STP). At STP, one mol of gas occupies 22.4L

10 Relationship between V&T: Charles Law As T goes up (at constant pressure P atm ), gas expands V = V 0 + α V 0 T cel, T cel in 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 0 o C, water boils at 100 o C by definition! Easy. On Celcius scale, α = 1/( o C) has a weird result when T= o C Absolute zero. Can t get below o C. Absolute temperature scale T (Kelvin) = T cel (Celcius)

11 Relationship between V and T

12 Charles Law in Kelvin T scale If we substitute T cel = T (Kelvin) , we get V = a T, where a = V 0 / So now (V 1 /V 2 ) = (T 1 /T 2 ) (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?

13 Ideal Gas Law Combines Charles Law and Boyle s Law V α nt / P Volume 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 = L atm mol -1 K -1 = J mol -1 K -1 Can do lots of easy problems relating P, V, n, T of a gas using this simple equation

14 Example problem A gas cylinder weighs 1.5 kg empty and 2.0 kg when filled with CO 2 gas. If the cylinder has a volume of 1.0 L, what s the pressure of the gas at 25 o C?

15 Ideal 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, T

16 Gases 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 NH 3 (g) + NaOCl (aq) N 2 H 4 (aq) + NaCl (aq) + H 2 O (l) If our ammonia is at 10 o C and 3.63 atm, how much of it (in L) do we need?

17 Mixtures of gases Suppose 3 containers of equal volume V, each of which contained 1 mol of gas at 1 atm of pressure H 2 O 2 N 2 V, T, 1atm, 1mol V, T, 1atm, 1mol V, T, 1atm, 1mol What happens if we take the O 2 and N 2 from the 2 nd and 3 rd containers and put them in the 1 st container at constant T (and of course constant V)? What s the total pressure?

18 Mixtures of gases, cont d H 2, O 2 N 2 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 P tot, n tot P H2 = n H2 R T / V, etc. P tot = n tot R T / V Therefore, P H2 / P tot = n H2 / n tot ( = 1/3 for this example). This is also called the mole fraction, X H2 P H2 = P tot x X H2 ( = 1/3 Ptot for this example) V, T 1 mol H 2, 1 mol O 2, 1 mol N 2

19 Kinetic Theory of Gases Tries to explain gas behavior using basic physics Molecules of a gas fly around in random directions with a distribution of speeds The molecules are pictured as hard objects undergoing elastic collisions with each other and the walls of the container Pressure results from the many collisions of the gas molecules with the walls of the container. P = F/A, P α (impulse per collision) x (rate of collisions with walls)

20 Origin of pressure P = F/A P α (impulse per collision) x (rate of collisions with walls) P α (m x u) x [(N/V) x u] = Nmu 2 / V, where u = speed of molecules m = mass of molecules (N/V) = number of molecules per unit volume (more molecules = more collisions) note faster molecules (u) = more collisions

21 Origin of pressure, cont d So far we have PV α Nmu 2 Problem: not just one speed u, lots of them Solution: ok to use an average over u 2, the mean square speed <u 2 > Proportionality constant works out to be 1/3, so PV = (1/3) Nm<u 2 >. But we also know PV = nrt, so nrt = (1/3) Nm<u 2 >, or RT = (1/3) N 0 m<u 2 > (because N is just n times N 0, Avogadro s number)

22 Origin of pressure, cont d So we see that RT = (1/3) N 0 m<u 2 > Temperature is therefore due to the kinetic energy of the gas molecules KE = ½ m u 2 Average KE per mol is ½ (N 0 m) <u 2 > = 3/2 RT, or <u 2 > = 3RT / M (since molar mass M = N 0 m) So molecules move faster at higher T, and slower if they are more massive!

23 Maxwell-Boltzmann distribution of molecular speeds in N 2 at 3 temps Note: u rms u mp u av

24 Measurement of speed distributions

25 Root mean square (RMS) speed U rms = sqrt(<u 2 >) = sqrt(3rt/m) Example: He at 298K has what RMS speed?

26 Diffusion Result of previous example seems to large e.g., odors don t seem to travel this fast! Reason: direction of molecule keeps changing due to collisions with other gas molecules Diffusion: random motion of a molecule due to collisions with other molecules. Typically about collisions per second! Typically goes about ~ 10-7 m between collisions (mean free path)

27 Rates of effusion and Effusion: molecules escape through a very small hole into vacuum Gaseous diffusion: molecules pass through a (large) porous barrier into another container The rates of both of both processes are inversely proportional to the molar mass of the gas Gaseous diffusion used to separate 235 U from 238 U in World War II gaseous diffusion

28 Real gases PV=nRT is the ideal gas law Gases are not ideal. Implicitly assumes Gas molecules are ideal point particles with no size No attraction between molecules In reality, gas molecules do take up some volume, and there is some attraction between gas molecules which can cause clustering First effect reduces volume available to gas, and second reduces pressure exerted by gas Van der Waals equation of state (P + a n 2 /V 2 ) (V - nb) = nrt is more accuate. a,b depend on gas, are tabulated. n 2 /V 2 is # of pairs per volume, and nb is excluded volume

29 Reliability of ideal gas law Different molecules deviate differently Works best at low pressures Deviations at very large pressures can be a factor of 2 or more