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PVT properties of gases
Dalton's Law of Partial Pressure: The total pressure of an ideal mixed gas is equal to the sum of the pressures produced when each component exists alone at T and V of the mixed gas (T and V remain unchanged).
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PVT properties of gases
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- Outline
PVT properties of gases
P,V,T
①Clear physical meaning
②Easy to measure
ideal gas equation of state
low pressure law
Boyle's law
Gay-Lussac's law
Avogadro's law
When T=273.15k, p=101.325kPa, 1mol gas Vm=22.4*10^-3 m3
ideal gas equation of state
Pay attention to physical quantity units
Ideal gas definition and microscopic model
ideal gas
Gases that comply with pv=nRT at any temperature and pressure
micro model
①The molecule itself does not occupy volume
②No interaction between molecules
for real gases
When p tends to 0, it can be approximated as an ideal gas under low pressure.
The higher the temperature and the lower the pressure, the closer it is to an ideal gas.
Gas constant R
Extrapolation
①The quantity describing the trend is used as the independent variable (abscissa)
②The quantity to be measured is used as the dependent variable (ordinate)
③The points drawn in the figure (actual measurement points) are drawn as a straight line, extending the intersection of the straight line and the vertical axis (the corresponding value when the independent variable approaches zero)
calculate
A state, knowing three things and seeking one
Calculation between two states
Grasp the invariants and establish equivalent relationships
①R remains unchanged
②n is certain
③T must be
④P must be
⑤V is certain
Calculation of exported quantities
pM=ρRT
Given pressure, temperature, and material, density can be found
ideal gas mixture
Mixture composition
mole fraction
Gas mixtures generally use y
Liquid mixtures generally use x
quality score
Volume fraction
The ratio of the volume of pure B before mixing to the sum of the volumes of each pure component
Application of the Ideal Gas Equation to Ideal Gas Mixtures
The PVT properties of ideal gases have nothing to do with the type of gas
n=ntotal=m/Mmix
Mmix ---Molar mass of the mixture
Dalton's law of partial pressures
Partial pressure = total pressure * mole fraction
Applicable conditions: actual gas mixture/ideal gas mixture
The total pressure of an ideal mixed gas is equal to the sum of the pressures produced when each component exists alone at T and V of the mixed gas (T and V remain unchanged)
Applicable conditions: ideal gas mixture
Distinguish between partial pressure and Dalton's law of partial pressure
Amaga's law of fractional volumes
The total volume of an ideal gas mixture is equal to the sum of the volumes of its components (T and P remain unchanged)
The partial volume can be found using the ideal gas equation of state.
The total volume V of an ideal gas mixture is additive
The relationship between the two
PB/P=VB/V=nB/n=yB
PB/PC=VB/VC=nB/nC
Calculation when state changes
Grasp the invariants
①Constant pressure
②The vinyl chloride and ethylene systems do not change
kinetic theory of gas molecules
Microscopic model of gas molecular motion
Gas molecules are composed of a large number of molecules. Gas molecules can be regarded as volumeless particles or hard spheres.
Gas molecules are in constant, irregular thermal motion
There is no interaction between molecules other than collisions with each other
Collision is elastic collision
ideal gas pressure
root mean square rate
The pressure on the unit wall (pressure)
Both temperature and pressure are related to the motion of ideal gas molecules
ideal gas temperature
Average translational kinetic energy=2/3 kT
Proof of the six laws
Boyle's law
Gay-Lussac's Law
Avogadro's law
ideal gas equation of state
Dalton's law of partial pressures
Amaga's law of partial volumes
Corresponding state principle and generalized compression factor diagram
corresponding state principle
Comparison parameters
Pr=P/Pc
Tr=T/Tc
Vr=Vm/Vc
Non-polar gases (H2, He, Ne)
If two contrasting state parameters of different gases are equal to each other, then the two gases are in corresponding states.
When different gases are in corresponding states, some physical properties are the same or have simple relationships.
Compression factor map
Given T and P, find Z and Vm
Given T and Vm, to find Z and Pr, you need to make auxiliary lines on the compression factor diagram.
Liquefaction and critical parameters of real gases
saturated vapor pressure of liquid
saturated vapor
saturated liquid
saturated vapor pressure
properties unique to pure matter
is a single-valued function of temperature
As T increases, the saturated vapor pressure increases
The saturated vapor pressure of a liquid at a constant temperature is the minimum pressure required to liquefy its vapor at that temperature
boiling point
The temperature at which the saturated vapor pressure of a liquid is equal to the external pressure
normal boiling point
101.325kpa
P-Vm diagram of real gas
T>Tc
No matter how much pressure is applied, the gas will no longer turn into a liquid
T=Tc
T<Tc
critical parameters
critical temperature Tc
The maximum temperature allowed for a gas to liquefy
Critical pressure Pc
critical volume Vc
Critical compression factor Zc
The curve of saturated vapor pressure P*=f(T) ends at the critical temperature
example
real gas equation of state
The difference between real gas and ideal gas
①When the actual gas temperature is constant, pVm changes continuously with the pressure
②The volume of actual gas molecules is more difficult to compress than that of ideal gases
③ Actual gas molecules have interaction forces (mainly gravity) and are easier to compress than ideal gases
④The attraction between actual gas molecules allows it to be liquefied
PVm-P diagram of real gas
T>TB
T=TB
T<TB
TB---Boyle temperature
The higher the Boyle temperature, the easier it is for the gas to liquefy
Compression factor of real gases
multiplication factor
Z<1 easy to compress
Z>1 is difficult to compress
Z=1 ideal gas
The size of the compression factor only indicates whether it is easy to compress, and has nothing to do with whether it is easy to liquefy.
van der Waals equation
(Total pressure on gas molecules) * (Free space for 1 mol molecule) = RT
(p a/Vm^2)(Vm-b)=RT
a, b can be obtained by looking up the table
virial equation
virial coefficient
Second virial coefficient
Reflects the impact of the interaction between two molecules on the gas PVT relationship
third virial coefficient
Reflect the influence of the interaction between three molecules on the gas PVT relationship
When p tends to 0, Vm tends to infinity
The Vely equation tends to the ideal gas equation of state