Unit 2: Gases Chapter 5 Pressure Force exerted per unit area by gas molecules as they strike surfaces around them. Units
mm Hg atm kPa torr 1 mm Hg=1 torr
1 atm=760 mm Hg=101.325 kPa Practice Problem 1 How many atmospheres are in 79 kPa? SIMPLE GAS LAWS Gas Relationships Pressure (P)
Volume (V) Number of moles (n) Temperature (T) Boyles Law Volume and pressure have an inverse relationship Charless Law Volume and temperature have a direct relationship
Gas Relationships Avogadros Law Volume and number of moles have a direct relationship Practice Problem 2 A 6.0 liter container has a pressure of 10.0 mm Hg. If we increase the volume to 10.0 L, what is the pressure of the container? What is the pressure in atm?
Ideal Gas Law PV=nRT Lets calculate R based on a 1 mole of a gas at standard temperature and pressure! One mole at standard temperature and pressure (STP)
P=1.00 atm T=273 K n= 1 mol V=22.4 L R=0.08206
Modifications of Ideal Gas Law PV=nRT Rearrange to solve for moles/liter This is the molar density because its moles/liter To get density (in grams/liter) Or use modified ideal gas equation to solve for molar mass (if you have only one mole of the gas). Where M=molar mass and m=mass
***If you want to memorize more equations or if youre good at manipulating equations, this is the slide for you! If you would rather solve for number of moles and then use dimensional analysis to find density, molar mass, etc., thats fine too!*** Practice Problem 3 A 6.0 liter container of bromine gas has a pressure of 10 atm at 310 K. How many grams of bromine are in the container?
MIXTURES OF GASES Mixtures of Gases Daltons Law of Partial Pressures: Mole Fraction You can use the mole fraction to determine pressure of one gas in a mixture
Note: when collecting gases over water, you must consider the vapor pressure of water in calculations (varies at different temperatures). Gas Stoichiometry Same as normal stoichiometry, just use in conjunction with other gas equations. If reaction occurs at STP, you can use the molar volume (22.4 L) as a conversion factor.
Kinetic Molecular Theory Key Principles: Assume that the size of particles is negligible Average kinetic energy of particles is directly proportional to the temperature Collisions between particles are completely elastic (do not lose energy)
Gas Laws Explained Boyles Law Boyles Law says that the volume of a gas is inversely proportional to the pressure Decreasing the volume forces the molecules into a smaller space. More molecules will collide with the container at any one instant, increasing the pressure.
Gas Laws Explained Charless Law Charless Law says that the volume of a gas is directly proportional to the absolute temperature. According to kinetic molecular theory, when we increase the temperature of a gas, the average speed, and thus the average kinetic energy, of the particles increases. The greater volume spreads the collisions out over a greater surface area, so that the pressure is unchanged.
Gas Laws Explained Avogadros Law Avogadros Law says that the volume of a gas is directly proportional to the number of gas molecules. Increasing the number of gas molecules causes more of them to hit the wall at the same time. To keep the pressure constant, the volume must then increase.
Gas Laws Explained Daltons Law Daltons law: the total pressure of a gas mixture is the sum of the partial pressures. According to kinetic molecular theory, the particles have negligible size and they do not interact. Particles of different masses have the same average kinetic energy at a given temperature.
Because the average kinetic energy is the same, the total pressure of the collisions is the same. Molecular Velocities Lighter particles tend to travel faster (on average) than heavier ones. The average velocity of gas particles is directly proportional to temperature and inversely related to the molar mass.
Temperature versus Molecular Speed As the temperature of a gas sample increases, the velocity distribution of the molecules shifts toward higher velocity. The distribution function spreads out, resulting in
more molecules with faster speeds. 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.
Diffusion and Effusion Diffusion: Gas particles spread out towards areas of lower concentration. Effusion: The process where gases escape a container into a vacuum through a hole. Grahams Law of Effusion
Heavier molecules effuse more slowly Example: In a gaseous mixture of helium and argon at 273 K: Which of the atoms have a greater average kinetic energy? They have the same average kinetic energy (temperature) Which of the atoms have the greater average velocity? Argon is larger, so it will move slower in order to have the same KE Which exerts a greater partial pressure?
They will exert the same partial pressure Which will effuse faster? Helium (its lighter) Ideal Behavior of Gases Gases are considered ideal when The volume of the particles (size) is small The forces acting between particles is small
Therefore, ideal behavior breaks down at Higher pressures Particles themselves begin to occupy a lot of the space of the gas Lower temperatures Collisions between particles occur with lower kinetic energy, allowing more of the attraction between particles to occur
Modification of the Ideal Gas Equation In 1873, Johannes van der Waals (18371923) modified the ideal gas equation to fit the behavior of real gases at high pressure. 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. The Effect of Intermolecular Attractions At high temperature, the pressure of the gases is nearly identical to that of an ideal gas. But at lower temperatures, the pressure of gases is less than that of
an ideal gas. At the lower temperatures, the gas atoms spend more time interacting with each other and less time colliding with the walls, making the actual pressure less than that predicted by the ideal gas law. The Effect of Intermolecular Attractions Van der Waals modified the ideal gas equation
to account for the intermolecular attractions. a is another van der Waals constant and is different for every gas because their molecules have different strengths of attraction.
PV/RT Plots Practice Problem C2H4(g) + 3O2(g) 2CO2(g) + 2H2O(g) How many liters of water are formed if 1.25 liters of ethylene are consumed in this reaction at STP? Example Problems: Gas Laws
A 100 g sample of an ideal gas occupies a volume of 3.2 L at 40C and exerts a pressure of 2 atm. What is its molar mass? A sample of oxygen gas occupies 25 L at 720 torr and 30C. What volume will it occupy at STP? If I have 5.6 liters of gas in a piston at a pressure of 1.5 atm and compress the gas until its volume is 4.8 L, what will the new pressure inside the piston be? Partial pressures
A gas mixture contains nitrogen at 215 torr, oxygen at 102 torr, and helium at 117 torr. What is the total pressure of the mixture? What is the mole fraction of each element? Gas Stoichiometry In the following reaction, 4.58 L of oxygen was formed at P=745 mm Hg and T=308 K. How many grams of Ag2O decomposed?
2Ag2O (s) 4 Ag (s) + O2 (g) Practice Problem In a gaseous mixture of argon and neon, Which will have smaller kinetic energy? Which will have slower velocity? Which effuses slower?
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