Gases Chapters 10 & 11

Kinetic-Molecular Theory Used to describe the properties of solids, liquids, & gases Based on the idea that particles are always in motion Ideal gas: an imaginary gas that perfectly fits all the assumptions of the kinetic-molecular theory

The Kinetic-Molecular theory assumes the following about gases: Gas particles do not attract or repel each other. Gas particles are much smaller than the distances between them. Gas particles are in constant, random motion. No kinetic energy is lost when gas particles collide with each other. All gases have the same average kinetic energy at a given temperature.

Gas Laws Most gases obey 3 simple laws. When a gas obeys these laws, it is an ideal gas. These laws include: Boyle’s Law Charles’s Law Gay-Lussac’s Law

(1) Boyle’s Law If temperature is constant, then volume is inversely proportional to pressure P1V1 = P2V2

Problem A sample of oxygen gas has a volume of 150mL when its pressure is 0.947 atm. What will the volume of the gas be at a pressure of 0.987 atm if the temperature remains constant?

(2) Charles’ Law If pressure is constant, then volume is proportional to temperature V1 = V2 T1 T2

Temperature must be expressed in Kelvin units. Tkelvin= 273 + Tcelsius

Problem A sample of neon gas occupies a volume of 752mL at 25°C Problem A sample of neon gas occupies a volume of 752mL at 25°C. What volume will the gas occupy at 50°C if the pressure remains constant?

(3) Gay-Lussac’s Law If volume is constant, then pressure is proportional to temperature P1 = P2 T1 T2

Problem The gas in an aerosol can is at a pressure of 3.00 atm at 25°C. Directions on the can warn the user not to keep the can in a place where the temperature exceeds 52°C. What would the gas pressure in the can be at 52°C?

Combined Gas Law If all 3 variables change & none are held constant, the combined gas law is used to state the relationship among pressure, volume, & temperature. P1V1 = P2V2 T1 T2

Problem A helium-filled balloon has a volume of 50L at 25°C and 1 Problem A helium-filled balloon has a volume of 50L at 25°C and 1.08 atm. What volume will it have at 0.855 atm and 10°C?

Avogadro’s Principle States that equal volume of gases at the same temperature & pressure contain the same number of particles

Molar Volume Avogadro’s principle allows us to find the molar volume of molecules of gas Molar volume: the volume that 1 mole occupies at 0°C (273K) & 1 atm This specific temperature & pressure is called standard temperature & pressure (STP).

Cont’d… 1 mole of any gas at STP will occupy a volume of 22.4L. This conversion factor is very useful when you want to find the number of moles, the mass, or the number of particles in a gas sample

How many moles are there in 3.72L of a gas? Problem How many moles are there in 3.72L of a gas?

Ideal Gas Law Describes the physical behavior of an ideal gas in terms of pressure, volume, temperature, & number of moles of gas present PV= nRT P= pressure V= volume n= number of moles R= ideal gas constant T= temperature in Kelvin units

Ideal Gas Constant The value of R (the ideal gas constant) depends on the units of pressure If pressure is in atm, R= 0.0821 If pressure is in kPa, R= 8.314 If pressure is in mmHg or torr, R= 62.4

The ideal gas law can also be used to find the molar mass & density of a gas. d= P x MM R x T d=density P=pressure MM= molar mass R=ideal gas constant T=temperature

Problem What is the pressure in atmospheres exerted by a 0 Problem What is the pressure in atmospheres exerted by a 0.500 mol sample of nitrogen gas in a 10.0L container at 298K?

Dalton’s Law of Partial Pressure States that the total pressure of a mixture of gases is equal to the sum of the pressures of all gases in the mixture Ptotal= P1 + P2 + P3 + … Pn

Problem What is the pressure of sample containing oxygen, hydrogen, & nitrogen at 0.125 atm, 0.087 atm, & 0.442 atm respectively?