Chapter 10 Gases

Characteristics of Gases Unlike liquids and solids, gases Expand to fill their containers. Are highly compressible. Have extremely low densities. Homogeneous mixing Effusion and Diffusion

Pressure F P = A Pressure is the amount of force applied to an area: Atmospheric pressure is the weight of air per unit of area.

Standard Pressure Normal atmospheric pressure at sea level is referred to as standard pressure. It is equal to 1.00 atm 760 torr (760 mmHg) = 76 cm Hg 101.325 kPa 1.01325 bar

Gas laws Boyle’s Law: The volume of a fixed quantity of gas at constant temperature is inversely proportional to the pressure. The volume of Charles’s Law a fixed amount of gas at constant pressure is directly proportional to its absolute temperature. Avogadro’s Law: The volume of a gas at constant temperature and pressure is directly proportional to the number of moles of the gas.

P V = n R T Ideal-Gas Equation So far we’ve seen that V  1/P (Boyle’s law) V  T (Charles’s law) V  n (Avogadro’s law) Combining these, we get P V = n R T (0.0821) atm L mol (atm.L/mol .K) K

Sample Exercise 10.4 Using the Ideal-Gas Equation Calcium carbonate, CaCO3(s), the principal compound in limestone, decomposes upon heating to CaO(s) and CO2(g). A sample of CaCO3 is decomposed, and the carbon dioxide is collected in a 250-mL flask. After decomposition is complete, the gas has a pressure of 1.3 atm at a temperature of 31 C. How many moles of CO2 gas were generated?

Sample Exercise 10.6 Calculating the Effect of Changing P and T on Gas Volume An inflated balloon has a volume of 6.0 L at sea level (1.0 atm) and is allowed to ascend until the pressure is 0.45 atm. During ascent, the temperature of the gas falls from 22 C to 21 C. Calculate the volume of the balloon at its final altitude.

Sample Exercise 10.5 Calculating the Effect of Temperature Changes on Pressure The gas pressure in an aerosol can is 1.5 atm at 25 C. Assuming that the gas obeys the ideal-gas equation, what is the pressure when the can is heated to 450 C?

Molecular mass and densities of gases P V = n R T P V = (Wt/M) R T P M = (Wt / V) R T P M = d R T

Sample Exercise 10.7 Calculating Gas Density What is the density of carbon tetrachloride vapor at 714 torr and 125 C?

Sample Exercise 10.8 Calculating the Molar Mass of a Gas A large evacuated flask initially has a mass of 134.567 g. When the flask is filled with a gas of unknown molar mass to a pressure of 735 torr at 31 C, its mass is 137.456 g. When the flask is evacuated again and then filled with water at 31 C, its mass is 1067.9 g. (The density of water at this temperature is 0.997 g/mL.) Assuming the ideal-gas equation applies, calculate the molar mass of the gas.

Sample Exercise 10.9 Relating a Gas Volume to the Amount of Another Substance in a Reaction Automobile air bags are inflated by nitrogen gas generated by the rapid decomposition of sodium azide, NaN3: 2 NaN3(s)  2 Na(s) + 3 N2(g) If an air bag has a volume of 36 L and is to be filled with nitrogen gas at 1.15 atm and 26.0 C, how many grams of NaN3 must be decomposed?

Dalton’s Law of Partial Pressures The total pressure of a mixture of gases equals the sum of the pressures that each would exert if it were present alone. In other words, Ptotal = P1 + P2 + P3 + … Start here 6/18/10 P1 = X1Pt Where X1 is the mole fraction (n1/nt).

Pt = PO2 + PCH4 = 0.281 atm + 0.841 atm = 1.122 atm Sample Exercise 10.10 Applying Dalton’s Law of Partial Pressures A mixture of 6.00 g O2(g) and 9.00 g CH4(g) is placed in a 15.0-L vessel at 0 C. What is the partial pressure of each gas, and what is the total pressure in the vessel? Pt = PO2 + PCH4 = 0.281 atm + 0.841 atm = 1.122 atm

Partial Pressures Ptotal = Pgas + Pwater When one collects a gas over water, there is water vapor mixed in with the gas. To find only the pressure of the desired gas, one must subtract the vapor pressure of water from the total pressure. Ptotal = Pgas + Pwater

Sample Exercise 10.12 Calculating the Amount of Gas Collected over Water When a sample of KClO3 is partially decomposed in the setup shown in Figure 10.15, the volume of gas collected is 0.250 L at 26 C and 765 torr total pressure. (a) How many moles of O2 are collected? (b) How many grams of KClO3 were decomposed? PO2 = 765 torr  25 torr = 740 torr

Effusion Effusion is the escape of gas molecules through a tiny hole into an evacuated space.

Effusion The difference in the rates of effusion for helium and argon, for example, explains why a helium balloon would deflate faster.

Diffusion Diffusion is the spread of one substance throughout a space or throughout a second substance.

Graham's Law of Effusion Consider two gases with molar masses M1 and M2, with effusion rates, r1 and r2, respectively: • The relative rate of effusion is given by Graham’s law:

Sample Exercise 10.15 Applying Graham’s Law An unknown gas composed of homonuclear diatomic molecules effuses at a rate that is 0.355 times the rate at which O2 gas effuses at the same temperature. Calculate the molar mass of the unknown and identify it.