Gas Laws

Gas Laws

Gas Laws Gases in Real Life Properties of Gases Highest energy of all states of matter There is a lot of free space in a gas Gases can be expanded infinitely Gases fill containers uniformly and completely

Gases diffuse and mix rapidly Gas Law Variables Gas properties can be modeled using math. Model depends on V = volume of the gas (L) T = temperature (K) ALL temperatures in the entire chapter MUST be in Kelvin!!! No Exceptions! n = amount (moles) P = pressure (atmospheres) R= Universal Gas Constant (0.0821 )

Kinetic Molecular Theory Kinetic Molecular Theory= a theory that describes the behavior of gas particles (5 parts to the theory) 1. Gases consist of tiny particles (atoms or molecules) 2. These particles are so small, compared with the distances between them, that the volume (size) of the individual particles can be assumed to be negligible (zero) 3. These particles are in constant random motion, colliding with the walls of the container. These collisions with the walls cause the pressure exerted by the gas. 4. The particles are assumed to not attract or repel each other. 5. The average kinetic energy of the gas particles is directly proportional to the Kelvin temperature of the gas.

Diffusion and Effusion Diffusion is the gradual mixing of molecules of different gases. Think about a person wearing perfume walking into a room The person closest to the perfume smells it the most and the person furthest away smells it the least The perfume is slowing diffusing and mixing with the air in the room Effusion is the movement of molecules through a small hole. Think about a tire with a small hole. What happens to the air in the tire? It slowly effuses out STP STP stands for Standard Temperature and Pressure

Gases behavior change when temperature and pressure are changed For this reason we have a standard temperature and pressure STP allows us to compare gases Standard Temperature= 273 K Standard Pressure= 1 atmosphere At STP 1 mole of gas occupies 22.4L of space Temperature Temperature is a measure of average kinetic energy Temperature can be measured in F , C , or K Every problem this unit needs to be in units of K K= C + 273

Matter cannot be cooled to temperature lower than -273 C , therefore this temperature is called absolute zero -273 C = 0 K Temperature at STP is 273 K Pressure Pressure= how often and how hard molecules collide with the container they are in Atmospheric pressure is measured with a BAROMETER Mercury (Hg) rises in tube until force of Hg (down) balances the force of atmosphere (pushing up). (Just like a straw in a drink)

Column height measures Pressure of atmosphere Units of pressure @ STP: = 1 standard atmosphere (atm) *we use atm = 760 mm Hg = 760 torr = 29.92 inches Hg = 14.7 pounds/in2 (psi) = 101.3 kPa = about 34 feet of water! *Recognize these different units of pressure *we will use these values as conversion factors Pressure Conversions

A. What is 475 mm Hg expressed in atm? 475 mm Hg 1 atm 760 mm Hg = 0.625 atm B. The pressure of a tire is measured as 29.4 psi. What is this pressure in mm Hg? 29.4 psi 760 mm Hg

14.7 psi = 1520 mm Hg Pressure Conversions C. What is 2 atm expressed in torr? D. The pressure of a tire is measured as 32.0 psi. What is this pressure in kPa? Gases in the Air The % of Gases in Air 78.08% N2

Partial Pressure at STP 593.4 mm Hg 20.95% O2 159.2 mm Hg 0.94% Ar 0.03% CO2 7.1 mm Hg 0.2 mm Hg

The total pressure in the air is equal to the sum of all of the partial pressures caused by each gas in air PAir = PN2 + PO2 + PAr + PCO2 PAir = 593.4 mm Hg + 159.2 mm Hg + 7.1 mm Hg + 0.2 mm Hg Daltons Law of Partial Pressures Daltons Law of Partial Pressures: The total pressure in a container is equal to the sum of the partial pressures of each gas within the container Ptotal = PA + PB + PC + PD + Example 1: What is the total pressure in a flask containing the following: 2 H2O2 (l) ---> 2 H2O (g) + O2 (g)

0.32 atm 0.16 atm Ptotal = PH2O + PO2 = 0.48 atm Daltons Partial Pressure Practice Example 2: Oxygen and chlorine gas are mixed in a container with partial pressures of 401 mmHg and 0.639 atm, respectively. What is the total pressure inside the container (in atm)? Example 3: Container A contains a gas under 3.24 atm of pressure. Container B contains a gas under 2.82 atm of pressure. Container C contains a gas under 1.21 atm of pressure. If all of these gases are put into Container D, what is the pressure in Container D?

Boyles Law P 1/V This means Pressure and Volume are INVERSELY PROPORTIONAL if moles and temperature are constant (do not change). For example, P goes up as V goes down. WHY? P1V1 = P2 V2 P1V1 = initial pressure and volume P2V2 = final pressure and volume *n and T are held constant Robert Boyle

(1627-1691). Son of Earl of Cork, Ireland. Boyles Law Practice 1. A sample of oxygen gas occupies a volume of 250 mL at 740 torr pressure. What volume will it occupy at 810 torr? V1= 250 mL P1= 740 torr V2= ? P2= 810 torr P1V1 = P2 V2

(740)(250)=(810) V2 V2 = 228.4 mL Charless Law VT V and T are directly proportional. They increase together and they decrease together. WHY? * n and P are constant Jacques Charles (17461823). Isolated boron and studied gases. Balloonist.

Charless Law Practice 2. A sample of nitrogen gas occupies a volume of 250 mL at 25 C. What volume will it occupy at 95 C? = 250 mL = 25 C = 298 K =? = 95 C = 368 K = 308.7 mL Gay-Lussacs Law PT

P and T are directly proportional. They increase together and they decrease together. WHY? * n and V are constant Joseph Louis GayLussac (1778-1850) Gay-Lussacs Law Practice 3. A sample of gas has at a pressure of 75kPa and 0C . The pressure is increased to 125 kPa, what is the new temperature? = 75 kPa = 0C = 273 K = 125 kPa

= 455 K =? Combined Gas Law All of the gas laws can be can be combined into one gas law called the Combined Gas Law *n is held constant Example 4: A gas occupies 3.0L of space at 1.5 atm and 20C, if the pressure is increased to 2.5 atm and the temperature rises to 30C , how much space will the gas occupy? = 1.9 L

Combined Gas Law All of the gas laws can be can be combined into one gas law called the Combined Gas Law *n is held constant Example 4: A gas occupies 3.0L of space at 1.5 atm and 20C, if the pressure is increased to 2.5 atm and the temperature rises to 30C , how much space will the gas occupy? = 1.9 L Avogadro's Hypothesis

Equal volume of gases at the same T and P have the same number of molecules Vn V and n are directly proportional. They increase together and they decrease together. WHY? * T and P are constant Avogadros Hypothesis Practice 5. Suppose we have a 12.2 L sample containing 0.50 moles of oxygen gas, O2 . If all of this O2 is converted to ozone, O3 what is the new volume of the gas? 3O2 (g) 2O3 (g)

= 12.2 mL = 0.50 moles =? = you must use stoichiometry to solve moles O = 0.50 moles O = 20.33 moles O3 2 3 3 moles O2

= 8.0 mL Ideal Gas Law An ideal gas is a hypothetical gas that exactly obeys the ideal gas law no gases are ideal, but treating them ideal allows us to do calculations Ideal Gas Law: PV= nRT R is the universal gas constant R= 0.0821 Ideal Gas Law Practice

PV= nRT 6. How much space does 1 mole of oxygen gas occupy at STP? (SHOW WORK) P= 1 atm (1)V= (1) (0.0821)(273) V= ? n= 1 mole V= 22.4 L R= 0.0821 T= 273 K Summary Of Gas Laws

Name Boyles Law Charless Law Gay-Lussacs Law Avogadros Law Combined Gas Law

Law/ Equation Relationship between variables (direct or inverse) Variables held constant Ideal Gas Law= R= Daltons Law of Partial Pressure= X

Formula Sheet K = C + 273 PV = nRT R= (0.0821 ) Units of pressure @ STP: = 1 atmosphere = 760 mm Hg = 760 torr = 29.92 inches Hg = 14.7 pounds/in2 (psi)

= 101.3 kPa = about 34 feet of water!

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