Combined and ideal gas laws

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Combined and ideal gas laws
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Combined gas law

• If we combine all of the relationships from the 3
  laws covered thus far (Boyles, Charless, and
  Gay-Lussacs) we can develop a mathematical
  equation that can solve for a situation where 3
  variables change

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Combined gas law

• Amount is held constant
• Is used when you have a change in volume,
  pressure, or temperature

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Example problem
A gas with a volume of 4.0L at STP. What is its
volume at 2.0atm and at 30C?
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Example problem

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Avogadros Law

• So far weve compared all the variables except
  the amount of a gas (n).
• There is a lesser known law called Avogadros Law
  which relates ____.
• It turns out that they are _________ related to
  each other.
• As ____________ increases then V increases.

V/n k
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Ideal Gas Law

• Which leads us to the ideal gas law
• The fourth and final variable is amount
• ___________________________.
• We can set up a much more powerful eqn, which can
  be derived by combining the proportions expressed
  by the previous laws.

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Ideal Gas Law

• If we combine all of the laws together including
  Avogadros Law mentioned earlier we get

Where R is the universal gas constant
Normally written as
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Ideal Gas Constant (R)

• R is a constant that connects the 4 variables
• R is dependent on the units of the variables for
  P, V, T
• Temp is always in ________
• Volume is in ________
• Pressure is in either ____________ ____________

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Ideal Gas Constant

• Because of the different pressure units there are
  3 possibilities for our ideal gas constant

• If pressure is given in atm

• If pressure is given in mmHg

• If pressure is given in kPa

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Using the Ideal Gas Law
What volume does 9.45g of C2H2 occupy at STP?
P ?
R ?
V ?
T ?
n ?
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(______)
(V)

(_______)
(___K)
V ______L
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A camping stove propane tank holds 3000g of C3H8.
How large a container would be needed to hold
the same amount of propane as a gas at 25C and a
pressure of 303 kpa?
P ?
R ?
V ?
T ?
n ?
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(______)
(V)

(___K)
(____ mol)
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Classroom Practice

1. Use the Ideal Gas Law to complete the following
   table for ammonia gas (NH3).

Pressure Volume Temp Moles Grams
2.50 atm 0?C 32.0
75.0 ml 30?C 0.385
768 mmHg 6.0 L 100?C
195 kPa 58.7 L 19.8
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Ideal Gas Law Stoichiometry
What volume of hydrogen gas must be burned to
form 1.00 L of water vapor at 1.00 atm
pressure and 300C?
(____ atm)
(___ L)
nH2O
(___K)
(____L atm/mol K)
nH2O _______ mols
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Ideal Gas Law Stoichiometry
2H2 O2 ? 2H2O
.021257 mol
_____ L H2
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Classroom Practice
To find the formula of a transition metal
carbonyl, one of a family of compounds having the
general formula Mx(CO)y, you can heat the solid
compound in a vacuum to produce solid metal and
CO gas. You heat 0.112 g of Crx(CO)y Crx(CO)y(s)
? x Cr(s) y CO(g) and find that the CO
evolved has a pressure of 369 mmHg in a 155 ml
flask at 27?C. What is the empirical formula of
Crx(CO)y?
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Variations of the Ideal Gas Law

• We can use the ideal gas law to derive a version
  to solve for MM.
• We need to know that the unit mole is equal to m
  MM, where m is the mass of the gas sample

PV nRT
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Variations of the Ideal Gas Law

• We can then use the MM equation to derive a
  version that solves for the density of a gas.
• Remember that D m/V

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Classroom Practice 1

1. A gas consisting of only carbon and hydrogen has
   an empirical formula of CH2. The gas has a
   density of 1.65 g/L at 27?C and 734 mmHg.
   Determine the molar mass and the molecular
   formula of the gas.
2. Silicon tetrachloride (SiCl4) and trichlorosilane
   (SiHCl3) are both starting materials for the
   production of electro-nics-grade silicon.
   Calculate the densities of pure SiCl4 and pure
   SiHCl3 vapor at 85?C and 758 mmHg.

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Real Vs. Ideal

• All of our calculations with gases have been
  assuming ideal conditions and behaviors.
• We assumed that there was ____ __________
  established between particles.
• We assumed that each particle has _____________
  of its own.
• Under normal atmospheric conditions gases tend to
  behave as we expect and as predicted by the KMT.

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Real Vs. Ideal

• However, under ______________ and
  _______________, gases tend to deviate from ideal
  behaviors.
• Under extreme conditions we tend to see a
  tendency of gases to not behave as independently
  as the ideal gas law predicts.
• Attractive forces between gas particles under
  high pressures or low temperature cause the gas
  not to behave predictably.

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Loose Ends of Gases

• There are a couple more laws that we need to
  address dealing with gases.
• Daltons Law of Partial Pressures
• Grahams Law of Diffusion and Effusion.

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Daltons Law of Partial Pressure

• States that the total pressure of a mixture of
  gases is equal to the sum of the partial
  pressures of the component gases.

• What that means is that each gas involved in a
  mixture exerts an independent pressure on its
  containers walls

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Daltons Law of Partial Pressure

• Therefore, to find the pressure in the system you
  must have the ____ ______________of all of the
  gases involved.
• This becomes very important for people who work
  at _____ altitudes like mountain climbers and
  pilots.
• For example, at an altitude of about 10,000m air
  pressure is about ____ of an atmosphere.

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Daltons Law of Partial Pressure

• The partial pressure of oxygen at this altitude
  is less than ___ mmHg.
• By comparison, the partial pressure of oxygen in
  human alveolar blood needs to be about _____
  mmHg.
• Thus, respiration cannot occur normally at this
  altitude, and an outside source of oxygen is
  needed in order to survive.

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Simple Daltons Law Calculation

• Three of the primary components of air are CO2,
  N2, and O2. In a sample containing a mixture of
  these gases at exactly 760 mmHg, the partial
  pressures of CO2 and N2 are given as PCO2
  0.285mmHg and PN2 593.525mmHg. What is the
  partial pressure of O2?

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Simple Daltons Law Calculation
PT PCO2 PN2 PO2
760mmHg ______ mmHg _________ mmHg P__
PO2 _____mmHg
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Daltons Law of Partial Pressure

• Partial pressures are also important when a gas
  is collected through water.
• Any time a gas is collected through water the gas
  is ____________ with water vapor.
• You can determine the pressure of the dry gas by
  __________ out the water vapor

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Atmospheric Pressure
Ptot Patmospheric pressure Pgas PH2O

• The waters vapor pressure can be determined from
  ___ and subtract-ed from the atmospheric pressure

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WATER VAPOR PRESSURES WATER VAPOR PRESSURES WATER VAPOR PRESSURES
Temp (C) (mmHg) (kPa)
0.0 4.6 .61
5.0 6.5 .87
10.0 9.2 1.23
15.0 12.8 1.71
15.5 13.2 1.76
16.0 13.6 1.82
16.5 14.1 1.88
17.0 14.5 1.94
17.5 15.0 2.00
18.0 15.5 2.06
18.5 16.0 2.13
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WATER VAPOR PRESSURES WATER VAPOR PRESSURES WATER VAPOR PRESSURES
Temp (C) (mmHg) (kPa)
19.0 16.5 2.19
19.5 17.0 2.27
20.0 17.5 2.34
20.5 18.1 2.41
21.0 18.6 2.49
21.5 19.2 2.57
22.0 19.8 2.64
22.5 20.4 2.72
23.0 21.1 2.81
23.5 21.7 2.90
24.0 22.4 2.98
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WATER VAPOR PRESSURES WATER VAPOR PRESSURES WATER VAPOR PRESSURES
Temp (C) (mmHg) (kPa)
24.5 23.1 3.10
25.0 23.8 3.17
26.0 25.2 3.36
27.0 26.7 3.57
28.0 28.3 3.78
29.0 30.0 4.01
30.0 31.8 4.25
35.0 42.2 5.63
40.0 55.3 7.38
50.0 92.5 12.34
60.0 149.4 19.93
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WATER VAPOR PRESSURES WATER VAPOR PRESSURES WATER VAPOR PRESSURES
Temp (C) (mmHg) (kPa)
70.0 233.7 31.18
80.0 355.1 47.37
90.0 525.8 70.12
95.0 633.9 84.53
100.0 760.0 101.32
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Simple Daltons Law Calculation

• Determine the partial pressure of oxygen
  collected by water displace-ment if the water
  temperature is 20.0C and the total pressure of
  the gases in the collection bottle is 730 mmHg.

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Simple Daltons Law Calculation
PT PH2O PO2
PH2O ____ mmHg
PT ___ mmHg
___mmHg _______ PO2
PO2 _____ mmHg
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Grahams Law

• Thomas Graham studied the _______ and ________ of
  gases.
• __________ is the mixing of gases through each
  other.
• _______ is the process whereby the molecules of a
  gas escape from its container through a tiny hole

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Grahams Law

• Grahams Law states that the rates of effusion
  and diffusion of gases at the same temperature
  and pressure is dependent on the size of the
  molecule.
• The _________ the molecule the slower it moves
  the __________ it mixes and escapes.

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Grahams Law

• Kinetic energy can be calculated with the
  equation ___________
• __ is the mass of the object
• __ is the velocity.
• If we work with two different gases at the same
  ______________ their energies would be equal and
  the equation can be rewritten as

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• M represents molar mass
• v represents molecular velocity
• A is one gas
• B is another gas

• If we want to compare both gases velocities, to
  determine which gas moves faster, we could write
  a ____ of their velocities.
• Rearranging things and taking the ____________
  would give the eqn

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• This shows that the velocities of two different
  gases are inversely propor-tional to the square
  roots of their molar masses.
• This can be expanded to deal with rates of
  diffusion or effusion

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Grahams Law

• The way you can interpret the equation is that
  the number of times faster A moves than B, is the
  square root of the ratio of the molar mass of B
  divided by the Molar mass of A
• So if A is half the size of B than it effuses or
  diffuses ____ times faster.

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Grahams Law Example Calc.
If equal amounts of helium and argon are placed
in a porous container and allowed to escape,
which gas will escape faster and how much faster?
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Grahams Law Example Calc.
Rate of effusion of He

Rate of effusion of Ar
Helium is ____ times faster than Argon.
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Classroom Practice 2

1. A mixture of 1.00 g H2 and 1.00 g He is placed in
   a 1.00 L container at 27?C. Calculate the
   partial pressure of each gas and the total
   pressure.
2. Helium is collected over water _at_ 25?C and 1.00
   atm total pressure. What total volume of gas
   must be collected to obtain 0.586 g of He?
3. The rate of effusion of a gas was meas-ured to be
   24.0 ml/min. Under the same conditions, the rate
   of effusion of pure CH4 gas is 47.8 ml/min. What
   is the molar mass of the unknown gas?