Gases

Pressure Is caused by the collisions of molecules with the walls of a container is equal to force/unit area SI units = Newton/meter2 = 1 Pascal (Pa) 1 atmosphere = 101,325 Pa 1 atmosphere = 1 atm = 760 mm Hg = 760 torr

Measuring Pressure The first device for measuring atmospheric pressure was developed by Evangelista Torricelli during the 17th century. The device was called a “barometer”   Baro = weight   Meter = measure

An Early Barometer The normal pressure due to the atmosphere at sea level can support a column of mercury that is 760 mm high.

Standard Temperature and Pressure “STP” P = 1 atmosphere, 760 torr T = 0°C, 273 Kelvins The molar volume of an ideal gas is 22.42 liters at STP

Converting Celsius to Kelvin Gas law problems involving temperature require that the temperature be in KELVINS! Kelvins = C + 273 °C = Kelvins - 273

Boyle’s Law Pressure is inversely proportional to volume when temperature is held constant.

P1V1 = P2V2 P1 = P2V2/V1 P1 = 3.00 cm Hg x 0.240 cm3/200 cm3 A sample of helium gas at 25°C is compressed from 200 cm3 to 0.240 cm3. Its pressure is now 3.00 cm Hg. What was the original pressure of the helium? P1 = ? V1 = 200 cm3 P2 = 3.00 cm V2 = 0.240 cm3 Hg P1V1 = P2V2 P1 = P2V2/V1 P1 = 3.00 cm Hg x 0.240 cm3/200 cm3 P1 = 3.60 x 10-3 cm Hg

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

Gay Lussac’s Law The pressure and temperature of a gas are directly related, provided that the volume remains constant.

A sample of oxygen gas has a volume of 2. 73 dm3 at 21. 0 oC A sample of oxygen gas has a volume of 2.73 dm3 at 21.0 oC.  At what temperature would the gas have a volume of 4.00 dm3? V1 = V2 T1 T2 T1 = 294 K V1 = 2.73 dm3 T2 = ? V2 = 4.00 dm3 2.73 dm3 = 4.00 dm3 ----------- ------------- 294 K T2 T2 = 294 K x 4.00 dm3        -----------------------               2.73 dm3 T2  = 431 K

The Combined Gas Law The combined gas law expresses the relationship between pressure, volume and temperature of a fixed amount of gas. Boyle’s law, Gay-Lussac’s law, and Charles’ law are all derived from this by holding a variable constant.

A 350 cm3 sample of helium gas is collected at 22. 0 oC and 99. 3 kPa A 350 cm3 sample of helium gas is collected at 22.0 oC and 99.3 kPa.  What volume would this gas occupy at STP ? V1 = 350 cm3 P1 = 99.3 kPa T1 = 295 K V2 = ? P2 = 101.3 kPa (standard press) T2 = 273 K (standard temp)) P1 V1 = P2 V2 ---------- -------------- T1 T2 (99.3 kPa )(350 cm3 ) = (101.3 kPa) V2 --------------------------------------- ___________________ ( 295 K) (273 K) V2 = 320 cm3

------------------------------------ Avogadro’s Law For a gas at constant temperature and pressure, the volume is directly proportional to the number of moles of gas. V = an a = proportionality constant V = volume of the gas n = number of moles of gas 31. D 32. D 33. D 34. C 35. C 36. B 37. B ------------------------------------

Ideal Gases Ideal gases are imaginary gases that perfectly fit all of the assumptions of the kinetic molecular theory. Gases consist of tiny particles that are far apart relative to their size. Collisions between gas particles and between particles and the walls of the container are elastic collisions No kinetic energy is lost in elastic collisions

Ideal Gases (continued) Gas particles are in constant, rapid motion. They therefore possess kinetic energy, the energy of motion There are no forces of attraction between gas particles The average kinetic energy of gas particles depends on temperature, not on the identity of the particle.

The Nature of Gases Gases expand to fill their containers Gases are fluid – they flow Gases have low density 1/1000 the density of the equivalent liquid or solid Gases are compressible Gases effuse and diffuse Effusion, molecules moving at a high rate of speed will eventually “collide” with a hole and escape. Effusion is gas escaping through a hole, Example: air escaping through a hole in your tire Diffusion, again because the molecules are moving at a high rate of speed, they will spread out Example: perfume diffusing through air Example: Liquids also diffuse: food coloring in water

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

What volume is occupied by 5. 03 g of O2 at 28°C and a pressure of 0 What volume is occupied by 5.03 g of O2 at 28°C and a pressure of 0.998 atm? P = 0.998 atm V= ? Mass = 5.03 g O2 / 1 mol O2 / = / 32 g O2 / n= 0.157 moles R = 0.08206 L atm mol K T = 28°C + 273 = 301 K PV = nRT (0.998 atm) V = (0.157 mol) (0.08206 L atm ) ( 301 K) mol K =3.89 L

Standard Molar Volume Equal volumes of all gases at the same temperature and pressure contain the same number of molecules. - Amedeo Avogadro

Density and the Ideal Gas Law Combining the formula for density with the Ideal Gas law, substituting and rearranging algebraically: M = Molar Mass P = Pressure R = Gas Constant T = Temperature in Kelvins dRT = molar P mass

Gas Stoichiometry #1 If reactants and products are at the same conditions of temperature and pressure, then mole ratios of gases are also volume ratios. 3 H2(g) + N2(g)  2NH3(g) 3 moles H2 + 1 mole N2  2 moles NH3 3 liters H2 + 1 liter N2  2 liters NH3

Gas Stoichiometry #2 How many liters of ammonia can be produced when 12 liters of hydrogen react with an excess of nitrogen? 3 H2(g) + N2(g)  2NH3(g) 12 L H2 2 L NH3 = L NH3 8.0 3 L H2

Gas Stoichiometry #3 How many liters of oxygen gas, at STP, can be collected from the complete decomposition of 50.0 grams of potassium chlorate? 2 KClO3(s)  2 KCl(s) + 3 O2(g) 50.0 g KClO3 1 mol KClO3 3 mol O2 22.4 L O2 122.55 g KClO3 2 mol KClO3 1 mol O2 = L O2 13.7

Gas Stoichiometry #4 How many liters of oxygen gas, at 37.0C and 0.930 atmospheres, can be collected from the complete decomposition of 50.0 grams of potassium chlorate? 2 KClO3(s)  2 KCl(s) + 3 O2(g) 50.0 g KClO3 1 mol KClO3 3 mol O2 = “n” mol O2 122.55 g KClO3 2 mol KClO3 0.612 mol O2 = 16.7 L

Dalton’s Law of Partial Pressures For a mixture of gases in a container, PTotal = P1 + P2 + P3 + . . . This is particularly useful in calculating the pressure of gases collected over water. nTotal = n1 + n2 + n3 + . . .

Dalton’s law of partial pressures collecting gases over water Mixture of gas and water vapor. PT = pgas + pvap(H2O)

Ptotal = Pgas + P water vapor Hydrogen gas is collected over water at a total pressure of 95.0 kPa and a temperature of 25 C. What is the partial pressure of hydrogen gas? According to a water vapor pressure table, the vapor pressure of water at 25C is 3.17 kPa. Ptotal = Pgas + P water vapor 95.0 kPa = X + 3.17 kPa X = 91.8 kPa

e. g. , If 6. 00 g of O2 and 9. 00 g of CH4 are placed in a 15 e.g., If 6.00 g of O2 and 9.00 g of CH4 are placed in a 15.0-L container at 0ºC, what is the partial pressure of each gas and the total pressure in the container.

Kinetic Energy of Gas Particles At the same conditions of temperature, all gases have the same average kinetic energy.

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

Kinetic Molecular Theory Particles of matter are ALWAYS in motion Volume of individual particles is  zero. Collisions of particles with container walls cause pressure exerted by gas. Particles exert no forces on each other. Average kinetic energy µ Kelvin temperature of a gas.  

Diffusion Diffusion: describes the mixing of gases. The rate of diffusion is the rate of gas mixing.

Effusion Effusion: describes the passage of gas into an evacuated chamber.

Kinetic Molecular Theory Gases have certain properties that can be explained by the KMT. Low Density, because the molecules are moving at a high rate of speed and are not held back by electrostatic attractions, they, spread out. And because gases have small volume as well as being spread out, they have low density Compressibility, because the molecules have space between them, they can be forced to compress unlike liquids and solids where there is little space between the molecules Expansion, because the molecules are moving at a high rate of speed, they will spread out if given the opportunity Diffusion, again because the molecules are moving at a high rate of speed, they will spread out Example: perfume diffusing through air Example: Liquids also diffuse: food coloring in water Effusion, molecules moving at a high rate of speed will eventually “collide” with a hole and escape. Effusion is gas escaping through a hole, Example: air escaping through a hole in your tire

Graham’s Law Rates of Effusion and Diffusion

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