Prentice Hall © 2003Chapter 10 Chapter 10 Gases CHEMISTRY The Central Science 9th Edition

Prentice Hall © 2003Chapter 10 Gas Properties: highly compressible occupy the full volume of their containers volume decreases with increasing pressure gases only occupy about 0.1 % of the volume of their containers 10.1: Characteristics of Gases

Prentice Hall © 2003Chapter 10 Text, P. 366

Prentice Hall © 2003Chapter 10 Pressure is the force acting on an object per unit area: Gravity exerts a force on the earth’s atmosphere 10.2: Pressure

Prentice Hall © 2003Chapter 10 Text, P. 367

Prentice Hall © 2003Chapter 10 Atmosphere Pressure and the Barometer Atmospheric pressure is measured with a barometer If a tube is inserted into a container of mercury open to the atmosphere, the mercury will rise 760 mm up the tube Standard atmospheric pressure Units: 1 atm = 760 mmHg = 760 torr =  10 5 Pa = kPa

Text, P. 368

The pressures of gases not open to the atmosphere are measured in manometers –If P gas < P atm then P gas + P h = P atm –If P gas > P atm then P gas = P atm + P h

Prentice Hall © 2003Chapter 10 The Pressure-Volume Relationship: Boyle’s Law Weather balloons are used as a practical consequence to the relationship between pressure and volume of a gas As the balloon ascends, the volume increases the atmospheric pressure decreases Boyle’s Law: the volume of a fixed quantity of gas is inversely proportional to its pressure 10.3: The Gas Laws

Text, P. 371 The V of the gas decreases due to increased P from more Hg

Prentice Hall © 2003Chapter 10 Mathematically: A plot of V versus P is a hyperbola Similarly, a plot of V versus 1/P must be a straight line passing through the origin Text, P. 372

Prentice Hall © 2003Chapter 10 The Temperature-Volume Relationship: Charles’s Law Hot air balloons expand when they are heated Charles’s Law: the volume of a fixed quantity of gas at constant pressure increases as the temperature increases Mathematically:

Prentice Hall © 2003Chapter 10 A plot of V versus T is a straight line When T is measured in  C, the intercept on the temperature axis is  C We define absolute zero, 0 K =  C Text, P. 373

Prentice Hall © 2003Chapter 10 The Quantity-Volume Relationship: Avogadro’s Law Gay-Lussac’s Law of combining volumes: at a given temperature and pressure, the volumes of gases which react are ratios of small whole numbers Text, P. 373

Prentice Hall © 2003Chapter 10 Avogadro’s Hypothesis: equal volumes of gas at the same temperature and pressure will contain the same number of molecules Avogadro’s Law: the volume of gas at a given temperature and pressure is directly proportional to the number of moles of gas Mathematically we can show that 22.4 L of any gas at 0  C contain 6.02  gas molecules: Text, P. 374

Prentice Hall © 2003Chapter 10

Prentice Hall © 2003Chapter 10 Consider the three gas laws We can combine these into a general gas law: 10.4: The Ideal Gas Equation Boyle’s Law: Charles’s Law: Avogadro’s Law:

Prentice Hall © 2003Chapter 10 If R is the constant of proportionality (called the gas constant), then The ideal gas equation is: R = L·atm/mol·K = J/mol·K

Text, P. 375

Prentice Hall © 2003Chapter 10 We define STP (standard temperature and pressure) as conditions of 0  C ( K) and 1 atm Volume of 1 mol of gas at STP is:

Prentice Hall © 2003Chapter 10 Relating the Ideal-Gas Equation and the Gas Laws If PV = nRT and n and T are constant, then PV = constant and we have Boyle’s law Other laws can be generated similarly In general, if we have a gas under two sets of conditions, then

Prentice Hall © 2003Chapter 10 Gas Densities and Molar Mass Density has units of mass over volume Rearranging the ideal-gas equation with M as molar mass we get 10.5: Further Applications of the Ideal-Gas Equation

Prentice Hall © 2003Chapter 10 The molar mass of a gas can be determined as follows: Volumes of Gases in Chemical Reactions The ideal-gas equation relates P, V, and T to number of moles of gas The n can then be used in stoichiometric calculations

Prentice Hall © 2003Chapter 10 Sample Problems from the end of Chapter 10: # 33, 37, 41, 47

Prentice Hall © 2003Chapter 10

Prentice Hall © 2003Chapter 10 Since gas molecules are so far apart, we can assume they behave independently Dalton’s Law: in a gas mixture the total pressure is given by the sum of partial pressures of each component: Each gas obeys the ideal gas equation: 10.6: Gas Mixtures and Partial Pressures

Prentice Hall © 2003Chapter 10 Combining the equations Partial Pressures and Mole Fractions Let n i be the number of moles of gas i exerting a partial pressure P i, then where  i is the mole fraction (n i /n t )

Prentice Hall © 2003Chapter 10 Collecting Gases over Water It is common to synthesize gases and collect them by displacing a volume of water To calculate the amount of gas produced, we need to correct for the partial pressure of the water (Appendix B): Text, P. 385

Prentice Hall © 2003Chapter 10 Sample Problems from the end of Chapter 10: # 49, 55, 59

Prentice Hall © 2003Chapter 10

Prentice Hall © 2003Chapter 10 Theory of moving molecules Assumptions: –Molecules in constant random motion –Volume of individual molecules is negligible –Intermolecular forces are negligible –Energy can be transferred between molecules, but total KE is constant at constant T –Average KE of molecules is proportional to T 10.7: Kinetic Molecular Theory

Prentice Hall © 2003Chapter 10 Amount of pressure depends on frequency and magnitude of molecular collisions Gas molecules have an average kinetic energy –Each molecule has a different energy Average KE increases with increasing T

Prentice Hall © 2003Chapter 10 As kinetic energy increases, the velocity of the gas molecules increases Root mean square speed, u, is the speed of a gas molecule having average kinetic energy Average kinetic energy, , is related to root mean square speed:

Prentice Hall © 2003Chapter 10 Kinetic Energy has a set value at a specified temperature Mathematically: 10.8: Molecular Effusion and Diffusion Molar mass in the denominator, so an increase in molar mass will decrease the u of the molecules R = This value of R allows u to have velocity units

Prentice Hall © 2003Chapter 10 Graham’s Law of Effusion Effusion is the escape of a gas through a tiny hole (a balloon will deflate over time due to effusion)

Prentice Hall © 2003Chapter 10 Consider two gases with molar masses M 1 and M 2. The relative rate of effusion is given by: Only those molecules that hit the small hole will escape through it The higher the root mean square speed (rms), the more likely a gas molecule will hit the hole Graham’s Law

Prentice Hall © 2003Chapter 10 Diffusion and Mean Free Path Diffusion of a gas is the spread of the gas through space Diffusion is faster for light gas molecules Diffusion is significantly slower than rms speed consider someone opening a perfume bottle: it takes a while to detect the odor, but rms speed at 25  C is about 1150 mi/hr Diffusion is slowed by gas molecules colliding with each other

Prentice Hall © 2003Chapter 10 Average distance traveled by a gas molecule between collisions is called mean free path Varies with pressure At sea level, mean free path is about 6  cm

Prentice Hall © 2003Chapter 10 Sample Problems # 67, 69

Prentice Hall © 2003Chapter 10

Prentice Hall © 2003Chapter 10 From the ideal gas equation, we have For 1 mol of gas, PV/RT = 1 for all pressures In a real gas, PV/RT varies from 1 significantly The higher the pressure the greater the deviation from ideal behavior 10.9: Real Gases: Deviations from Ideal Behavior

Prentice Hall © 2003Chapter 10 As the gas molecules get closer together, the intermolecular distance decreases attractive forces take over (real gas) Text, P. 394

Prentice Hall © 2003Chapter 10 As temperature increases, the gas molecules move faster and further apart more energy is available to break intermolecular forces Therefore, the higher the temperature, the more ideal the gas Text, P. 394

Prentice Hall © 2003Chapter 10 The assumptions in kinetic molecular theory show where ideal gas behavior breaks down: –the molecules of a gas have finite volume –molecules of a gas do attract each other

Prentice Hall © 2003Chapter 10 The van der Waals Equation Two terms are added to the ideal gas equation: correct for volume of molecules correct for intermolecular attractions The correction terms generate the van der Waals equation:

Prentice Hall © 2003Chapter 10 where a and b are empirical constants General form of the van der Waals equation: Corrects for molecular volume Corrects for molecular attraction

Prentice Hall © 2003Chapter 10 Text, P. 395

Prentice Hall © 2003Chapter 10 Sample Problem # 77

Prentice Hall © 2003Chapter 10 End of Chapter 10: Gases