Roy Kennedy Massachusetts Bay Community College Wellesley Hills, MA 2008, Prentice Hall Chemistry: A Molecular Approach, 1 st Ed. Nivaldo Tro

Mixtures of Gases when gases are mixed together, their molecules behave independent of each other therefore, in certain applications, the mixture can be thought of as one gas Tro, Chemistry: A Molecular Approach2

Partial Pressure the pressure of a single gas in a mixture of gases is called its partial pressure we can calculate the partial pressure of a gas if the sum of the partial pressures of all the gases in the mixture equals the total pressure Dalton’s Law of Partial Pressures because the gases behave independently Tro, Chemistry: A Molecular Approach3

Composition of Dry Air Tro, Chemistry: A Molecular Approach4

The partial pressure of each gas in a mixture can be calculated using the ideal gas law Tro, Chemistry: A Molecular Approach5

Example P He =341 mmHg, P Ne =112 mmHg, P tot = 662 mmHg, V = 1.00 L, T=298 K Find the partial pressure of neon in a mixture with total pressure 3.9 atm, volume 8.7 L, temperature 598 K, and 0.17 moles Xe.

Mole Fraction Tro, Chemistry: A Molecular Approach7 the fraction of the total pressure that a single gas contributes is equal to the fraction of the total number of moles that a single gas contributes the ratio of the moles of a single component to the total number of moles in the mixture is called the mole fraction,  for gases, = volume % / 100% the partial pressure of a gas is equal to the mole fraction of that gas times the total pressure

Deep Sea Divers & Partial Pressure its also possible to have too much O 2, a condition called oxygen toxicity P O2 > 1.4 atm oxygen toxicity can lead to muscle spasms, tunnel vision, and convulsions its also possible to have too much N 2, a condition called nitrogen narcosis also known as Rapture of the Deep when diving deep, the pressure of the air divers breathe increases – so the partial pressure of the oxygen increases at a depth of 55 m the partial pressure of O 2 is 1.4 atm divers that go below 50 m use a mixture of He and O 2 called heliox that contains a lower percentage of O 2 than air Tro, Chemistry: A Molecular Approach8

9 Mountain Climbing & Partial Pressure our bodies are adapted to breathe O 2 at a partial pressure of 0.21 atm Sherpa, people native to the Himalaya mountains, are adapted to the much lower partial pressure of oxygen in their air partial pressures of O 2 lower than 0.1 atm will lead to hypoxia unconsciousness or death climbers of Mt Everest carry O 2 in cylinders to prevent hypoxia on top of Mt Everest, P air = atm, so P O2 = atm

Partial Pressure & Diving Tro, Chemistry: A Molecular Approach10

Example Find the mole fractions and partial pressures in a 12.5 L tank with 24.2 g He and 4.32 g O 2 at 298 K A diver breathes a heliox mixture with an oxygen mole fraction of What must the total pressure be for the partial pressure of oxygen to be 0.21 atm?

Collecting Gases gases are often collected by having them displace water from a container the problem is that since water evaporates, there is also water vapor in the collected gas the partial pressure of the water vapor, called the vapor pressure, depends only on the temperature if you collect a gas sample with a total pressure of mmHg* at 25°C, the partial pressure of the water vapor will be mmHg – so the partial pressure of the dry gas will be mmHg Table 5.4* Tro, Chemistry: A Molecular Approach12

Vapor Pressure of Water Tro, Chemistry: A Molecular Approach13

Collecting Gas by Water Displacement Tro, Chemistry: A Molecular Approach14

Examples 1.02 L of O 2 collected over water at 293 K with a total pressure of mmHg. Find mass O moles of H 2 is collected over water in a 10.0 L container at 323 K. Find the total pressure.

Tro, Chemistry: A Molecular Approach16 Reactions Involving Gases the principles of reaction stoichiometry from Chapter 4 can be combined with the gas laws for reactions involving gases in reactions of gases, the amount of a gas is often given as a volume the ideal gas law allows us to convert from the volume of the gas to moles; then we can use the coefficients in the equation as a mole ratio when gases are at STP, use 1 mol = 22.4 L P, V, T of Gas Amole Amole BP, V, T of Gas B

Examples How many grams of H 2 O form when 1.24 L H 2 reacts completely with O 2 at STP? O 2 (g) + 2 H 2 (g) → 2 H 2 O(g) What volume of O 2 at atm and 313 K is generated by the thermolysis of 10.0 g of HgO? 2 HgO(s)  2 Hg(l) + O 2 (g)

Tro, Chemistry: A Molecular Approach18 Properties of Gases expand to completely fill their container take the shape of their container low density much less than solid or liquid state compressible mixtures of gases are always homogeneous fluid

Tro, Chemistry: A Molecular Approach19 Kinetic Molecular Theory the particles of the gas (either atoms or molecules) are constantly moving the attraction between particles is negligible when the moving particles hit another particle or the container, they do not stick; but they bounce off and continue moving in another direction like billiard balls

Tro, Chemistry: A Molecular Approach20 Kinetic Molecular Theory there is a lot of empty space between the particles compared to the size of the particles the average kinetic energy of the particles is directly proportional to the Kelvin temperature as you raise the temperature of the gas, the average speed of the particles increases

Tro, Chemistry: A Molecular Approach21 Gas Properties Explained – Indefinite Shape and Indefinite Volume Because the gas molecules have enough kinetic energy to overcome attractions, they keep moving around and spreading out until they fill the container. As a result, gases take the shape and the volume of the container they are in.

Tro, Chemistry: A Molecular Approach22 Gas Properties Explained - Compressibility Because there is a lot of unoccupied space in the structure of a gas, the gas molecules can be squeezed closer together

Tro, Chemistry: A Molecular Approach23 Gas Properties Explained – Low Density Because there is a lot of unoccupied space in the structure of a gas, gases do not have a lot of mass in a given volume, the result is they have low density

Tro, Chemistry: A Molecular Approach24 Density & Pressure result of the constant movement of the gas molecules and their collisions with the surfaces around them when more molecules are added, more molecules hit the container at any one instant, resulting in higher pressure also higher density

Tro, Chemistry: A Molecular Approach25 Gas Laws Explained – Dalton’s Law of Partial Pressures Dalton’s Law says that the total pressure of a mixture of gases is the sum of the partial pressures kinetic-molecular theory says that the gas molecules are negligibly small and don’t interact therefore the molecules behave independent of each other, each gas contributing its own collisions to the container with the same average kinetic energy since the average kinetic energy is the same, the total pressure of the collisions is the same

Tro, Chemistry: A Molecular Approach26 Dalton’s Law & Pressure since the gas molecules are not sticking together, each gas molecule contributes its own force to the total force on the side

Tro, Chemistry: A Molecular Approach27 Calculating Gas Pressure

Tro, Chemistry: A Molecular Approach28 Kinetic Energy and Molecular Velocities average kinetic energy of the gas molecules depends on the average mass and velocity KE = ½mv 2 gases in the same container have the same temperature, the same average kinetic energy if they have different masses, the only way for them to have the same kinetic energy is to have different average velocities lighter particles will have a faster average velocity than more massive particles

Tro, Chemistry: A Molecular Approach29 Molecular Speed vs. Molar Mass in order to have the same average kinetic energy, heavier molecules must have a slower average speed

Tro, Chemistry: A Molecular Approach30 Temperature vs. Molecular Speed as the absolute temperature increases, the average velocity increases the distribution function “spreads out,” resulting in more molecules with faster speeds

Tro, Chemistry: A Molecular Approach31 Mean Free Path molecules in a gas travel in straight lines until they collide with another molecule or the container the average distance a molecule travels between collisions is called the mean free path mean free path decreases as the pressure increases

Tro, Chemistry: A Molecular Approach32 Diffusion and Effusion the process of a collection of molecules spreading out from high concentration to low concentration is called diffusion the process by which a collection of molecules escapes through a small hole into a vacuum is called effusion both the rates of diffusion and effusion of a gas are related to its rms average velocity for gases at the same temperature, this means that the rate of gas movement is inversely proportional to the square root of the molar mass

Tro, Chemistry: A Molecular Approach33 Effusion

Tro, Chemistry: A Molecular Approach34 Graham’s Law of Effusion for two different gases at the same temperature, the ratio of their rates of effusion is given by the following equation:

35 Ideal vs. Real Gases Real gases often do not behave like ideal gases at high pressure or low temperature Ideal gas laws assume 1) no attractions between gas molecules 2) gas molecules do not take up space based on the kinetic-molecular theory at low temperatures and high pressures these assumptions are not valid

Tro, Chemistry: A Molecular Approach36 The Effect of Molecular Volume at high pressure, the amount of space occupied by the molecules is a significant amount of the total volume the molecular volume makes the real volume larger than the ideal gas law would predict van der Waals modified the ideal gas equation to account for the molecular volume b is called a van der Waals constant and is different for every gas because their molecules are different sizes

Tro, Chemistry: A Molecular Approach37 Real Gas Behavior because real molecules take up space, the molar volume of a real gas is larger than predicted by the ideal gas law at high pressures

Tro, Chemistry: A Molecular Approach38 The Effect of Intermolecular Attractions at low temperature, the attractions between the molecules is significant the intermolecular attractions makes the real pressure less than the ideal gas law would predict van der Waals modified the ideal gas equation to account for the intermolecular attractions a is called a van der Waals constant and is different for every gas because their molecules are different sizes

Tro, Chemistry: A Molecular Approach39 Real Gas Behavior because real molecules attract each other, the molar volume of a real gas is smaller than predicted by the ideal gas law at low temperatures

Tro, Chemistry: A Molecular Approach40 Van der Waals’ Equation combining the equations to account for molecular volume and intermolecular attractions we get the following equation used for real gases a and b are called van der Waal constants and are different for each gas

Tro, Chemistry: A Molecular Approach41 Real Gases a plot of PV/RT vs. P for 1 mole of a gas shows the difference between real and ideal gases it reveals a curve that shows the PV/RT ratio for a real gas is generally lower than ideality for “low” pressures – meaning the most important factor is the intermolecular attractions it reveals a curve that shows the PV/RT ratio for a real gas is generally higher than ideality for “high” pressures – meaning the most important factor is the molecular volume

Tro, Chemistry: A Molecular Approach42 PV/RT Plots