Chap 13 Gases

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Chap 13 Gases

• Kinetic Molecular Theory
• Gas Laws
• Daltons Law

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Essential questions

• 1. How do you use Charles and Boyles laws to
  solve gas problems
• 2. How and when do you use the Ideal Gas
  Equation
• 3. What is the kinetic molecular theory and how
  does it apply to the states of matter

3
What are 6 common characteristics of gases

• have mass
• Compressible
• expand to fill their container
• exert pressure
• gases diffuse easily
• a gas pressure depends upon temperature

4
What are the postulates of the kinetic molecular
theory

• Gases are consist of tiny particles
• the particles have no volume
• the particles are in rapid, random motion
• there are no attractions between the particles
• Collisions are elastic
• the av KE of the particles is directly propor to
  the Kelvin Temp Molecules in Motion Java Applet

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What is pressure

• Force per unit area.
• The result of the collision of gas particles
  with the walls of its container
• Collision demo

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How do you measure pressure

• With a manometer
• a manometer used to measure air pressure is
  called a barometer

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What does a barometer measure presure (how does
it work)

• The mercury barometer works on the principle of
  balancing the weight of a column of air by the
  weight of a column of mercury.

From Zumdahl Intro Chemistry p 373
There is no air above the column. The force of
the air the force(wt) of the column of Hg
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What is standard pressure

• 1 atmosphere
• Wt(force) of the 100miles of air at sea level

9
Write all of the conversions of standard
pressure

• 760 mm Hg
• 760 torr
• 101 kPa
• 1.01 bar
• 14 lbs/in2

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What is STP

• Standard Temperature and Pressure
• 0oC (273K) and 1 atm

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What is Boyles Law

• The volume of a gas varies inversely with the
  pressure with constant temperature
• go here PVnRT applet

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What is the mathematical expression for Boyles
Law

• V x P constant
• V1 x P1 V2 x P2

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What is Charles Law

• The volume of a gas will expand by 1/273 of its
  original for each degree centigrade with pressure
  constant(Volume varies directly with temperature
• go here charles' law and avagadro's law demo

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What is the mathematical expression for Charles
Law

• V1 V2 T1 T2

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What is the combined Law

• P1V1 P2V2
• T1 T2

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Why do we have to use Kelvin when working with
gases

• Mathematically you can not divide by 0
• a gas will not double its volume if you double
  its temperature in centigrade(see Charles Law)

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What is Avogadros Law

• Equal volumes of gases at the same conditions
  contain the same number of particles(moles)

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How do you use it

• V1 V2
• n1 n2

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What is Daltons Law of Partial Pressure

• The total pressure of a system is equal to the
  sums of the individual (partial)pressure of each
  gas that makes up the system.
• PT Pa Pb

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What is partial press

• the pressure the gas would exert if it were alone
  in the container

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What is its expression Mathematically

• P total ntotal RT V
• PT Pa Pb
• PT na RT nb RT nc RT ... V V
  V

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What would a problem say in order for you to use
this law

• What is the partial pressure
• collected over water

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What is the ideal Gas Equation

• PV nRT

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What is n

• moles of the gas

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What is R

• the ideal gas constant
• 0.0821 L atm mol K

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What is an ideal gas

• see Kinetic molecular theory

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How do real and ideal gases compare

• Ideal gases have no attractions between the
  particles and the particles take up no space.
• Real gases have attractive forces (London,
  dipole-dipole, H bonding, metallic, ion) and the
  particles make up some of the volume of the gas

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What is an ideal gas

• One that follows the KMT.
• It will not condense into a liquid no matter what
  the temp or pressure
• The gas laws only work on ideal gases

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What is a real gas

• All gases are real
• There are some attractions between the Particles.
  The particles do take up some space(but very
  small compared to the space between the
  particles).
• This means at Low temps or high pressures or both
  real gases will condense into liquids.

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How can we use the gas laws with real gases

• at normal temps and pressures real gases act like
  ideal gases

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How are temp and pressure related

• With temperature comes K.E. (motion) moving
  particles collide with the walls of the container
  producing pressure.
• As temp is increased so is the energy of motion
  and therefore so is pressure?Remember the
  diagram from before

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How does density relate to gases

• at STP the density of a gas can be calculated by
  molar mass 22.4L
• Of course the temp and pressure will affect
  density also

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How does diffusion compare to effusion

• diffusion is when we have a gas working its way
  through another gas.
• Effusion is when a gas in a container escapes
  through an opening

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How can we work with this mathematically

• If we use the same conditions there are a few
  things we can do
• Avagadros law equal vol at same conditons have
  same number of particles (moles)

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How can we compare gases contd

• We can also use Grahams law.
• Since the gases are at the same temp their av
  K.E. must be the same

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Grahams Law

• Av K.E. 1/2mv2 so both gases must have the same
  mv2
• Because m and v are inversely related if mass
  goes up velocity must go down

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Grahams Law contd

• Putting this into math
• (1/2mv2)A (1/2mv2)B
• vA mBvB mA

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Some important vocab

• V velocity a rate distance/time
• We can substitute density for mass
• We can substitute molecular wt for mass

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Some important vocab

• If you just use time the equation changes to
• tB mBtA mA
• You can figure this out from the rate if you want.

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Some important vocab

• Another thing is some teminology
• When gases are working their way through other
  gases we use the term diffusion

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Some important vocab

• When gases leave through an opening it is called
  effusion. The greater rate of effusion the
  smaller the time is .

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What is the ratio of the rates of diffusion of
helium to nitrogen

• a fraction is a ratio. A whole number is also a
  ratio 4 4/1
• He 4g/mol N2 28 g/mol
• He to N mean m1 He and m2 N
• V1 28V2 4

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What is the ratio of the rates of diffusion of
helium to nitrogen

• v1 2.7 v2
• which means helium travels 2.7 times faster than
  N2

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If the average speed of He is 0.71 miles/sec,
what will be the speed of Oxygen at the same temp?

• He 4 g/mol while O2 32 g/mol
• plug into (you must designate what is 1 and what
  is 2)
• 0.71 miles/sec 32 x 0.25
• x 4

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If it takes 35 sec for an amount of helium gas to
effuse from a container, how long will it take an
equal amount of methane to effuse?

• Grahams Law(effusion and time)
• No special order for info just make sure to keep
  values together
• This has time and not rate. We need to adjust
  the equation

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If it takes 35 sec for an amount of helium gas to
effuse from a container, how long will it take an
equal amount of methane to effuse?

• Methane 16 g/mol He 4 g/mol
• T2 m2 T1 m1

x 16 x 70 sec 35 4
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What is the molar volume

• 22.4 liters per mole

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How can you use the ideal Gas law and
stoichiometry

• in a mass-vol problem if the conditions are not
  at STP,we cant just use our facts we learned
  earlier(22.4l/mol).
• There are two ways to solve

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Cont.

• 1st solve regular grams
  x L coeff x PT 22.4 x coeff
• Then use P1V1 P2V2 T1
  T2
• 760 torr(vol from prob) given P(ans) 273
  K given T

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Cont.

• 2nd Use factor label to find moles of product g
  x 1mole x mole prod PT mole react
• Then PV nRT
• P T from problem n from above R const

51
Zinc metal reacts vigorously with chlorine gas to
form zinc chloride Zn(s) Cl2(g) ?
ZnCl2(s) What volume of chlorine gas at 35oC
and 1.01 atm is required to react completely with
1.13 g of zinc?

• This is stoich at non std conditions.
• Because we are given g and want vol at non STP we
  must do stoich first and then change the
  conditions from STP to those given.
• MUST BE AT STP TO DO STOICH

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volume of chlorine gas at 35oC and 1.01 atm is
required to react completely with 1.13 g of zinc?

• 1.13g x LZn(s) Cl2(g) ?
  ZnCl2(s)65g 22.4L
• X 0.39L at STP which is 0oC and 1 atmthese are
  the 1s and the 2s are 35oC and 1.01 atm
• Now use VP/T to solve

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Contd

• VP VP T T
• (0.39L)(1atm) V(1.01atm) 273K
  308K
• 0.43L

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Science Way

• 1.13g Zn x 1 mol Zn x 1mol Cl2 0.015mol
  65g Zn 1 mol Zn
• Now use PVnRT to finish
• P 1.01 atm, T 35273 R 0.0821 Latm/mol K,
  n .015V .43L

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• If 4g of oxygen and 4 g of hydrogen are placed in
  a 5 liter vessel at 65oC,
• what will be the partial pressure of each gas and
• what is the total pressure in the vessel?

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Givens 4g of O2, 4g H2 5 liter vessel,
65oC,wantwhat will be the partial pressure of
each gas

• Since g given will use PVnRT
• P is x, V 5L, n 4/32, R .0821L?atm/mol?K
• Do the same for H2
• For 2nd half, add the Ps together.

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• 350ml of hydrogen gas is collected over water at
  25oC and 750 mmHg
• 1. what is the volume at STP
• 2. how many g of hydrogen are present

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Givens 350ml H2 , collected over water , 25oC
and 750 mmHg

• I know now to use PTPgas Pvaporwhich is
  really Pgas Pgiven P w.v
• 750-23.8 726.2 mmHg P
• Want Vol at STP and have V, P, and T so
• 350ml(726mmHg) V(760mmHg) 298K
  273K
• 306ml

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Givens 306ml H2 , at STP

• I know 1 mol any gas at STP 22.4L
• 306ml 22400ml x mol 1 mol
  or
• 306ml x 1mol 22400ml

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• If 46.2g of oxygen occupy a vol of 100L at STP
• what vol would 5 g occupy

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Avagadros Law

• Have gs and vol and no changes in P or T.
• Can find moles
• Use n n V V
• 46.2g/32g/mol 1.44mol 5g/320.16mol
• 1.44mol 0.16 mol 100ml x
• 10.8 ml

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• From the equation H2O2 ? H2O O2 what
  volume of oxygen collected at 27oC and 764 mmHg
  would be generated by the decomposition of 125g
  of a 50 soln of hydrogen peroxide

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Wants a vol at non STP, Gives H2O2 and wants O2

• 125g but only 50 is cmpd so, H2O2 is 62.5 g
• 62.5g x L 2H2O2 ?2 H2O O2
  34g x2 22.4L
• X 20.6 L at STP which is 0oC and 1 atmthese are
  the 1s and the 2s are 27oC and 764 mmHg
• Now use VP/T to solve

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Contd

• VP VP T T
• (20.6L)(760mmHg) V(764mmHg) 273K
  300K
• 20.5L

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Science Way

• 62.5g H2O2 x 1 mol H2O2 x 1mol O2
  34g H2O2 2 mol H2O20.92mol
• Now use PVnRT to finish
• P 764/760, T 27273 R 0.0821 Latm/mol K,
  n .92V 20.5L