What are the four variables that define the state of a gaseous sample?
pressure, volume, temp, and number of moles
What is an ideal gas?
a hypothetical gas with molecules that have no intermolecular forces and occupy no volume
What is a real gas?
something that deviates from ideal behavior at high pressures and low temps
(although this is true, many compressed real gases demonstrate behavior close to ideal)
ideal gas law
PV=nRT
where R is the ideal gas constant: 8.21x10^-2
What is the ideal gas law most commonly used to determine?
volume or pressure at any given number of moles and temp; can also be used to determine gas density and molar mass
what is number of moles equal to?
mass (m)/molar mass (M)
How do you rearrange the ideal gas law to solve for the density of a gas?
rho=m/V=PM/RT
What is the combined gas law?
P1V1/T1=P2V2/T2
use this equation when trying to calculate the volume of a gas at STP, using "273K" for T2 and 1 atm for P2
What is the STP volume of one mole of gas?
22.4 L/mol
What is molarity equal to in terms of gas?
M=rho at STP * 22.4 L/mol
How do you find the molar mass of a sample when given the sample's mass, temp, pressure, and having been told it is a gas?
1st: set up the density equation to keep in mind what density would be at the given conditions
2nd: rearrange the combined gas law and use it to calculate the Volume of the gas at standard temp and pressure (remembering to make P2=1 atm and T2=273K)
3rd:
Avagadro's principle
all gases at constant temp and pressure occupy volumes that are directly proportional to the number of moles of gas present, and equal amts of all gases at the same temp and pressure occupy equal volumes:
n/V=k or n1/V1=n2/V2
When do you use Avogadro's principle?
if pressure and temp are held constant!
Boyle's Law
P1V1=P2V2
Boyle's Law mnemonic
Boy
s
P
lay
V
ideogames
Boy
le's Law relates
P
ressure and
V
olume
When do you use Boyle's Law?
if number of moles and temp are held constant! (isothemal conditions)
Charles's Law
V1/T1=V2/T2
Charles's Law mnemonic
Charl
ie Brown has a
T
V
show
Charl
es's Law relates
T
emp and
V
olume
When do you use Charles's Law?
when n and P are held constant (isobaric expansion conditions)
Gay-Lussac's Law
P1/T1=P2/T2
Gay-Lussac's Law mnemonic
Gay-Lussac
used
T
P
on his Maypole
Gay-Lussac's law relates
T
emp and
P
ressure
When do you use Gay Lussac's Law
when n and V are held constant (isovolumetric heating conditions)
When must you refer to another law of gases other than the combined gas law? What do you use in this case?
when 2+ gases that don't chemcically interact are found in 1 vessel; then each gas will behave independently of others-each gas will behave as if it were the only gas in the container; in this case the pressure of each gas is a partial pressure
Dalton's law of Partial Pressures
the total pressure of a gaseous mixture is equal to the sum of the partial pressures of the individual components:
Ptot= Pa+Pb+Pc+Pd+...
How do you find the partial pressure of a gas in relation to its mole fraction?
Pa=Xa*Ptot
where Pa= the partial pressure of the gas in question
Ptot= the total pressure of the container
and Xa= mole fraction = moles of gas A/total moles of gas
How do you calculate the partial pressure of each gas if given the moles of each gas in the container?
1st: determine the mole fraction of each gas
2nd: calculate the partial pressures using the mole fractions and the total pressure (which should be given)
Henry's Law
[A]1/P1=[A]2/P2=kH
where [A] is the concentration of A in soln, kH is Henry's constant, and P1 or P2 represent partial pressures
kinetic molecular theory
heavier gases diffuse more slowly than lighter ones bc of their differing avg speeds
What are the assumptions made for the simplified version of the kinetic molecular theory?
1. Gases are made up of particles with volumes that are negligible compared to the container volume
2. Gas atoms neither attract or repel each other
3. Gas particles are in continuous, random motion, undergoing collisions w/ other particles and the contai
kinetic E
KE= (1/2)mv^2=(3/2)KbT
where Kb= boltzmann constant (1.38 x 10^-23 J/K)
root-mean-square speed
symbol: mu sub(rms)
root-mean-squared speed= sqrt(3RT/M)
where: R=ideal gas constant
T=temp
M=molar mass
When do you use the root-mean-squared equation?
when trying to find the
average
speed of molecules of gas!
1st: remember the value for the ideal gas constant (8.314 J/Kmol) and determine the molar mass of the molecule by adding the masses of each cmpd (found on periodic table)
2nd: convert the units of
Graham's Law of Diffusion and Effusion
particles with greater mass travel at a slower avg speed
Graham's Law
r1/r2=sqrt(M2/M1)
where r=diffusion rate of the gas
When do you use Graham's Law
under isothermal and isobaric conditions
What is effusion?
the flow of gas particles under pressure from 1 compartment to another thru a small opening;
the relationship of the rates of effusion in terms of molar mass are the same as that for diffusion
What are deviations due to pressure in real gas as opposed to ideal gas?
ideal gases assume that gas can be compressed to take up zero volume, but that isn't true of real gases: the particles of gas themselves will take up space
What are deviations due to temp in real gas as opposed to ideal gas?
the closer a gas is to BP, the less ideally it acts, and at low temps, the real gas will take up more space than predicted by ideal gas law bc gases will occupy more space than predicted by ideal gas law
van der Waals equation of state
(P+(n^2a)/V^2)*(V-nb)=nRT
where a and b are physical constants for each gas
Mnemonic: a is term for attractive forces
b is term for big particles
When do you use the van der Waals equation of state?
when asked questions like "what is the percentage of real pressure that deviates from the ideal pressure" in a case like this:
1st: calculate the pressure in terms of the ideal gas law
2nd: calculate the pressure in terms of the van der Waals equation of