Gases Kinetic Theory of Gases Explains Gas behavior

Gases

Kinetic Theory of Gases Explains Gas behavior: 4 parts: 1) Gas particles do not attract or repel each other (no I. M. forces).

2)Gas particles are much smaller than the space between them. 3)Gas particles are in constant, random motion. 4)Collisions between gas particles are elastic.

TEMPERATURE Measures the Average Kinetic Energy of a gas. Temperature and Average Kinetic Energy are directly proportional. At the same temp. all gases have the same average kinetic energy.

Pressure Created by the collision of particles with each other and objects.

Elevation and Atmospheric pressure are INVERSELY proportional. Higher elevation=less air =less collision = less pressure

So, how do we measure gas pressure?

With a Barometer. SI unit is Pascal.

Equivalent Units of Pressure 1 atm (atmosphere) 760 millimeters Mercury (mm Hg) 760 Torr 101. 3 k. Pa (kilopascals) 14. 7 psi (pounds/square inch)

STP Standard Temperature and Pressure 0°C and 1 atm

Temperature Conversion All gas temperatures are calculated using Kelvin °C + 273 = K

Absolute Zero Temperature at which all molecular motion ceases. Occurs at 0 K or -273 °C

Pressure Conversions To convert from one pressure unit to another: 1) Set up a “box”. 2) Choose conversion factor from equivalent list. 3) Solve.

Examples: What pressure, in atm, is equivalent to 456 mm Hg? How many Torr equal 3. 4 k. Pa?

Gas Laws

The relationship between the volume, pressure, and temperature of a gas can be mathematically determined.

Combined Gas Law V 1 P 1 = V 2 P 2 T 1 T 2

Boyle’s Law The volume of a gas is inversely related to the pressure, at a constant temperature.

http: //www. chem. iastate. edu/group/Green bowe/sections/projectfolder/flashfiles/gasla w/boyles_law_graph. html V 1 P 1 = V 2 P 2

Example A sample of helium gas in a balloon is compressed from 4. 0 L to 250 m. L at a constant temperature. If the original pressure of the gas is 210 k. Pa, what will be the pressure of the compressed gas?

Charles’ Law The volume of a gas is directly proportional to the temperature, at a constant pressure.

http: //www. chem. iastate. edu/group/Green bowe/sections/projectfolder/flashfiles/gasla w/charles_law. html V 1 = V 2 T 1 T 2

Example… At a pressure of 658 mm Hg, what is the volume of the air in a balloon that occupies 0. 620 L at 25°C if the temperature is lowered to 0. 0°C?

Gay-Lussac’s Law The pressure of a gas is directly proportional to the temperature (K) if the volume remains constant. P 1 = P 2 T 1 T 2

Example… The pressure in an automobile tire is 1. 88 atm at 25°C. What will the pressure be if the temperature warms up to 37. 0°C?

Example… 2. 00 L of a gas is confined in a container at a pressure of 131. 96 k. Pa at a temperature of 5. 0°C. If the bottle is dropped into a lake and sinks to a depth at which the pressure is 1155 Torr and a temperature of 2. 1°C, what will be the new volume of the gas?

Gas Law Calculations at STP Example. A sample of gas has a volume of 2050 m. L at 0. 95 atm and 36°C. What will be the volume of the gas at STP?

Example- What is the new volume of a 3. 75 Liter sample of carbon dioxide gas at STP if it is heated until the temperature is 32 °C and the pressure is 955 Torr?

More Calculations!!!

Dalton’s Law of Partial Pressure The total pressure of a mixture of gases is equal to the sum of the partial pressures of each component gas.

P t = P 1 + P 2 + P 3…

Example… A scuba tank contains a mixture of gases including 0. 42 atm N 2, 205 torr O 2 and 35. 5 k. Pa CO 2. What is the total pressure inside the tank, in atmospheres?

Example. What is the partial pressure of He gas in a mixture of He, Ar, and Ne if the total pressure of the mixture is 5. 8 atm, and the partial pressure of Ne is 1. 2 atm and Ar is 0. 9 atm?

Sometimes a gas is collected by bubbling it through water in a container. (by water displacement)

Pwet = Pdry gas + Pwater vapor This is still a partial pressure calculation!

Example- A sample of oxygen gas was collected over water at 20. 0°C and a barometric pressure of 731. 0 mm. Hg. What is the pressure of the dry gas?

Graham’s Law of Effusion: The escape of a gas through a tiny opening.

Graham’s Law of Effusion The rates of effusion of gases at the same temperature and pressure are inversely proportional to the square roots of their molar masses. rate. A = √MB rate. B √MA

So, this means? ? ? The smaller the mass of a gas, the faster the rate of escape. OR The larger the mass of a gas, the slower the rate of escape.

Example- What is the ratio of the effusion rates of nitrogen and neon?

Example- What is the rate of effusion for a gas that has a molar mass twice that of a gas that effused at a rate of 3. 6 mol/min?

Moles revisted…. . Avogadro’s Principle: Equal volumes of gases at the same temperature and pressure contain equal numbers of particles!

Molar Volume – the volume of 1 mole of any gas at STP. 1 molegas = 22. 4 L (new) = 6. 022 x 1023 particles = Molar Mass (in grams)

Examples… What size (volume) container would be needed to hold 0. 0459 moles of N 2 gas at STP?

What mass of carbon dioxide gas is in a 2. 5 L flask at STP?

How many atoms of He are present in a 1. 75 L balloon?

Ideal Gas Law

Ideal gases follow all gas laws under all conditions of temperature and pressure.

Real gases deviate most from ideal gas behavior at extremely high pressure and low temperature. This explains why real gases can be liquified.

Allows you to calculate the amount of a gas (particle density).

PV = n. RT Where P = pressure V = volume in Liters n = number of moles R = ideal gas constant T = temperature (Kelvin)

Calculate R, the Ideal Gas Constant… 1 mol of gas at STP and molar volume R = 0. 0821 atm·L mol·K R = 62. 4 mm. Hg·L mol·K R = 8. 314 k. Pa·L mol·K

Example… Calculate the number of moles of gas contained in a 3. 0 L vessel at 33°C and a pressure of 1. 50 atm.

Determine the Celsius temperature of 2. 49 mols of gas contained in a 0. 75 L vessel at a pressure of 143 k. Pa.

Variations… n = m/M so… PVM = m. RT where M = Molar mass m = given mass

d= m/V so… PM = d. RT where d = density (in g/L)

Example- Calculate the grams of N 2 present in a 0. 600 L sample kept at 765 mm. Hg and a temperature of 22. 0°C.

Example- What is the density of NO 2 at 681 Torr and 23°C?

Stoichiometry (revisited!)… Remember: use known information about one substance, and a mole ratio from a balanced equation to determine an unknown quantity of another substance in the same reaction.

Remember…. 1 Mole = ___ grams = 6. 022 x 1023 atoms, mlc, fmu 22. 4 liters (new)

HOW? 1. Write and balance equation. 2. Set up a 3 step “box”. 3. Solve.

Example – When 25 Liters of butane combusts in an excess amount of air (oxygen), carbon dioxide and water are produced.

A)What is the balanced equation for this reaction?

A)How many grams of water can be produced?

A)How many liters of butane will be required?

How would you calculate? 1) Choose which gas will be “A”, and which will be “B”. (it doesn’t matter which is which) 2) Calculate the molar mass for each and plug into the formula. 3) Do the math!