GAS LAWS

Gases exerts pressure

Pressure  = Force per unit of area

      P = Force    (Newtons = kg m/sec²)

            Area    m²

Pascal (Pa) = N/m²

Barometer: measures atmospheric pressure

Manometer: measures pressure of confined gas T-78, 79

Standard press @ sea level:

1 atm    = 760 mm Hg

                        = 29.9 in Hg

                        = 760 torr

                        = 101.325 kPa

                        = 14.7 psi

STP = Standard Temp and Press   (273 K and 1 atm)

ALL TEMPS ARE IN KELVINS!!!!

Why?         K = C^o    +  273

Law	Variables	Constant	Relation	Equation
Charles
Boyles
Gay-Lussac’s
Combined
Ideal

Avogadro’s hypothesis: vol of gases @ same Temp and Press contain = # molec.

Avogadro’s Law: gas @ const temp and press, the vol of gas is α to # moles of gas

PV= nRT

R = dif. values, depending on other variables

R =       0.08206 L x atm

                    mol x K

R = 8.314  Joules

                mol x K

Density ρ = mass

                  Vol

PV = nRT

Molar Mass = mass

                      Moles

Dalton’s Law of Partial Pressure:

Total pressure of mixture of gases is sum of its parts

P _tot      = P _{gas 1} +    P _{gas 2}    + P _{gas 3}       + …

Corrections for gas pressure

Suppose you collect a gas over water…like diagram

P _{inside tube}    =    P _gas      +    P _{water vapor}

If level of liquid inside is = outside liquid level

To compare atm press (in mmHg) to water pressure inside, must consider Hg is 13.6x heavier than water

Mole Fraction X

X _a =  moles a (certain gas)

         Total moles in substance (gas)

Kinetic-Molecular Theory:

1.   

2.

3.

4.

5.

absolute temp of subst α avg. KE of particles

root-mean square (rms) u : speed of a molecule possessing the avg. KE (similar to avg speed)

ε = ½ m u ²

ε = avg KE of the gas molecules

m = mass of the molecule

u = 3 RT                   R = 8.314  Joules

√ MM                                       mol x K

Diffusion:  the spreading of one substance through another (one gas through other gases)

Effusion:  escape of a gas through a small hole

Which molecules will diffuse faster, He or Ar?

Can be calculated through Graham’s Law

Assume two gases @ same temp (KE are =)

                  ½ m_Hev_He² =  ½ m_Arv_Ar²

↑ masses particles travel slower than ↓ massed molecules

Compare the rates of diffusion of oxygen to helium:

Mean Free Path: avg dist traveled by a molec. betw collisions

Diffusion of gases much slower than molecular speeds due to molec collisions

↑ density    ↓ mean free path

Real vs. Ideal gases:

Ideal gases: 

· assume molecules don’t take up space, no intermolecular forces between particles

· works @ low press and high temp (so molecules are far apart)

Real gases:

· @ ↑  press: molecules close together, intermolecular F attract particles AND sm vol of gas becomes signif.

o so real volume decreases

· @ ↓ temp: molecules moving slower, intermolecular F attract particles

o  real volume decreases (gases liquefy)

Van der Waals Equation:

Corrections for finite volume of gas particles, attractive F betw particles

Attractive F ↑  # molec. per vol

a = magnitude of strength of attraction

L² x atm

            mol ²

Vol of gas ↓ : gas molec HAVE vol

b = amt vol particles have per mol

L

            Mol

P +  n²a (V  -  nb)    = nRT

      V

a and b dif for ea gas

↑ as MM ↑