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)

STP Standard Temperature and Pressure Standard Temp = 273K Standard Pressure = 1 atm (101.3kPa, 760torr, 760mmHg)

Gas Laws Boyle’s Law Charles’s Law Gay-Lussac’s Law Avogadro’s Law Combined Gas Law Ideal Gas Law Dalton’s Law of Partial Pressures

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

Problem #1 Oxygen occupies a volume of 66L at 6.0atm. What volume will it occupy at 920kPa?

Problem #2 At 25°C a gas has a volume of 6.5mL. What volume will the gas have at 50.°C?

Problem #3 Initially you have gas at 640mmHg, 2.5L, and 22°C. What is the new temperature at 750mmHg and 5L?

Extensions! 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

What is the density of water vapor at STP? D = P∙MM D = (1 atm)(18.02g/mol) R∙T (.0821atm∙L)(273K) mol∙K D = 0.804 g/L 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!