Gas Laws Chapters 13.1 + 14

Review Temperature Pressure Volume Average kinetic energy Collisions of gas particles between each other and container walls Volume Amount of space

Ideal Gas Don’t exist Model to explain behavior of all gases

Kinetic Molecular Theory The particles in a gas are constantly moving in rapid, random, straight-line motion. Gas particles have no volume compared to the volume of the gas. No attraction between particles All collisions are completely elastic

Gas Laws Boyle’s Law Charles’s Law Amontons’s Law Combined Gas Law Avogadro’s Law Dalton’s Law of Partial Pressures Ideal Gas Law

Boyle’s Law Relationship between pressure and volume Constant Temperature Mathematical relationships As pressure is increasing, volume is decreasing As pressure is decreasing, volume is increasing

Boyle’s Law V P

Boyle’s Law PV = constant Temperature remains constant

Example A 40 L sample of gas at 1atm of pressure is compressed to 10 L. What is the new pressure of the gas? P1V1 = P2V2 (1atm)*(40L) = P2*(10L) P2 = 4 atm

Example The pressure of a 25 L sample is changed from 2 atm to 0.4 atm. What is the new volume of the gas? P1V1 = P2V2 (2atm)*(25L) = (0.4atm)*V2 V2 = 125 L

Real Life

Charles’s Law Relationship between volume and temperature Constant Pressure Mathematical relationships As temperature is increasing, volume is increasing As temperature is decreasing, volume is decreasing

Charles’s Law T V

Charles’s Law V/T = constant Temperature must be in Kelvin Pressure remains constant Temperature must be in Kelvin

Example A 4L sample of gas at 300K is heated to 600K. What is the new volume?

Example A gas occupying 45L at 27°C is cooled until its volume is 15L. What is the new temperature of the gas?

Amontons's Law In the winter the tire sensors on my wife’s car beep, indicating that there is low pressure in the tires. Why? What factor is changing with the weather? What factor is responding to this change? Which factor(s) remain constant?

Amontons's Law Mathematical relationships As temperature increases, pressure increases As temperature decreases, pressure decreases

Amontons's Law T P

Amontons's Law P/T = constant Temperature must be in Kelvin Volume remains constant (rigid container) Temperature must be in Kelvin

Example In a pressure cooker, a sample of gas at 1 atm and 300K is heated to 400K. What is the pressure at this temperature?

Example A sample of gas at 101.3 kPa and 27°C is heated until its pressure is 3.5atm. What is the new temperature?

Combined Gas Law Goal Understands how to use the gas laws to predict the behavior of gases. Pressure vs. volume (Boyle) Volume vs. temperature (Charles) Volume, temperature, and pressure (Combined)

Review Boyle’s Law Charles’s Law Amontons's Law

Question How often do only 2 properties of a gas change while the other remains constant? Rarely Need a gas law that incorporates all three properties (PTV) changing

Combined Gas Law Combines Boyle’s, Charles’s, and Amontons's Laws together

Example

Example

Worksheet

Combined Gas Law Goal Understands how to use the gas laws to predict the behavior of gases. Pressure vs. volume (Boyle) Volume vs. temperature (Charles) Volume, temperature, and pressure (Combined)

Review 1 mole of ANY gas occupies 22.4L of volume at STP

Avogadro’s Law Relationship between the amount of gas and the volume of the gas Mathematical relationships As the amount of gas increases, volume increases As the amount of gas decreases, volume decreases

Avogadro’s Law n V

Avogadro’s Law V/n = constant Pressure and Temperature remains constant

Avogadro’s Law Equal volumes of gas at the same Temperature and Pressure have the same number of particles At the same temperature and pressure, which sample contains the same number of moles of particles as 1 liter of O2(g)? A. 1 L Ne(g) B. 0.5 L SO2(g) C. 2 L N2(g) D. 4 L H2O(g)

Dalton’s Law Demonstration Assume each jelly bean represents 1 mole of gas How many moles are in the flask? What fraction is green? Does color make a difference in pressure when shaken?

Dalton’s Law Mole Fraction (XA) Partial Pressure (PA) Moles of one gas divided by total moles of gas Partial Pressure (PA) Pressure exerted by one gas in a sample of gas

Dalton’s Law of Partial Pressures How does partial pressure relate to total pressure? Sum of partial pressures equals total pressure PT = PA + PB + PC…

Dalton’s Law of Partial Pressures How can we relate mole fraction to partial pressure and total pressure?

Example A container has 1 mol of hydrogen, 1 mol of nitrogen, and 1 mol of oxygen. What is the mole fraction of hydrogen? Moles of Hydrogen Total Moles

Example A container has 1 mol of hydrogen, 1 mol of nitrogen, and 1 mol of oxygen. If the total pressure is 6 atm, what is the partial pressure of nitrogen? Moles of Nitrogen Total Moles

Review Boyle’s Law Charles’s Law Amontons's Law Avogadro’s Law

All Together Now Constant If we add Avogadro’s Law into the Combined Gas Law: Constant

Ideal Gas Law PV = nRT R = Universal Gas Constant Ideal Gases follow assumptions of the Kinetic Molecular Theory

Kinetic Theory of Gases The particles in a gas are constantly moving in rapid, random, straight-line motion. Gas particles have no volume compared to the volume of the gas. No attraction between particles All collisions are completely elastic

Ideal Gases When do real gases act most like an ideal gas? High Temperature Low Pressure When do real gases act least like an ideal gas? Low Temperature High Pressure

Gas Laws Boyle’s Law Charles’s Law Amontons's Law Combined Gas Law Avogadro’s Law Dalton’s Law of Partial Pressures Ideal Gas Law