GASES Chapter 5

A Gas Uniformly fills any container. Mixes completely with any other gas Exerts pressure on its surroundings.

Simple barometer invented by Evangelista Torricelli

Pressure is equal to force/unit area SI units = Newton/meter2 = 1 Pascal (Pa) 1 standard atmosphere = 101,325 Pa 1 standard atmosphere = 1 atm = 760 mm Hg = 760 torr

Pressure Unit Conversions The pressure of a tire is measured to be 28 psi. What would the pressure in atmospheres, torr, and pascals. (28 psi)(1.000 atm/14.69 psi) = 1.9 atm (28 psi)(1.000 atm/14.69 psi)(760.0 torr/1.000atm) = 1.4 x 103 torr (28 psi)(1.000 atm/14.69 psi)(101,325 Pa/1.000 atm) = 1.9 x 105 Pa

Simple Manometer

Volume of a gas decreases as pressure increases at constant temperature

P vs V V vs 1/P BOYLE’S LAW DATA

Boyle’s Law* (Pressure)( Volume) = Constant (T = constant) P1V1 = P2V2 (T = constant) V  1/P (T = constant) (*Holds precisely only at very low pressures.)

Boyle’s Law Calculations A 1.5-L sample of gaseous CCl2F2 has a pressure of 56 torr. If the pressure is changed to 150 torr, will the volume of the gas increase or decrease? What will the new volume be? Decrease P1 = 56 torr P2 = 150 torr V1 = 1.5 L V2 = ? V1P1 = V2P2 V2 = V1P1/P2 V2 = (1.5 L)(56 torr)/(150 torr) V2 = 0.56 L

Boyle’s Law Calculations In an automobile engine the initial cylinder volume is 0.725 L. After the piston moves up, the volume is 0.075 L. The mixture is 1.00 atm, what is the final pressure? P1 = 1.00 atm P2 = ? V1 = 0.725 L V2 = 0.075 L V1P1 = V2P2 P2 = V1P1/V2 P2 = (0.725 L)(1.00 atm)/(0.075 L) P2 = 9.7 atm Is this answer reasonable?

A gas that strictly obeys Boyle’s Law is called an ideal gas.

Plot of PV vs. P for several gases at pressures below 1 atm.

Plot of V vs. T(oC) for several gases

Volume of a gas increases as heat is added when pressure is held constant.

Charles’s Law The volume of a gas is directly proportional to temperature, and extrapolates to zero at zero Kelvin. V = bT (P = constant) b = a proportionality constant

Charles’s Law

Charles’s Law Calculations Consider a gas with a a volume of 0.675 L at 35 oC and 1 atm pressure. What is the temperature (in Co) of the gas when its volume is 0.535 L at 1 atm pressure? V1 = 0.675 L V2 = 0.535 L T1 = 35 oC + 273 = 308 K T2 = ? V1/V2 = T1/T2 T2 = T1 V2/V1 T2 = (308 K)(0.535 L)/(0.675 L) T2 = 244 K -273 T2 = - 29 oC

At constant temperature and pressure, increasing the moles of a gas increases its volume.

Avogadro’s Law For a gas at constant temperature and pressure, the volume is directly proportional to the number of moles of gas (at low pressures). V = an a = proportionality constant V = volume of the gas n = number of moles of gas

AVOGADRO’S LAW V1/V2 = n1/n2

AVOGADRO’S LAW A 12.2 L sample containing 0.50 mol of oxygen gas, O2, at a pressure of 1.00 atm and a temperature of 25 oC is converted to ozone, O3, at the same temperature and pressure, what will be the volume of the ozone? 3 O2(g) ---> 2 O3(g) (0.50 mol O2)(2 mol O3/3 mol O2) = 0.33 mol O3 V1 = 12.2 L V2 = ? n1 = 0.50 mol n2 = 0.33 mol V1/V2 = n1/n2 V2 = V1 n2/n1 V2 = (12.2 L)(0.33 mol)/(0.50 mol) V2 = 8.1 L

COMBINED GAS LAW V1/ V2 = P2 T1/ P1 T2

COMBINED GAS LAW What will be the new volume of a gas under the following conditions? V1 = 3.48 L V2 = ? P1 = 0.454 atm P2 = 0.616 atm T1 = - 15 oC + 273 = 258 K T2 = 36 oC + 273 T2= 309 K V1/ V2 = P2 T1/ P1 T2 V2 = V1P1T2/P2T1 V2 = (309 K)(0.454 atm)(3.48 L) (258 K)(0.616 atm) V2 = 3.07 L

Pressure exerted by a gas increases as temperature increases provided volume remains constant.

P1 / P2 = T1 / T2 If the volume of a gas is held constant, then V1 / V2 = 1. Therefore: P1 / P2 = T1 / T2

Ideal Gas Law An equation of state for a gas. “state” is the condition of the gas at a given time. PV = nRT

IDEAL GAS 1. Molecules are infinitely far apart. 2. Zero attractive forces exist between the molecules. 3. Molecules are infinitely small--zero molecular volume. What is an example of an ideal gas?

REAL GAS 1. Molecules are relatively far apart compared to their size. 2. Very small attractive forces exist between molecules. 3. The volume of the molecule is small compared to the distance between molecules. What is an example of a real gas?

Ideal Gas Law PV = nRT Holds closely at P < 1 atm R = proportionality constant = 0.08206 L atm  mol P = pressure in atm V = volume in liters n = moles T = temperature in Kelvins Holds closely at P < 1 atm

Ideal Gas Law Calculations A 1.5 mol sample of radon gas has a volume of 21.0 L at 33 oC. What is the pressure of the gas? p = ? V = 21.0 L n = 1.5 mol T = 33 oC + 273 T = 306 K R = 0.08206 Latm/molK pV = nRT p = nRT/V p = (1.5mol)(0.08206Latm/molK)(306K) (21.0L) p = 1.8 atm

Ideal Gas Law Calculations A sample of hydrogen gas, H2, has a volume of 8.56 L at a temperature of O oC and a pressure of 1.5 atm. Calculate the number of moles of hydrogen present. p = 1.5 atm V = 8.56 L R = 0.08206 Latm/molK n = ? T = O oC + 273 T = 273K pV = nRT n = pV/RT n = (1.5 atm)(8.56L) (0.08206 Latm/molK)(273K) n = 0.57 mol

Standard Temperature and Pressure “STP” P = 1 atmosphere T = C The molar volume of an ideal gas is 22.42 liters at STP

GAS STOICHIOMETRY 1. Mass-Volume 2. Volume-Volume

Molar Volume pV = nRT V = nRT/p V = (1.00 mol)(0.08206 Latm/molK)(273K) (1.00 atm) V = 22.4 L

Gas Stoichiometry Not at STP (Continued) p = 1.00 atm V = ? n = 1.28 x 10-1 mol R = 0.08206 Latm/molK T = 25 oC + 273 = 298 K pV = nRT V = nRT/p V = (1.28 x 10-1mol)(0.08206Latm/molK)(298K) (1.00 atm) V = 3.13 L O2

Gases at STP A sample of nitrogen gas has a volume of 1.75 L at STP. How many moles of N2 are present? (1.75L N2)(1.000 mol/22.4 L) = 7.81 x 10-2 mol N2

Gas Stoichiometry at STP Quicklime, CaO, is produced by heating calcium carbonate, CaCO3. Calculate the volume of CO2 produced at STP from the decomposition of 152 g of CaCO3. CaCO3(s) ---> CaO(s) + CO2(g) (152g CaCO3)(1 mol/100.1g)(1mol CO2/1mol CaCO3) (22.4L/1mol) = 34.1L CO2 Note: This method only works when the gas is at STP!!!!!

Volume-Volume If 25.0 L of hydrogen reacts with an excess of nitrogen gas, how much ammonia gas will be produced? All gases are measured at the same temperature and pressure. 2N2(g) + 3H2(g) ----> 2NH3(g) (25.0 L H2)(2 mol NH3/3 mol H2) = 16.7 L NH3

MOLAR MASS OF A GAS n = m/M n = number of moles m = mass M = molar mass

MOLAR MASS OF A GAS P = mRT/VM or P = DRT/M therefore: M = DRT/P

Molar Mass Calculations M = ? d = 1.95 g/L T = 27 oC + 273 p = 1.50 atm T = 300. K R = 0.08206 Latm/mol K M = dRT/p M = (1.95g/L)(0.08206Latm/molK)(300.K) (1.5atm) M = 32.0 g/mol

Dalton’s Law of Partial Pressures For a mixture of gases in a container, PTotal = P1 + P2 + P3 + . . .

Dalton’s Law of Partial Pressures Calculations A mixture of nitrogen gas at a pressure of 1.25 atm, oxygen at 2.55 atm, and carbon dioxide at .33 atm would have what total pressure? PTotal = P1 + P2 + P3 PTotal = 1.25 atm + 2.55 atm + .33 atm Ptotal = 4.13 atm

Water Vapor Pressure 2KClO3(s) ----> 2KCl(s) + 3O2(g) When a sample of potassium chlorate is decomposed and the oxygen produced collected by water displacement, the oxygen has a volume of 0.650 L at a temperature of 22 oC. The combined pressure of the oxygen and water vapor is 754 torr (water vapor pressure at 22 oC is 21 torr). How many moles of oxygen are produced? Pox = Ptotal - PHOH Pox = 754 torr - 21 torr pox = 733 torr

MOLE FRACTION -- the ratio of the number of moles of a given component in a mixture to the total number of moles of the mixture. 1 = n1/ ntotal 1 = V1/ Vtotal 1 = P1 / Ptotal (volume & temperature constant)

Kinetic Molecular Theory 1. Volume of individual particles is  zero. 2. Collisions of particles with container walls cause pressure exerted by gas. 3. Particles exert no forces on each other. 4. Average kinetic energy  Kelvin temperature of a gas.

Plot of relative number of oxygen molecules with a given velocity at STP (Boltzmann Distribution).

Plot of relative number of nitrogen molecules with a given velocity at three different temperatures.

The Meaning of Temperature Kelvin temperature is an index of the random motions of gas particles (higher T means greater motion.)

Diffusion: describes the mixing of gases Diffusion: describes the mixing of gases. The rate of diffusion is the rate of gas mixing. Effusion: describes the passage of gas into an evacuated chamber.

Effusion of a gas into an evacuated chamber

Effusion: Diffusion:

Real Gases Must correct ideal gas behavior when at high pressure (smaller volume) and low temperature (attractive forces become important).

Plots of PV/nRT vs. P for several gases at 200 K. Note the significant deviation from ideal behavior.

Real Gases   corrected pressure corrected volume Pideal Videal

Concentration for some smog components vs. time of day

What substances represent intermediates? NO2(g) NO(g) + O(g) O(g) + O2(g)  O3(g) NO(g) + 1/2 O2(g)  NO2(g) __________________________ 3/2 O2(g)  O3(g) What substances represent intermediates? Which substance represents the catalyst?

Chemistry is a gas!!