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Physical Chemistry Chapter 1 pVT Relationship of Gases
Microscopic model of gas molecular motion: 1. Gas is composed of a large number of molecules, and gas molecules can be regarded as volumeless particles or hard balls; 2. Gas molecules are in endless irregular thermal motion.
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Physical Chemistry Chapter 1 pVT Relationship of Gases
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- Outline
pVT relationship for gases
1. ideal gas equation of state
1. Ideal gas equation of state
1. Low pressure law
Boyle's law
pV=constant (n, T are certain)
Guy-Lussac's law
V/T=constant (n and p are certain)
Avogadro's law
V/n=constant (T and p are certain)
2. Ideal gas equation of state
unit
2. Definition and microscopic model of ideal gas
1. Macroscopic definition of ideal gas
A gas that conforms to the ideal gas equation of state (pV=nRT) at any temperature and pressure
2. ideal gas microscopic model
The molecule itself does not occupy volume
No interaction between molecules
3. Discussion of real gases
conforms to ideal gas behavior when
Generally, it can be approximately considered as an ideal gas under low pressure.
The higher the temperature and the lower the pressure, the closer it is to an ideal gas.
3. Gas constant R
extrapolation method measured
is a constant
4. Calculation of p, V, and T properties of ideal gases
1. p, V, T, n know three and seek one.
2. Calculation between two states.
3. Calculation of derived quantities such as mass m, density, volume, etc.
2. ideal gas mixture
1. Composition of the mixture
1. Mole fraction x or y
The ratio of the amount of substance B to the total amount of substances in the mixture
The mole fraction of a gas mixture is generally represented by y The mole fraction of a liquid mixture is generally represented by x
2. Quality score
The ratio of the mass of substance B to the total mass of the mixture
3. Volume fraction
The ratio of the volume of pure B before mixing to the sum of the volumes of each pure component
4. Application of the ideal gas equation to ideal gas mixtures
Because there is no interaction between ideal gas molecules and the molecules themselves do not occupy volume, the pVT properties of ideal gases have nothing to do with the type of gas. Therefore, some molecules of an ideal gas are replaced by molecules of another ideal gas, forming a mixed ideal gas. , its pVT property does not change, but n in the ideal gas equation of state is the total amount of matter at this time.
5. Molar mass of mixture
The sum of the products of the molar masses of each substance in a mixture and its mole fractions
2. Dalton’s Law of Partial Pressure
1. partial pressure
Applicable conditions: real gas mixtures and ideal gas mixtures.
2. 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.
Applicable conditions: ideal gas mixture
Physical meaning: In an ideal gas mixture, the partial pressure of a component is equal to the pressure when the component exists alone and has the same temperature and volume as the mixture.
3. Arma’s law of divided volumes
1. Armaga’s Law of Partial Volume
The total volume V of an ideal gas mixture is the sum of the component volumes VB* of each component
Applicable conditions: ideal gas mixture
2. Partial volume of a component in an ideal gas mixture
Physical meaning: The partial volume VB* of substance B in an ideal gas mixture is equal to the volume occupied by pure gas B under the conditions of the temperature and total pressure of the mixture.
It shows that the volume of an ideal gas mixture is additive. At the same temperature and pressure, the total volume after mixing is equal to the sum of the volumes of the components before mixing.
4. The relationship between the two
`
Only two B subscripts can appear
5. Calculation of partial pressure of ideal gas mixture
1. Calculation under specified conditions
The required initial volume is
2. Calculation when status changes
3. kinetic theory of gas molecules
1. Microscopic model of gas molecular motion
1. Gas is composed of a large number of molecules. Gas molecules can be regarded as volumeless particles or hard balls. 2. Gas molecules are in endless and irregular thermal motion. 3. There is no interaction between gas molecules except for collisions with each other. 4. The collision between gas molecules and the gas against the wall are elastic collisions.
2. The pressure of ideal gas
3. Temperature of ideal gas
4. Proof of the Six Laws
4. real gas equation of state
1. The difference between real gas and ideal gas
1. In actual gases, when the temperature is constant, pV m constantly changes with the pressure.
2. Actual gas molecules themselves have a volume that is more difficult to compress than an ideal gas
3. Actual gas molecules have interaction forces (mainly gravity) and are easier to compress than ideal gases.
4. The attraction between actual gas molecules allows it to be liquefied
2. pVm-p diagram and Boyle temperature of real gas
1. pVm-p diagram of real gas
2. Boyle temperature
Boyle temperature is a property of matter (gas)
TB is generally 2 - 2.5 times that of Tc
Boyle temperature is high and gases tend to liquefy
3. Compression factor of real gas
definition
Z<1: easy to compress
Z>1: difficult to compress
Z=1: ideal gas
Note: 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.
4. Van der Waals equation
1. Pressure correction
2. Volume correction
5. Virial equation
5. Liquefaction and critical parameters of real gases
1. Saturated vapor pressure of liquid
1. Definition: The vapor pressure above the liquid surface when a pure liquid in a closed container is in gas-liquid equilibrium at a certain temperature and coexists.
2. Nature
Saturated vapor pressure is a unique property of pure substances and is determined by its nature
Saturated vapor pressure as a function of temperature
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 when the saturated vapor pressure of a liquid is equal to the external pressure
normal boiling point
The temperature when the saturated vapor pressure of the liquid is 101.325kPa
Relative humidity
2. p – Vm of real gas
1. T < Tc
Gas and liquid coexist on the gas-liquid equilibrium line g-l
2. T = Tc
At the critical point, the molar volumes and other properties of the gas and liquid phases are exactly the same, and the interface disappears and the gas and liquid phases cannot be distinguished. At this time
3. T > Tc
No matter how much pressure is applied, the gaseous state no longer changes to a liquid, and the isotherm becomes a smooth curve.
3. Critical parameters
When T=Tc, the liquid phase disappears and pressure can no longer liquefy the gas.
Tc Critical temperature: The highest temperature allowed for a gas to liquefy.
Since no liquid exists above the critical temperature, the curve for saturated vapor pressure p = f (T) ends at the critical temperature.
critical temperature Tc
The maximum temperature allowed for a gas to liquefy
critical pressure pc
Saturation vapor pressure at critical temperature The minimum pressure required to liquefy a gas at critical temperature
critical volume Vc
Volume at critical temperature and pressure
Critical parameters are characteristic parameters of matter
Critical compression factor Zc
6. Corresponding state principle and generalized compression factor diagram
1. Corresponding state principle
1. Define comparison parameters
pr=p/pc, Tr=T/Tc, Vr=Vm/Vc
2. Corresponding state principle
If two contrasting state parameters of different gases are equal to each other, the two gases are in corresponding states. When different gases are in corresponding states, certain physical properties (compression factor, fugacity coefficient, etc.) are the same or have a simple relationship
2. Compression factor diagram
3. Use of compression factor map
Given T and p, find Z and Vm
Given T and Vm, to find Z and pr, you need to draw auxiliary lines on the compression factor diagram.