UNIT 10
Pressure: F/A
http://chemlab.truman.edu/CHEM130Labs/CalorimetryFiles/ThermoBackground.asp
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There are four variable needed to define the physical state of a gas. They are:
o Temperature
o Pressure
o Volume
o Amount of gas (moles)
Relationship between pressure and volume
o What happens when a balloon at the earth’s surface is released into the
atmosphere? As it rises, the balloon _______________.
o Boyle’s law: PV = constant
§ Your lungs work by Boyle’s law. How?
Relationship between temperature and volume.
o Charles’s law: V/T = constant
Relationship between volume and quantity (moles)
o The more air I blow into a balloon, the larger the balloon becomes.
o Avogadro’s hypothesis: V/n = constant
Combining relationships. The Ideal Gas Equation.
o Bole’s law: V α 1/P (constant n, T)
o Charle’s law: V α T (constant n, P)
o Avogadro’s law: V α n (constant P, T)
o Thus, V α nT/P
o Rearranging, PV α nT
o Introducing a constant, R we get:
PV = nRT
(T must always be in Kelvin!)
o To use this equation, we must assume some things:
§ The gas molecules take up no space
§ The gas molecules are so far apart that they do not interact.
Question: What would happen if we did not make these assumptions?
Question: What is the volume of 1 mole of an ideal gas at 0 Celsius (273.15 K) and atmospheric
pressure (1 atm)? R = 0.08206 (L*atm/mol-K).
Note: STP (standard temperature and pressure) is defined as 0 Celsius and 1 atm.
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Relating Density to the Ideal Gas Equation.
o The definition of moles, n, is mass/molar mass.
o If we substitute this for n in the Ideal Gas Equation we get:
PV = (mass/molar mass)RT
o Because density is mass/V,
PV = V(d/molar mass) RT or P = (d/molar mass) RT
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o Rearrange this to get
o Molar mass of a gas = dRT/P
Partial Pressures (mixtures of gases).
o Dalton’s Law of Partial Pressures
§ The pressure exerted by a particular component of a mixture of gasses is
called the partial pressure of that component.
o Let Pt = the total pressure of the mixture
o For each gas in the mixture (1, 2, 3…):
P1 = n1(RT/V) P2 = n2(RT/V) P3 = n3(RT/V)
o All gases occupy the same volume and have the same temperature, thus:
Pt = (n1 + n2 + n3 + …..)(RT/V) = nt(RT/V)
o The number of moles of gas determines the total pressure of a gas mixture.
Question: A mixture of 6 g of O2 (g) and 9 g of CH4 (g) is placed in a 15 L vessel at 0 Celsius.
What is the partial pressure of each gas? What is the total pressure?
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Partial Pressures and Mole Fractions: n1/nt
Question: A study of the effects of certain gases on plant growth requires a synthetic atmosphere
composed of 1.5 mol percent of CO2, 18.0 mol percent of O2 and 80.5 percent Ar. Calculate the
partial pressure of O2 in the mixture if the total pressure is 745 torr. If this atmosphere is to be
held in a 121 L space at 295 K, how many moles of O2 are needed?
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Kinetic Molecular Theory of Gases. Explains the relationships between P, V, n, R, and T.
o Gases consist of large numbers of molecules/atoms/particles that are in
continuous random motion.
o The combined volume of all the particles is negligible relative to the total volume
of the container
o Attractive and repulsive forces between gas molecules are negligible.
o Energy can be transferred between particles during collisions but, as long as
temperature remains constant, the average kinetic energy of the molecules does
not change with time.
o The average kinetic energy of the molecules is proportional to the absolute
temperature. At a particular temperature the molecules of all gases have the same
average kinetic energy.
Speed of gas particles.
o Although gas particles at a particular temperature have an average speed, the
individual particles have different speeds.
http://www.chemistry.wustl.edu/~edudev/LabTutorials/CourseTutorials/Tutorials/Airbags/gas_0
6.htm
Question: A sample of oxygen gas initially at STP is compressed to a smaller volume at constant
temperature. What effect does this change have on: 1) the average kinetic energy of the
molecules 2) their average speed, 3) the number of collisions they make with the container walls
per unit time.
Question: How is the average speed of gas particles in a container changed by: 1) an increase in
temperature, 2) an increase in volume, 3) mixing with a sample of Ar at the same temperature.
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Real Gases. Deviation from ideal behavior.
Question: As temperature decreases, gases deviate from ideal behavior. How and Why?
Remember the assumptions we made for ideal gas behavior.
Question: If the pressure of a gas increases by decreasing the volume of the container, how
would this lead to a deviation from ideal gas behavior?
Question: At low temperatures and high pressures, deviations from ideal gas behavior are large.
Why?
http://chemwiki.ucdavis.edu/Physical_Chemistry/Physical_Properties_of_Matter/Phases_of_Mat
ter/Gases/Real_Gases
Question: Describe the deviations from ideal behavior in the above graph.
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van der Waals Equation (real gases).
(P + n2a/V2)(V-nb) = nRT
Let’s start with PV = nRT
Rearranged: P = nRT/V
1) First correction term: the pressure of real gas is smaller than what is calculated by the
ideal gas equation.
P = nRT/V- n2a/V2
n2a/V2 is the correction for the fact that a real gas has smaller pressure due to intermolecular
forces than an ideal gas does.
Rearranged: (P + n2a/V2) =nRT/V
2) Second correction term: gases do take up space. The ideal gas law calculates a volume
that is too high when you assume that gases take up no space.
(P + n2a/V2) =nRT/(V-nb)
Rearranged: (P + n2a/V2)(V-nb) = nRT