GAS LAWS

Properties of Gases  Composed of randomly scattered particles  No definite _________ or ___________  Spread out to fill the space of their container  Lack intermolecular forces that hold liquids and solids together (ideally)  Molecules move in a straight line and only change direction after hitting another molecule or the wall of the container  Can be compressed easily (because of all that _________________)  Exert ______________ on its surroundings (created by molecules hitting the surface)

Kinetic Molecular Theory  Gases are made of particles in rapid, random motion.  Not affected by the force of gravity in a container (do not fall to the bottom)  The gas is mostly ___________________.  Collisions are ___________ (no loss of kinetic energy).

Ideal vs Real Gases  ____________ gases follow KMT  _________ gases come close (especially at high temperatures and low pressures)  Small attractions between particles can be found

Pressure Created by gas molecules bouncing off the surface of an object Defined as: Force per unit area (F/A) SI Unit is pascal (Pa) which equals N/m 2 Pascal unit is small so often _____ is used instead Other pressure units Atmosphere (atm) mm of Hg (mmHg) and in of Hg (in Hg) Torr bar and millibar (mb) Pounds per square inch (lb/in 2 or psi)

Converting Between Pressure Units  All of these are equal to each other  kPa  1 atm  760 mmHg  760 Torr  in Hg  bar  psi

Pressure Conversions  If the pressure inside a container is measured at 1.22 atm, what is the pressure in mm Hg?  If a pressure is given as 720 Torr, what is the pressure in kPa?

Atmospheric Pressure  Pressure from gas particles in the atmosphere

Measuring Pressure  Barometer  Device measuring atmospheric pressure  Consists of a tube of mercury being placed in bowl of mercury  Mercury will flow into the bowl until the pressure from the height of the column equals the atmospheric pressure pressing on the mercury in the bowl  The height of the mercury column is measured  At sea level, atmospheric pressure is ____________________

Measuring Pressure (cont)  Manometer  Measures the pressure of other gases  ___________-end manometers  Mercury rests in a U-shaped tube  Without gas- mercury level is equal on both sides  With gas- mercury level will rise on the far side  Gas pressure is represented by the difference between the two heights  __________________  Greater the difference the greater the pressure

Measuring Pressure (cont)  ________-end manometers  Mercury rests in a U-shaped tube  Without gas or with gas whose pressure is lower than atmospheric- mercury level will rise on side away from open end  __________________  With gas whose pressure is equal to atmospheric- mercury level is equal on both sides  ________________  With gas whose pressure is higher than atmospheric- mercury level will rise on the far side  _______________________

Manometer Problems  In a closed-ended manometer, the mercury column in the arm is raised to a height of 780 mm above the other side, what is the pressure of the gas in atm?  In an open-ended manometer, the mercury column in the atmospheric arm is 28.2 mm lower than the other side. If the atmospheric pressure is 762 mm Hg, what is the pressure of the gas attached to manometer?

Dalton’s Law of Partial Pressures  Many gases are actually mixtures of different types of gases (like air)  States: The total pressure exerted by a mixture of gases is equal to the sum of the partial pressures exerted by the separate gases.  In other words: P total = P 1 + P 2 + P 3 …

Collecting Gases over Water  A method of collecting and measuring gases produced as a product of a reaction  Relies on water displacement.  Gas sample will actually contain gas collected and water vapor  P dry gas = P total – P water vapor  This is just a rearrangement of P total = P dry gas + P water vapor  Water vapor pressure is dependent on the water temperature

Partial Pressure Problems  A container holds three gases (oxygen, carbon dioxide, and helium). The partial pressures of the gases are 2.00 atm, 3.00 atm, and 4.00 atm respectfully. What is the total pressure in the container?  What is the partial pressure of oxygen in air at 770 Torr and containing 21% of O 2 ?  If 60.0 L of nitrogen is collected over water at 40.0°C when the atmospheric pressure is mm Hg, what is the partial pressure of the nitrogen? The water vapor pressure at 40.0°C is 55.3 mm Hg.

Ideal Gas Law  Gives information about a gas at a single time point  R= (PV)/(nT)  R = L atm mol -1 K -1  P = ___________  V = ___________  n = ________________  T = ________________  Temperature K = Temperature °C  Can also be rewritten M= (mRT)/PV  n has been replaced with m/M  m = _______________  M = ______________________

STP  Standard Temperature and Pressure  Temperature is ______________  Pressure is ______________

Ideal Gas Law Problems  If 25g of oxygen gas is placed in a 2 liter container at a temperature of 292 K, what is the pressure in the container?  What is the molar mass of a gas when 3.84g of the gas is placed in a 570mL container at STP?

Reactions with Gases  Ideal Gas Law can be used to find the number of __________ reacted or produced.  _______________ can be used to get information about other reactants or products.  Conditions for the equations such as _________ and _____________ and given in the problem  At STP only, conversion factor _____________ can be used

Gas Densities  Very _________ compared to solids and liquids  Often given in _______ instead of g/ml  D = m/V = (MP)/RT

Gas Density Problems  What is the density of oxygen gas at STP?  What is the mass of 3.2 L of carbon dioxide at STP?  What would the volume be of 367g of C 2 H 6 at 765 mm Hg and

Combined Gas Law  Gives information about a gas at two time points  (P 1 V 1 )/(n 1 T 1 ) = (P 2 V 2 )/(n 2 T 2 )  1- Values at first time point  2- Values at second time point  P and V can be in any units but they must match on both sides  n must be in moles  T must be in Kelvin

Combined Gas Law Problems  In a thermonuclear device, the pressure of liters of gas within the bomb casing reaches 4.0 x 10 6 atm. When the bomb casing is destroyed by the explosion, the gas is released into the atmosphere where it reaches a pressure of 1.00 atm. What is the volume of the gas after the explosion?

Combined Gas Law Problems (cont)  The temperature inside my refrigerator is about 4 °C. If I place a balloon in my fridge that initially has a temperature of 22 ° C and a volume of 0.5 liters, what will be the volume of the balloon when it is fully cooled by my refrigerator?

Combined Gas Law Problems (cont)  A gas that has a volume of 28 liters, a temperature of 45 °C, and an unknown pressure has its volume increased to 34 liters and its temperature decreased to 35 °C. If I measure the pressure after the change to be 2.0 atm, what was the original pressure of the gas?

Combined Gas Law Problems (cont)  If I have 2.9 L of gas at a pressure of 5 atm and a temperature of 50 °C, what will be the temperature of the gas if I decrease the volume of the gas to 2.4 L and decrease the pressure to 3 atm?

Boyle’s Law  Discovered in 1662  Determines the relationship between pressure and volume of a gas  States: For a fixed amount of a gas at a constant temperature, the volume of a gas varies inversely with its pressure  Boils down to  P 1 V 1  P 2 V 2

Charles’s Law  Discovered in 1787  Determined the relationship between volume and temperature  Temperature must be in Kelvin (K)  States: The volume of a fixed amount of gas at a constant pressure is directly proportional to its Kelvin temperature.  Boils down to:  V 1 /T 1 = V 2 /T 2

Gay-Lussac’s Law  Discovered in 1802  Determined the relationship between pressure and temperature  Temperature must be in Kelvin  States: The pressure and Kelvin temperature of a gas are directly proportional, provided that the volume remains constant.  Boils down to:  P 1 /T 1 = P 2 /T 2

Avogadro’s Law  Proposed in 1811  Determined the relationship between the amount of gas (number of molecules) and the volume  States: At a fixed temperature and pressure, the volume of a gas is directly proportional to the amount of gas (that is, to the number of moles of gas, n, or to the number of molecules of gas).  At STP, one mole of a gas = _____________  Boils down to V 1 /n 1 = V 2 /n 2

Using Avogadro’s Law  What is the mass in kg of 4.55 x 10 3 L of methane gas (CH 4 ) at STP?  If 125 mg of Ar(g) is added to a 505 mL sample of Ar(g) at STP, what volume will the sample occupy when the conditions of STP are restored?

Diffusion and Effusion  Diffusion- mixing of two gases together  Effusion- Rate at which gas molecules escape from a container with a small opening

Graham’s Law  The rate of effusion and diffusion is inversely proportional to the square root of the molar mass of the molecules.  Gases with molecules of lower molar mass have higher velocities and therefore diffuse or effuse faster  Rate A = rate of diffusion or effusion for gas A  Rate B = rate of diffusion or effusion for gas B  Mass A = molar mass of gas A  Mass B = molar mass of gas B Rate A =  Mass B Rate B  Mass A

Using Graham’s Law  A certain gas effuses 4 times as fast as oxygen gas. What is the molar mass of the unknown gas?  A sample of N 2 effuses through a hole in 38 seconds. What must be the molecular weight of gas that effuses in 55 seconds under identical conditions?