Gas Laws

Properties of Gases Particles far apart Particles move freely Indefinite shape Indefinite volume Easily compressed Motion of particles is constant and random

Gas Pressure Gas pressure is the result of collisions of particles with their container. More collisions = more pressure Less collisions = less pressure Unit = kPa or atm

Units of Pressure 1 atm = 101.3 kPa =760 torr = 760 mmHg 1 atm = 101,325 Pa 1 atm = 14.70 lb/in2 1 bar = 100,000 Pa = 0.9869 atm atm = atmosphere

Amount of Gas If you add gas, then you increase the number of particles Increasing the number of particles increases the number of collisions Increasing the number of collisions = increase in gas pressure Unit = mole

Volume Decreasing the volume of a container increases the compression. Increasing compression results in more collisions with the side of the container and therefore an increase in gas pressure Unit = L

Temperature If the temp. of a gas increases, then the kinetic energy of the particles increase. Increasing KE makes the particles move faster. Faster moving particles hit the sides of the container more and increase gas pressure. Unit = Kelvin (K) (K = °C + 273)

Drill #1 3/34 & 25/2014 What is the density of water vapor at STP? Standard Temperature and Pressure Standard Temp = 273K Standard Pressure = 1 atm (101.3kPa, 760torr, 760mmHg) One mole of an ideal gas will occupy a volume of 22.4 liters at STP NOTE: STP is exact and does not count towards Sig Figs. Constants don’t either…so actually this problem doesn’t have a method to calculate SFs!

Answer D = 0.804 g/L

Drill – pd 4A 4/23/15 What volume would be occupied by 0.657 grams of hydrogen gas at a pressure of 2.01 atmospheres and a temperature of 35.0°C?

Answer 4.09 L H2

Standard Temperature and Pressure STP Standard Temperature and Pressure Standard Temp = 273K Standard Pressure = 1 atm (101.3kPa, 760torr, 760mmHg) One mole of an ideal gas will occupy a volume of 22.4 liters at STP

Gas Laws Dalton’s Law of Partial Pressures Boyle’s Law Charles’s Law Gay-Lussac’s Law – already have used Avogadro’s Law Combined Gas Law Ideal Gas Law Graham’s Law – last one to learn

P 1= P2 T 1 T2 Gay-Lussac’s Law As temperature of a gas increases, the pressure increases (if volume is constant). Direct relationship P 1= P2 T 1 T2

Graham’s Law

Diffusion and Effusion Diffusion – the gradual mixing of 2 or more gases due to their spontaneous, random motion Effusion – molecules of gas confined in a container randomly pass through a tiny opening in the container

The rates of diffusion and effusion depend on the velocities of the gas molecules. Velocity is determined by the equation KE = ½mv2

Kinetic energy is dependent on temperature, meaning two different gases will have the same kinetic energy at the same temperature ½m1v12 = ½m2v22

Graham’s Law of Diffusion: Rates of diffusion of gases at the same temp and pressure are inversely proportional to the square roots of their molar masses.

Compare the rates of diffusion of hydrogen and oxygen at the same temperature and pressure. rateH2 √MO2 √32.00g/mol rateO2 √MH2 √2.02g/mol Hydrogen diffuses 3.98 times faster than oxygen 3.98

Drill – pd 3 4/23/15 Compare the rate of effusion of carbon dioxide with that of hydrogen chloride at the same temperature and pressure.

Practice Prob. #1 Answer Carbon dioxide will effuse about 0.9 times as fast as hydrogen chloride.

Practice Problem #2 A sample of hydrogen effuses through a porous container about 9 times faster than an unknown gas. Estimate the molar mass of the unknown gas.

Practice Prob. #2 Answer 160 g/mol

Homework Mixed Practice Problems

Boyle’s Law As pressure of a gas increases, the volume decreases (if the temp is constant). Inverse relationship P1V 1= P2V2

Charles’s Law As temperature of a gas increases, the volume increases (if pressure is constant). Direct relationship V 1= V2 T 1 T2

P 1= P2 T 1 T2 Gay-Lussac’s Law As temperature of a gas increases, the pressure increases (if volume is constant). Direct relationship P 1= P2 T 1 T2

Combined Gas Law P1V1 = P2V2 T 1 T2

Avogadro’s Law Equal volumes of gases at the same temperature and pressure contain an equal number of particles V 1= V2 n 1 n2

Dalton’s Law of Partial Pressure The sum of the partial pressures of all the components in a gas mixture is equal to the total pressure of the gas in a mixture. So…all the individual pressures add up to the total pressure. Ptotal = P1 + P2 + P3 + …

Ideal Gas Law An Ideal Gas does not exist, but the concept is used to model gas behavior A Real Gas exists, has intermolecular forces and particle volume, and can change states.

PV = nRT Ideal Gas Law P = Pressure (kPa or atm) V = Volume (L) n = # of particles (mol) T = Temperature (K) R = Ideal gas constant 8.31 (kPa∙L) or 0.0821 (atm∙L) (mol∙K) (mol∙K)

At what temperature would 4 At what temperature would 4.0 moles of hydrogen gas in a 100 liter container exert a pressure of 1.00 atm? Use Ideal Gas Law when you don’t have more than one of any variable Ideal Gas Law PV = nRT T = PV/nR = (1.00atm)(100L) (4.0mol)(.0821atm∙L/mol∙K) = 304.5 K  300K

If we know the chemical formula for the gas we can convert moles PV = nRT n is moles. If we know the chemical formula for the gas we can convert moles to mass or to particles using Dimensional Analysis!

We could also use the fact that: moles = mass or n = m molar mass MM Plugging this in, we have PV = mRT MM This can be rearranged to solve for Density which is m/V m = P∙MM or D = P∙MM V R∙T R∙T