Dalton

1
Daltons Law

• The total pressure in a container is the sum of
  the pressure each gas would exert if it were
  alone in the container.
• The total pressure is the sum of the partial
  pressures.
• PTotal P1 P2 P3 P4 P5 ...
• For each P nRT/V

2
Dalton's Law

• PTotal n1RT n2RT n3RT ... V
  V V
• In the same container R, T and V are the same.
• PTotal (n1 n2 n3...)RT V
• PTotal (nTotal)RT V

3
The mole fraction

• Ratio of moles of the substance to the total
  moles.
• symbol is Greek letter chi c
• c1 n1 P1 nTotal PTotal

4
Examples

• The partial pressure of nitrogen in air is 592
  torr. Air pressure is 752 torr, what is the mole
  fraction of nitrogen?
• What is the partial pressure of nitrogen if the
  container holding the air is compressed to 5.25
  atm?

5
P1/PT n1/nT c1

• 592 torr /752 torr .787 cn
• .787 Pn/PTPn/5.25 atm 4.13atm

6
Examples
3.50 L O2
1.50 L N2
4.00 L CH4
0.752 atm
2.70 atm
4.58 atm

• When these valves are opened, what is each
  partial pressure and the total pressure?

7
Find the partial pressure of each gas

• P1V1P2V2
• 2.70atm(4.00L) P(9.00L) 1.20 atm
• 4.58atm(1.5L) P(9.00L) .76atm
• .752atm(3.50L) P(9.00L) .292atm
• 1.20atm .76atm .292atm 2.26atm

8
Vapor Pressure

• Water evaporates!
• When that water evaporates, the vapor has a
  pressure.
• Gases are often collected over water so the vapor
  pressure of water must be subtracted from the
  total pressure to find the pressure of the gas.
• It must be given. Table of vapors pressures as
  different temperatures

9
Example

• N2O can be produced by the following
  reaction NH4NO3 N2O 2H2O
• what volume of N2O collected over water at a
  total pressure of 785torr and 22ºC can be
  produced from 2.6 g of NH4NO3? ( the vapor
  pressure of water at 22ºC is 21 torr)

10

• 2.6gNH4NO3 1mol NH4NO3 1molN2O
  0.0325mol NO2
• 80.06g 1mol
  NH4NO3
• PVnRT VnRT/P
• V 0.0325mol(62.4torr L/mol K)(295K) / (785torr
  21torr)
• V .77L

11
Kinetic Molecular Theory

• Theory tells why the things happen.
• explains why ideal gases behave the way they do.
• Assumptions that simplify the theory, but dont
  work in real gases.
• The particles are so small we can ignore their
  volume.
• The particles are in constant motion and their
  collisions cause pressure.

12
Kinetic Molecular Theory

• The particles do not affect each other, neither
  attracting or repelling.
• The average kinetic energy is proportional to the
  Kelvin temperature.
• We need the formula KE 1/2 mv2

13
What it tells us

• (KE)avg 3/2 RT
• This the meaning of temperature.
• u is the particle velocity.
• u is the average particle velocity.
• u 2 is the average of the squared particle
  velocity.
• the root mean square velocity is Ö u 2
  urms

14
Combine these two equations

• For a mole of gas
• NA is Avogadro's number

15
Combine these two equations

• m is kg for one particle, so Nam is kg for a mole
  of particles. We will call it M
• Where M is the molar mass in kg/mole, and R has
  the units 8.3145 J/Kmol.
• The velocity will be in m/s

16
Example

• Calculate the root mean square velocity of
  carbon dioxide at 25ºC.
• Calculate the root mean square velocity of
  hydrogen gas at 25ºC.
• Calculate the root mean square velocity of
  chlorine gas at 250ºC.

17
Solutions

• CO2 urms (3(8.314J/molK)(298)/.04401kg/mol)1/2
  411 m/s
• H2 Urms
• (3(8.314J/molK)(298)/.00202kg/mol)1/2 1918m/s
• Cl2 Urms
• (3(8.314J/molK)(523)/.0709kg/mol)1/2
• 429m/s

18
Range of velocities

• The average distance a molecule travels before
  colliding with another is called the mean free
  path and is small (near 10-7)
• Temperature is an average. There are molecules of
  many speeds in the average.
• Shown on a graph called a velocity distribution

19
273 K
number of particles
Molecular Velocity
20
273 K
1273 K
number of particles
Molecular Velocity
21
Velocity

• Average increases as temperature increases.
• Spread increases as temperature increases.

22
Effusion

• Passage of gas through a small hole, into a
  vacuum.
• The effusion rate measures how fast this happens.
• Grahams Law the rate of effusion is inversely
  proportional to the square root of the mass of
  its particles.

23
Effusion

• Passage of gas through a small hole, into a
  vacuum.
• The effusion rate measures how fast this happens.
• Grahams Law the rate of effusion is inversely
  proportional to the square root of the mass of
  its particles.

24
Deriving

• The rate of effusion should be proportional to
  urms
• Effusion Rate 1 urms 1 Effusion Rate 2
  urms 2

25
Deriving

• The rate of effusion should be proportional to
  urms
• Effusion Rate 1 urms 1 Effusion Rate 2
  urms 2

26
Diffusion

• The spreading of a gas through a room.
• Slow considering molecules move at 100s of
  meters per second.
• Collisions with other molecules slow down
  diffusions.
• Best estimate is Grahams Law.

27
Helium effuses through a porous cylinder 3.20
times faster than a compound. What is its molar
mass? vX / v4g 3.2 vX 6.4g X 40.96g/mol

28

• If 0.00251 mol of NH3 effuse through a hole in
  2.47 min, how much HCl would effuse in the same
  time?
• vMNH3 / vMHCl v17 / v36.5 .687 times faster
• 2.51 x 10-3mol (.687) 1.72 x 10-3 mol HCl

29
A sample of N2 effuses through a hole in 38
seconds. what must be the molecular weight of gas
that effuses in 55 seconds under identical
conditions? vMN2 / vX 55/38 1.45 v28 /
1.45 vX 13.32g/mol X
30
Real Gases

• Real molecules do take up space and they do
  interact with each other (especially polar
  molecules).
• Need to add correction factors to the ideal gas
  law to account for these.

31
Volume Correction

• The actual volume free to move in is less because
  of particle size.
• More molecules will have more effect.
• Bigger molecules have more effect
• Corrected volume V V - nb
• b is a constant that differs for each gas.
• P nRT (V-nb)

32
Pressure correction

• Because the molecules are attracted to each
  other, the pressure on the container will be less
  than ideal gas
• Depends on the type of molecule
• depends on the number of molecules per liter.
• since two molecules interact, the effect must be
  squared.

33
Pressure correction

• Because the molecules are attracted to each
  other, the pressure on the container will be less
  than ideal
• depends on the number of molecules per liter.
• since two molecules interact, the effect must be
  squared.

34
Altogether

• Called the Van der Waals equation if
  rearranged
• Corrected Corrected Pressure Volume

35
Where does it come from

• a and b are determined by experiment.
• Different for each gas.
• Look them up
• Bigger molecules have larger b.
• a depends on both size and polarity.
• once given, plug and chug.

36
Example

• Calculate the pressure exerted by 0.5000 mol Cl2
  in a 1.000 L container at 25.0ºC
• Using the ideal gas law.
• Van der Waals equation
• a 6.49 atm L2 /mol2
• b 0.0562 L/mol