Chapter 5 Gases
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 A mole A mole B P, V, T of Gas B 2
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 0.750 atm and 313 K is generated by the thermolysis of 10.0 g of HgO? 2 HgO(s) 2 Hg(l) + O 2 (g)
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 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 4
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 5
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 6
Molecular Speed vs. Molar Mass in order to have the same average kinetic energy, heavier molecules must have a slower average speed 7
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 8
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 9
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 10
Graham s Law of Effusion 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 rate 1 MM for two different gases at the same temperature, the ratio of their rates of effusion is given by the following equation: rate rate gas gas A B Molar Mass Molar Mass gas gas B A 11
Examples Determine how much faster Helium atoms moves, on average, than a carbon dioxide molecule at the same temperature Calculate the molar mass of a gas that effuses at a rate 0.462 times N 2
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 13
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 V nrt P nb 14
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 15
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 P nrt V a n V 2 16
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 17
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 P a n V 2 V - nb nrt 18
Example A sample of 3.50 moles of NH 3 gas occupies 5.20 L at 47 o C. Calculate the pressure of the gas (in atm) using A) the ideal gas equation B) the van der Waals equation a = 4.17 atm L 2 /mol 2 b = 0.0371 L/mol
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 20
Mountain Climbing & Partial Pressure our bodies are adapted to breathe O 2 at a partial pressure of 0.21 atm 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 = 0.311 atm, so P O2 = 0.065 atm 21