Chapter 5: The Gaseous State

Chemistry 1061: Principles of Chemistry I

Andy Aspaas, Instructor

Pressure

• Pressure: force per unit area

– Force exerted on a surface area by molecules in motion

• Units:

1 atmosphere = 14.7 psi

1 atmosphere = 760 mm Hg

1 atmosphere = 101,325 Pascals

1 Pascal = 1 kg/m·s2

Boyle’s law

• Relates volume and pressure of a gas

• PV = constant

• PiVi=PfVf

Charles’s Law

• Relates volume and temperature of a gas

• V/T = constant

• Vi / Ti = Vf / Tf

Combined gas law

• Combines Charles’s and Boyle’s laws to give one equation

• (PiVi)/Ti = (PfVf)/Tf

Avogadro’s Law

• Relates volume with amount of gas

• Equal volumes of any two gases at the same temperature and pressure contain the same number of molecules

• Volume of 1 mole of gas = Vm, molar gas volume

• 22.4 L/mol at STP (standard temp & pressure, 0 °C and 1 atm)

• Nearly the same for any ideal gas!

Ideal gases

• An ideal gas follows the empirical gas laws exactly– A theoretical gas whose molecules have no

volume of their own, and whose molecules do not interact with each other

• R = molar gas constant, the constant of the combined gas equation when 1 mol of gas is used

Vm = R x (T / P) PV = nRT

• R = 0.0821 (L· atm)/(K · mol)

Using the ideal gas law

• If moles gas can be calculated…

– Moles mass density (if MW is known)– Moles MW (if mass is given)– Etc.

• Stoiciometry in equations can give number of moles

– Moles Liters by ideal gas law

Law of partial pressures

• The sum of partial pressures (PA) of all of the different gases in a mixture is equal to the total pressure of the mixture

• Related to mole fraction of a component of a mixture

– Mole fraction: fraction of moles of a certain substance in a mixture of several substances

– Mole fraction = (nA/n) = (PA/P)

• Vapor pressure of water, when collecting gases over water

Molecular speed and effusion

• Average molecular speed, (u) is dependent on the temperature and Molar mass of the gas

u = [(3RT) / (Mm)]1/2

• Effusion: process in which a gas flows through a small hole in a container

– Rate of effusion is proportional to 1/ (Mm)1/2

Real gases

• Ideal gas equation does not hold up, especially at high pressures

– Real volume is larger than the ideal gas law predicts, since molecules themselves take up space

– Actual pressure is smaller than ideal gas law predicts, since intermolecular attractions weaken collisions against the walls of the vessel

van der Waals equation

• V becomes V – nb

• P becomes P + n2a / V2

• van der Waals equation:

(P + n2a / V2)(V – nb) = nRT

• a and b values for many gases are known in the literature