Characteristics of Gases

1
Characteristics of Gases

• Vapor term for gases of substances that are
  often liquids/solids under ordinary conditions
• Unique gas properties
• Highly compressible
• Inverse pressure-volume relationship
• Form homogeneous mixtures with other gases

2
Pressures of Enclosed Gases and Manometers

• Barometer Used to measure atmospheric pressure
• Manometer Used to measure pressures of gases
  not open to the atmosphere
• Manometer is a bulb of gas attached to a U-tube
  containing Hg.
• If U-tube is closed, pressure of gas is the
  difference in height of the liquid.
• If U-tube is open, add correction term
• If Pgas lt Patm then Pgas Ph Patm
• If Pgas gt Patm then Pgas Ph Patm
• Alternative unit for atmospheric pressure is 1
  bar 105 Pa

3
Kinetic Molecular Theory

• Number of molecules
• Temp
• Volume
• Pressure
• Number of dancers
• Beat of music
• Size of room
• Number and force of collisions

4
Kinetic Molecular Theory

• Accounts for behavior of atoms and molecules
• Based on idea that particles are always moving
• Provides model for an ideal gas
• Ideal Gas Imaginary Fits all assumptions of
  the K.M theory
• Real gas Does not fit all these assumptions

5
5 assumptions of Kinetic-molecular Theory

1. Gases large numbers of tiny particles that are
   far apart.
2. Collisions between gas particles and container
   walls are elastic collisions (no net loss in
   kinetic energy).
3. Gas particles are always moving rapidly and
   randomly.
4. There are no forces of repulsion or attraction
   between gas particles.
5. The average kinetic energy of gas particles
   depends on temperature.

6
Physical Properties of Gasses

• Gases have no definite shape or volume they
  take shape of container.
• Gas particles glide rapidly past each other
  (fluid).
• Gases have low density.
• Gases are easily compressed.
• Gas molecules spread out and mix easily

7

• Diffusion mixing of 2 substances due to random
  motion.
• Effusion Gas particles pass through a tiny
  opening..

8
Real Gases

• Real gases occupy space and exert attractive
  forces on each other.
• The K-M theory is more likely to hold true for
  particles which have little attraction for each
  other.
• Particles of N2 and H2 are nonpolar diatomic
  molecules and closely approximate ideal gas
  behavior.
• More polar molecules less likely to behave like
  an ideal gas. Examples of polar gas molecules
  are HCl, ammonia and water.

9
Gas Behavior

• Particles in a gas are very far apart.
• Each gas particle is largely unaffected by its
  neighbors.
• Gases behave similarly at different pressures and
  temperatures according to gas laws.
• To identify a gas that is most ideal, choose
  one that is light, nonpolar and a noble gas if
  possible.
• Ex Which gas is most likely to DEVIATE from the
  kinetic molecular theory, or is the least
  ideal N2, O2, He, Kr, or SO2?
• Answer sulfur dioxide due to relative polarity
  and mass.

10
Boyles Law

• Pressure goes up if volume goes down.
• Volume goes down if pressure goes up.
• The more pressure increases, the smaller the
  change in volume.

11
Boyles law

• Pressure is the force created by particles
  striking the walls of a container.
• At constant temperature, molecules strike the
  sides of container more often if space is
  smaller.
• V1P1 V2P2
• Squeeze a balloon If reduce volume enough,
  balloon will pop because pressure inside is
  higher than the walls of balloon can tolerate.

12
Charles Law

• As temperature goes up, volume goes up.
• Assumes constant pressure.
• V1 V2
• T1 T2

T , V
13
Charles law

• As temperature goes up volume goes up.
• Adding heat energy causes particles to move
  faster.
• Faster-moving molecules strike walls of container
  more often. The container expands if walls are
  flexible.
• If you cool gas in a container, it will shrink.
• Air-filled, sealed bag placed in freezer will
  shrink.

14
Gay-Lussacs Law

• As temperature increases, pressure increases.
• Assumes volume is held constant.
• P1 P2
• T1 T2
• A can of spray paint will explode near a heat
  source.
• Example is a pressure cooker.

15
Combined Gas Law

• In real life, more than one variable may change.
  If have more than one condition changing, use the
  combined formula.
• In solving problems, use the combined gas law if
  you know more than 3 variables.
• V1P1 V2P2
• T1 T2

16
Using Gas Laws

• Convert temperatures to Kelvin!
• Ensure volumes and/or pressures are in the same
  units on both sides of equation.
• STP 0 C and 1 atm.
• Use proper equation to solve for desired value
  using given information.
• V1P1 V2P2 V1 V2 P1 P2 V1P1
  V2P2
• T1 T2 T1 T2
  T1 T2

17
Gay Lussacs law of combining volumes of gases

• When gases combine, they combine in simple whole
  number ratios.
• These simple numbers are the coefficients of the
  balanced equation.
• N2 3H2 2NH3
• 3 volumes of hydrogen will produce 2 volumes of
  ammonia

18
Avogadros Law and Molar Volume of Gases

• Equal volumes of gases (at the same temp and
  pressure) contain an equal number of molecules.
• In the equation for ammonia formation,
• 1 volume N2 1 molecule N2 1 mole N2
• One mole of any gas will occupy the same volume
  as one mole of any other gas
• Standard molar volume of a gas is the volume
  occupied by one mole of a gas at STP.
• Standard molar volume of a gas is 22.4 L.

19
Sample molar volume problem

• A chemical reaction produces 98.0 mL of sulfur
  dioxide gas at STP. What was the mass, in grams,
  of the gas produced?
• Turn mL to L first! (This way, you can can
  use 22.4 L)
• 98 mL 1 L 1 mol SO2 64.07g SO2 0.280g
  SO2
• 1000 mL 22.4 L 1 mol SO2

20
Sample molar volume problem 2

• What is the volume of 77.0 g of nitrogen dioxide
  gas at STP?
• 77.0 g NO2 1 mol NO2 22.4 L
  37.5 L NO2
• 46.01g NO2 1 mol NO2

21
Ideal Gas Law

• Mathematical relationship for PVT and number of
  moles of gas
• PV nRT n number of moles
• R ideal gas constant
• P pressure
• V volume in L
• T Temperature in K
• R 0.0821 if pressure is in atm
• R 8.314 if pressure is in kPa
• R 62.4 if pressure is in mm Hg

22
Sample Ideal Gas Law Problem

• What pressure in atm will 1.36 kg of N2O gas
  exert when it is compressed in a 25.0 L cylinder
  and is stored in an outdoor shed where the
  temperature can reach 59C in summer?
• V 25.0 L T 59273 332 K P ?
• R 0.0821L-atm n 1.36 kg converted to
  moles mol-K
• 1.36 kg N2O 1000 g 1 mol N2O 30.90 mol N2O
• 1 kg 44.02 g N2O
• PV nRT
• P 30.90 mol x 0.0821 L-atm x 332 K 33.7 atm
• 25.0 L mol-K

23
Volume-Volume Calculations

• Volume ratios for gases are expressed the same
  way as mole ratios we used in other stoichiometry
  problems.
• N2 3H2 2NH3
• Volume ratios are
• 2 volumes NH3 3 volumes H2 2 volumes NH3
• 3 volumes H2 1 volume N2 1 volume N2
  

24
Sample Volume-Volume Problem

• How many liters of oxygen are needed to burn 100
  L of carbon monoxide?
• 2CO O2 2CO2
• 100 L CO 1 volume O2 50 L O2
• 2 volume CO

25
Sample Volume-Volume Problem 2

• Ethanol burns according to the equation below.
  At 2.26 atm and 40 C, 55.8 mL of oxygen are
  used. What volume of CO2 is produced when
  measured at STP?
• C2H5OH 3O2 2CO2 3H2O
• Number moles oxygen under these conditions is?
• PV nRT 2.26 atm(.0558L) n 0.0049 mol O2
• (0.0821 L-atm)(313K)
• mol-K
• 0.0049 mol O2 2 mol CO2 22.4 L 0.073 L CO 2
• 3 mol O2 1 mol CO2

26
Gas Densities and Molar Mass

• Need units of mass over volume for density (d)
• Let M molar mass (g/mol, or mass/mol)
• PV nRT
• MPV MnRT
• MP/RT nM/V
• MP/RT mol(mass/mol)/V
• MP/RT density
• M dRT
• P

27
Sample Problem Density

• 1.00 mole of gas occupies 27.0 L with a density
  of 1.41 g/L at a particular temperature and
  pressure. What is its molecular weight and what
  is its density at STP?
• M.W. 1.41 g 27.0 L 38.1 g___
• L 1.0 mol mol
• M dRT d M P 38.1 g (1 atm)______________
  1.70 g/L
• P RT mol (0.0821 L-atm )(273K)
• ( mol-K )
• ORAT STP 38.1 g 1 mol 1.70 g/L
• mol 22.4 L

28
Example Molecular Weight

• A 0.371 g sample of a pure gaseous compound
  occupies 310. mL at 100. º C and 750. torr. What
  is this compounds molecular weight?
• nPV (750 torr)(.360L) 0.0116 mole
• RT 62.4 L-torr(373 K)
• mole-K
• MW x g_ 0.371 g 32.0 g/mol
• mol 0.0116 mol

29
Partial Pressures

• Gas molecules are far apart, so assume they
  behave independently.
• Dalton Total pressure of a mixture of gases is
  sum of the pressures that each exerts if it is
  present alone.
• Pt P1 P2 P3 . Pn
• Pt (n1 n2 n3 )RT/V ni RT/V
• Let ni number of moles of gas 1 exerting
  partial pressure P1
• P1 X1P1 where X1 is the mole fraction
  (n1/nt)

30
Collecting Gases Over Water

• It is common to synthesize gases and collect them
  by displacing a volume of water.
• To calculate the amount of a gas produced,
  correct for the partial pressure of water
• Ptotal Pgas Pwater
• The vapor pressure of water varies with
  temperature. Use a reference table to find.

31
Kinetic energy

• The absolute temperature of a gas is a measure of
  the average kinetic energy.
• As temperature increases, the average kinetic
  energy of the gas molecules increases.
• As kinetic energy increases, the velocity of the
  gas molecules increases.
• Root-mean square (rms) speed of a gas molecule is
  u.
• Average kinetic energy, e ,is related to rms
  speed
• e ½ mu 2 where m mass of molecule
• Average is of the energies of individual gas
  molecules.

32
Maxwell-Boltzmann Distribution

• Shows molecular speed vs. fraction of molecules
  at a given speed
• No molecules at zero energy
• Few molecules at high energy
• No maximum energy value (graph is slightly
  misleading curves approach zero as velocity
  increases)
• At higher temperatures, many more molecules are
  moving at higher speeds than at lower
  temperatures (but you already guessed that)
• Just for fun Link to mathematical details
  http//user.mc.net/buckeroo/MXDF.html

Source http//www.tannerm.com/maxwell_boltzmann.
htm
33
Molecular Effusion and Diffusion

• Kinetic energy e ½ mu 2
• u 3RT Lower molar mass M, higher rms
  speed u
• M
• Lighter gases have higher speeds than heavier
  ones, so diffusion and effusion are faster for
  lighter gases.

34
Grahams Law of Effusion

• To quantify effusion rate for two gases with
  molar masses M1 and M2
• r1 M2
• r2 M1
• Only those molecules that hit the small hole will
  escape thru it.
• Higher speed, more likely to hit hole, so
• r1/r2 u1/u2

35
Sample Problem Molecular Speed

• Find the root-mean square speed of hydrogen
  molecules in m/s at 20º C.
• 1 J 1 kg-m2/s2 R 8.314 J/mol-K
• R 8.314 kg-m2/mol-K-s2
• u2 3RT 3(8.314 kg-m2/mol-K-s2)293K
• M 2.016 g 1 kg___
• mol 1000g
• u2 3.62 x 106 m2/s2
• u 1.90 x 103 m/s

36
Example Using Grahams Law

• An unknown gas composed of homonuclear diatomic
  molecules effuses at a rate that is only 0.355
  times that of O2 at the same temperature. What is
  the unknown gas?
• rx MO2 0.355 32.0 g/mol
• rO2 Mx 1 Mx
• Square both sides 0.3552 32.0 g/mol
• Mx
• Mx 32.0 g/mol 254 g/mol ? Each atom is 127 g,
• 0.3552 so gas is I2

37
The van der Waals equation

• Add 2 terms to the ideal-gas equation to correct
  for
• The volume of molecules (V-nb)
• Molecular attractions (n2a/V2)
• Where a and b are empirical constants.
• P n2a (V nb) nRT
• V2
• The effect of these forcesIf a striking gas
  molecule is attracted to its neighbors, its
  impact on the wall of its container is lessened.