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Level 87

Real Gases

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describe molecular motion of real gases
constant above 0°K, random, straight line unless it collides
low concentration, by random collision
are gases most likely to go towards areas of high concentration or low concentration, why?
less molar mass
do gases with greater molar mass or less molar mass diffuse faster?
what does effusion describe?
the passage of bass into an evacuated container
they have definite volume, and IMF
why can't you use PV=nRT for real gases?
electrons that are closer to the nucleus have a _______ energy
higher molar mass
is a molecule with higher or lower molar mass going to be affected by IMF more.
Electron affinity tends to become from left to right across a row of the periodic table
Cl₂, more IMF
is O₂ or Cl₂ going to deviate more from an ideal gas? why?
? T :: ? collisions :: ? rate of reaction
Heat, q
path function
measuring S
3rd Law of Thermodynamics
Important Units for PV = nRT
P: Pa 1 bar = 1x10^5 Pa
Dalton's Law
intensive property
a physical property such as boiling point, density, or color that does NOT change when you change the size of an object.
What is one major flaw of Ideal Gases?
there would be no intermolecular interactions and therefore liquids and solids could not exist
a measure of how much the volume of matter decreases under pressure
critical point
critical temperature+critical pressure
supercritical fluid
heating above Tc
Equations of State
Virial Equation of State
polynomial expansions of the compressibility factor and can provide more "theoretically-grounded" equations of state
Van der Waal Equation of State
adjusts V to account for occupied space of e clouds (attractions ONLY!!!)
Law of Corresponding States
two gases have corresponding states if they have the same reduced T and reduced P
corresponding states
two states that have the same reduced V
state functions
What are internal energy changes?
Path Functions
properties that depend on the path taken (ex. W)
Expansion Coefficients (alpha or beta)
measure of the affect of T on V @ constant P
Isothermal Compressibility (k, kappa)
measure of the effect of P on V @ constant T
Inverse Rule
(dP/dT)v = 1/(dT/dP)v
Euler's Chain Rule
(dP/dV)t * (dV/dT)p * (dT/dP)v = -1
[d(dP/dT)/dV]t = [d(dP/dV)/dT]v
Variables in Succession rule
Adiabatic process
W =0
Isochoric process (constant V)
Heat Capacity, C
a substances response to heat flow
Enthalpy, H
ΔH = ΔU - W
Kirchoff's Law
uses a cycle of reactions and known ΔHf's to determine ΔHrxn's of a specific reaction
Coffee Cup Calorimeter
@constant P
Bomb Calorimeter
@ constant V
Differential Scanning Calorimetry
Heat flux model
Power Compensation Model
tries to keep both at the same temp.
Carnot Engine
reversible hat engine b/c all steps are reversible
Clausius's Inequality
explains engines that don't have perfectly reversible steps
Entropy of mixing
spontaneous process (irreversible w/o outside influence)
ideal gas
a gas in which the particles undergo elastic collisions (when particles collide, there is no loss in the speed of the particles)
size, particles, interactions, reality
ideal gas: the _______of the _______don't matter, _______ are not important, not _______
amount of mass per units volume
number of moles, pressure, gas
total _______ is directly proportional to total _______ regardless of _______
total number of moles is _______ proportional to total pressure regardless of gas
density, molar mass
_______is directly proportional to _______
temperature, velocity
as _______ changes, _______ changes
forces, speed, temperature, pressure,average velocity
_______ become significant when _______, _______, _______and _______ changes
molecular motion, temperature
_______ slows at lower _______
molecular motion slows at _______ temperature
higher, more
the _______the van der waals constant, the _______ intermolecular forces
van der waals, intermolecular forces
the higher the _______ constant, the more _______
van der waals
a modification of the ideal gas law that includes correction terms for molecular size and attractive forces
ideal gas law, molecular size, attractive forces
van der waals: a modification of the _______ that includes correction terms for _______ and _______
critical temperature
temperature above which liquid phase of substance cannot exist (i.e. above this point, no gas can be liquified regardless of pressure)
critical pressure
lowest pressure where it can stay a liquid state at critical temperature
Critical State
a fluid at its critical point
Reduced Pressure
Pr = P/Pc
Reduced Temperature
Tr = T/Tc
Reduced Volume
Vr = V/Vc
Why do real gases show deviations from perfect gases?
Molecules in a real gas interact with one another.
What forces between molecules assist expansion?
When are repulsive forces significant?
When molecules are almost in contact, they're short range interactions.
When are attractive forces ineffective?
When molecules are far apart.
What happens to IM forces when the temperature is low?
The molecules travel with such low mean speeds that they can be captured by one another.
What happens to a sample at low pressures?
When the sample occupies a large volume, the molecules are so far apart the IM forces don't play a significant role. The gas basically behaves ideally (perfectly)
Attractive forces dominate,
Which forces dominate at moderate pressures?
Repulsive forces,
Which forces dominate at high pressures?
Compression Factor (Z) of a Gas
Ratio of a gas's measured molar volume (Vm) to the molar volume of a perfect gas (Vm0)
Z = 1
What is the compression factor for a perfect gas?
Z > 1
What's the value for Z at high pressures?
Z < 1
What's the value for Z at intermediate pressures?
Vapor pressure
Force exerted by vapor particles directly above a liquid
Vander Waals Coefficients
Constants (a) and (b) in the vander waal equation of state.
Constant (a)
Represents the strength of the attractive interactions.
Constant (b)
Represents the strength of repulsive interactions.
Calculations of Excluded Volune
Closest distance of two hard sphere molecules of radius r...
Principle (1) of Van der Waal equation
Perfect gas isotherms are obtained at high temperatures and large molecular volumes.
Principle (1) Explained
At a high temp, RT is so large that the first term in the VDW eqn. >>>>> the 2nd term.
Principle (2) of Van der Waal equation
Liquids and gases coexist when cohesive and dispersing effects are in balance.
Principle 2 Explained
The 1rsr term arises from the KE of molecules and their repulsive interactions.
Principle (3) of Van der Waal equation
The critical constants are related to the Van der Waal coefficients.
Principle 3 explained
Vc = 3b
Principle of Corresponding States
Real gases at the same reduced volume and reduced temperature exert the same reduced pressure.
Under what conditions does the principle of corresponding states work best?
It works best for gases composed of spherical molecules. It fails sometimes for polar/non-spherical molecules.
Z = 1 + [b - (a/RT)] (1/Vm)
Two Expansions for Z based on the Van der Waal equation