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MindMap Gallery Physical Chemistry - Gas Properties
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Physical Chemistry - Gas Properties
Relevant basic content about gas properties in physical chemistry, including the compilation of "perfect gas", "dynamic theoretical model", "actual gas", etc. The main content comes from Physical Chemistry by Peter Atkins
Edited at 2022-08-02 18:09:14
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Physical Chemistry - Gas Properties
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- Outline
Gas properties
perfect gas
1. The equations related to perfect gases provide the basis for the establishment of many relations in thermodynamics. The perfect gas law is also a good first-order approximation to explain the properties of actual gases; 2. The perfect gas law established based on a series of experimental phenomena is the limit law of actual gases when the pressure tends to zero. As the pressure of actual gases decreases, the degree of compliance increases; (core idea).
1.1State variables The physical state of a substance is determined by its physical properties. Two samples of the same substance with the same physical properties are in the same state. The variables used to characterize the state of a system include the amount of material it contains n, the volume it occupies V, the pressure p and the temperature T.
1.1.1 Pressure
The force of gas comes from the force generated by the continuous impact of molecules on the container wall.
unit
1.1.2 Temperature
Temperature is a property that determines the direction in which energy is transferred thermally when two objects are in contact with each other through a thermal conductor: energy is transferred from a hot object to a cold object.
In this series of mind maps, the temperature marked with the Celsius temperature scale is marked with θ, and the unit is Celsius (℃) Gas pressure can be used to construct a perfect gas temperature scale, which is exactly the same as the thermodynamic temperature scale.
unit
In the thermodynamic temperature scale, temperature is represented by T, usually in Kelvin (K). The exact relationship between thermodynamic temperature and Celsius temperature is as follows: T/K=θ/℃ 273.15
1.2 Equation of state In principle, the state of a pure substance can be determined by specifying the values of n, V, p and T, but according to experience, only three variables are given. That is to say, each substance can be described by an equation that expresses the relationship between four variables, that is, the equation of state.
1.2.1 General formula of state equation
If n, V, and T of a specific substance are known, its p can also be determined.
Each substance has its own equation of state, but only in some specific cases are there clear and unambiguous laws
"Perfect gas" equation of state: p=nRT/V R is a constant independent of gas type
1.2.1.1 Empirical laws
Boyle's law: PV=constant, n and T are constant
Molecular level explanation: When the gas sample is compressed to half of its original volume, the number of molecules colliding with the wall of the device in a given period is twice that before compression, so the average force of the gas molecules on the wall will also double, so pV is still constant
charles law V=constant*T, n and p are constant p=constant*T, n and V are constant
limit law
The limit law is strictly true only at a specific limit (here p→0). Although many relationships are strictly true only when p→0, they are still reasonable and reliable at normal pressure (p≈1 bar) and are commonly used in chemical systems.
Avogadro's principle V=constant*n, T and p are constant
perfect gas law pV=nRT
The lower the pressure, the more a real gas behaves like a perfect gas. At standard room temperature and standard pressure (298.15K and 1bar), the molar volume of a perfect gas, Vm=V/n, can be obtained as Vm=24.789dm^3·mol^-1
1.2.1.2 Gas mixture
partial pressure
When working with gas mixtures, it is important to know the contribution of each component to the total pressure in the sample
partial pressure
The sum of all partial pressures equals the total pressure
When all components are perfect gases, the partial pressure of each component corresponds to the pressure that the gas would have if it were placed alone in a container of the same volume and at the same temperature. (Original meaning of the concept of partial pressure)
The basis of the original formula of Dalton's Law: The pressure of a mixed gas is the sum of the pressures that each component would have if it existed alone and occupied the same volume.
concept list
1. The physical state of matter, that is, physical conditions, is determined by its physical properties
2. Force balance is the condition that the pressure on both sides of the shared movable partition is equal.
3. The equation of state is an equation that relates the variables that determine the state of matter.
4. Boyle’s law and Charles’ law are both limit laws, which are only true at a certain limit (p→0)
5. Isotherms refer to curves corresponding to the same temperature
6. Isobars refer to curves corresponding to the same pressure
7. Isovolumetric lines refer to curves corresponding to the same volume along the way.
8. A perfect gas is a gas that obeys the perfect gas law under all conditions.
9. Dalton's law states that the pressure of a (perfect) gas mixture is the sum of the pressures that each component would have if it occupied the same volume.
dynamic theory model
Core idea: Gases are composed of molecules of negligible size that move irregularly and endlessly. Their collisions follow the laws of classical mechanics.
In the kinetic theory of gases (sometimes called kinetic molecular theory, kinetic molecular theory is abbreviated as KMT), it is assumed that gas energy comes only from the kinetic energy of the movement of gas molecules. The kinetic theory model is the most eye-catching and most important model in physical chemistry. One of the excellent models.
2.1 Model
Assumptions: 1. Gas is composed of molecules with mass m, which move irregularly and endlessly and obey the laws of classical mechanics; 2. Relative to the average distance that the molecules will move when they collide, the diameter of the molecule is very small and its size is negligible, similar to a "particle". 3. Molecules interact only through elastic collisions.
Elastic collision: elastic collision refers to a collision in which the total translational energy of molecules is conserved
Pressure and molecular velocity
Average square update rate
pressure and volume relationship
For a brief derivation process, please refer to Peter Atkins Physical Chemistry Special Topic 1B
Maxwell-Boltzmann rate distribution
The velocity distribution of individual gas molecules is very wide, and collisions ensure that the velocity of the gas molecules is constantly changing. If a molecule was moving quickly before a collision, it may accelerate at a faster rate after the collision and only slow down after the next collision. In order to calculate the mean square replacement rate, the fraction of molecules with a given rate at any instant must be known. The fraction of molecules in the range v to v dv is proportional to the width of the rate range and can be written as f(v)dv, where f(v) is called the rate distribution.
Maxwell-Boltzmann rate distribution function
For a brief derivation process, please refer to Peter Atkins Physical Chemistry Special Topic 1B
Gas constant (moles)
average value
Mean square rate<v^2>=3RT/M
Average square update rate V_rms=<v^2>^1/2=(3RT/M)^1/2
Average relative velocity (same molecules)
Mean relative velocity (perfect gas)
2.2 Collision
Collision frequency
Kinetic theory can be used to derive the collision frequency, z, which is the number of collisions of a molecule divided by the time interval in which these collisions occur
mean free path λ
The average distance a molecule moves between collisions
mean free path
Mean free path (perfect gas)
It can be seen that if the pressure is doubled, the mean free path is shortened to the original general
Typical gases such as oxygen and oxygen at 1 atm and 25°C can be thought of as a collection of molecules moving at an average speed of 500 m·s^-1 per month. Each molecule will collide once in about 1ns. Between the two collisions, it moves a distance of about 10^3 molecule diameters.
concept list
1. The theoretical model of gas molecular kinetics only considers the energy contribution from the kinetic energy of molecules.
2. Important conclusions of this model include the expressions of pressure and root-mean-square velocity
3. The Maxwell-Boltzmann rate distribution gives the fraction of molecules within a specified rate range
4. The collision frequency is equal to the average number of molecular collisions within a certain time interval divided by the length of the time interval.
5. The mean free path is the average distance that a molecule moves between collisions.
real gas
Real gases have different properties than perfect gases. Furthermore, studying deviations from perfect gas behavior can provide insights into the nature of intermolecular interactions. The attractive and repulsive forces between gas molecules explain modifications to the gas isotherm and illustrate its critical behavior.
3.1 Deviation from perfect gas behavior
The deviation of real gases from the perfect gas law is due to interactions between molecules. The repulsive force between molecules favors expansion, while the attractive force favors compression.
The repulsive force is significant only when the molecules are almost in contact, and the repulsive force is a short-range interaction, even as short as the diameter of the molecule. Because repulsive forces are short-range interactions, a significant contribution from repulsive forces can only be expected when the average distance between molecules is small.
Intermolecular attractions have a relatively long range and are effective within a few molecular diameters; they are strong when the molecules are relatively crystalline and have no contact, and are ineffective when the molecules are far apart. Intermolecular forces are also important when the temperature is so low that the molecules move at a rather slow average rate and the molecules can easily become trapped by other molecules.
3.1.1 Compression factor·
The compression factor Z is the ratio of the measured molar volume of a gas Vm=V/energy to the molar volume of a perfect gas at the same pressure and temperature.
∵The molar volume of a perfect gas is RT/p ∴The equivalent expression is Z=pVm/RT ∴There is pVm=RTZ
At very low pressures, all gases Z≈1 and tend to be perfect gases
At higher pressures, all gases have Z>1, indicating that their molar volumes are larger than those of perfect gases, and repulsive forces dominate.
At moderate pressures, most gases have Z < 1, indicating that attractive forces reduce molar volume relative to a perfect gas.
3.1.2 Virial coefficient
At large molar volumes and high temperatures, the isotherms for actual volumes are not very different from those for perfect gases. This small difference shows that; in fact the perfect gas law is the first term in the subordinate expression
virial equation of state
Coefficients B, C, etc. are related to temperature, and are the second, third... Virial coefficients respectively; The first virial coefficient is 1.
The value of the virial coefficient of a gas can be determined by measuring its compression factor
3.1.3 Critical constant
Critical temperature
Separating the two behavioral regions of matter plays a special role in the theory of states of matter.
The behavior of an isotherm below the critical temperature is: at a certain pressure, a gas condenses into a liquid, and there is a visible interface between the gas and the liquid. However, if compression occurs at the critical temperature, no interface separates the two phases appears, and the volumes at either end of the horizontal portion of the isotherm merge into a point, the critical point of the gas. The pressure and molar volume at the critical point become the critical pressure Pc and critical molar volume Vc of the substance. In summary, the critical constants of matter at critical pressure, critical volume, and critical temperature
At temperatures above the critical temperature, the sample is a single phase occupying the entire container. By definition, such a phase is a gas. Therefore, above the critical temperature, the liquid phase of a substance cannot form. When T>Tc, the single item that fills the entire container may be much denser than the gas usually considered, so it is more likely to be called a supercritical fluid.
van der Waals equation
van der Waals equation
a and b are both van der Waals coefficients
a represents the strength of the mutual attraction between molecules
b represents the strength of the mutual repulsion between molecules
Both are properties of each gas and are thought to be independent of temperature and related to physical properties of the strength of intermolecular interactions.
Main features
At high temperatures and large molar volumes, perfect gas isotherms are obtained.
When the effects of Xiyingli and repulsive forces are balanced, liquids and gases coexist
The critical constant is related to the van der Waals coefficient
contrastive state principle
In science, an important common technique for comparing the properties of different objects is to select relevant fundamental properties of the same kind and set a relative scale based on them. Critical constants are special properties of gases, so they can be used as rulers to establish relative quantities, while dividing the actual variable by the corresponding critical constant introduces a comparative variable of dimension 1 for the gas.
Under the same contrast volume and contrast temperature, different gases have the same contrast pressure. This phenomenon is compared with the state principle of Chen Wei.
This principle only approximately applies best to gases composed of spherical molecules; when the molecules are non-spherical or polar, the principle does not apply, sometimes quite badly.
concept list
1. Summarize the degree of deviation from perfect gas behavior by introducing a compression factor
2. The Virial equation of state is an empirical expansion of the perfect gas equation of state, which summarizes the behavior of actual gases under a series of conditions.
3. The isotherms of actual gases introduce the concept of critical behavior
4. A gas can be liquefied through compression only when its temperature is equal to or lower than its critical temperature.
5. The van der Waals equation is a model equation of the actual gas state represented by two parameters. One coefficient (a) represents the attraction of molecules, and the other coefficient (b) represents the repulsion of molecules.
6. The van der Waals equation captures the general characteristics of real gas behavior, including its critical behavior
7. By comparing variables to express the state equation, the properties of actual gases can be harmonized and unified.