The ideal gas equation of state, also known as the ideal gas law and the universal gas law, is a state equation describing the relationship between pressure, volume, mass of matter, and temperature when an ideal gas is in equilibrium. It is based on empirical laws such as Boyle-Maulio’s law, Charlie’s law, and Guy-Lussac’s law.
Its equation is pV = nRT.
This equation has 4 variables:
- p is the pressure of the ideal gas,
- V is the volume of the ideal gas,
- n is the amount of gaseous matter, and
- T is the thermodynamic temperature of the ideal gas,
- there is a constant: R is the ideal gas constant.
It can be seen that there are many variables in this equation. Therefore, this equation is famous for its many variables and wide application range, and it is approximately applicable to air at normal temperature and pressure.
Ideal gas equation of state
PV = nRT
, An equation describing the changing law of the ideal gas state. Caboron Yu merged Boyle’s law and Guy-Lussac’s law.
It is hereby clarified that some domestic textbooks equate the ideal gas equation of state with the Clapron equation, which is incorrect. Although the ideal gas equation of state was proposed by Klaberon, the Klaberon equation describes the physical quantities of phase equilibrium.
According to international conventions, the equation of state of ideal gas is called State Equation of Ideal Gas or Ideal Gas law, and the synonym of Clapeyron Equation is Clausius-Clapeyron Relation or Clapeyron Equation. A lot of Baidu knows and confuses this with the previous Baidu Encyclopedia.
Functional relationship between its state parameter pressure p, volume V and absolute temperature T
Where M and n are the molar mass and mass of the ideal gas, respectively, R is the gas constant. p is the ideal gas pressure in Pa. V is the gas volume in m3. n is the amount of gaseous substance, unit is mol, T is system temperature, unit is K.
For a mixed ideal gas, its pressure p is the sum of the partial pressures p1, p2, … of each component, so: (p1 + p2 + …) V = (n1 + n2 + …) RT, where n1, n2, … … is the amount of substance in each component.
The above two equations are the equations of state of the ideal gas and the mixed ideal gas, which can be derived from the gas law strictly followed by the ideal gas, and can also be derived from the gas kinetic theory according to the micro model of the ideal gas.
When the pressure is below a few atmospheric pressures, various actual gases approximately follow the equation of the ideal gas state. The lower the pressure, the better the compliance, and strictly adhere to the limit where the pressure approaches zero.
R is a proportionality coefficient, and the value is different under different conditions, and the unit is J / (mol · K).
In the equation of state expressed by moles, R is a proportional constant. For any ideal gas, R is constant, which is about 8.31441 ± 0.00026J / (mol · K).
If mass is used to represent the equation of state, pV = mrT, at this time r is related to the type of gas, r = R / M, M is the average molar mass of this gas.
This relationship is expressed in terms of density: pM = ρRT (M is the molar mass and ρ is the density).
The ideal gas equation of state is derived by studying the behavior of gases at low pressures. But each gas has some deviation when applying the ideal gas equation of state, the lower the pressure, the smaller the deviation, and the ideal gas equation of state can describe the gas behavior more accurately at very low pressure.
Very low pressure means that the distance between the molecules is very large, and the interaction between the molecules is very small, it also means that the volume occupied by the molecule itself is negligible compared with the very large volume of the gas at this time Therefore, the molecule can be approximated as a particle without a volume.
So triggered by the behaviour of very low pressure gas, the concept of ideal gas is abstracted.
The ideal gas has the characteristics of no interaction force between molecules and the molecule itself does not occupy volume.
Derivation of the law of experience
(1) Boyle’s Law (Bose – Ma’s Law) (Boyles’s Law)
When n and T are constant, V and p are inversely proportional, that is, V∝ (1 / p) ①
(2) Cover – Lussac’s Law (Gay-Lussac’s Law)
When p, n is constant, V, T is proportional, that is V∝T ②
(3) Charles’ law (Charles’s Law)
When n and V are constant, T and p are proportional, that is p∝T ③
(4) Avogadro’s law (Avogadro’s Law)
When T, p is constant, V, n is proportional, that is V∝n ④
V∝ （nT / p） ⑤
Adding ⑤ to the proportional coefficient R gives
V = (nRT) / p ie pV = nRT
Problems in real gas will be biased when the ideal gas equation of state is applied to real gas, because the basic assumption of ideal gas does not hold true in real gas.
For example, the volume of 1 mol acetylene at 20°C and 101kPa is 24.1 dm3, and also at 20°C, at 842 kPa, the volume is 0.114 dm3. They differ greatly because it is not an ideal gas to.
In general, the boiling point of the low gas at higher temperature and lower pressure, closer to an ideal gas, such as oxygen having a boiling point of -183 deg. C, hydrogen gas having a boiling point of -253 deg. C, at normal temperature and pressure are the molar volume and the ideal value differs only by about 0.1%, and the boiling point of sulfur dioxide is -10°C. The difference between the molar volume and the ideal value at normal temperature and pressure has reached 2.4%.
Although completely ideal gases are not possible, many actual gases, especially those that are not easy to liquefy and condensate (such as helium, hydrogen, oxygen, nitrogen, etc.), because helium is not only small in size but small in interaction with each other.
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It is also the most difficult to liquefy of all gases, so it is the gas closest to the ideal gas among all gases.) The properties at normal temperature and pressure are very close to the ideal gas.
In addition, sometimes only a rough estimate is needed, and using this equation will make the calculation a lot easier.
It is worth noting that the equivalent of the ideal gas equation to the Klaberon equation is incorrect. The general Craberon equation refers to the equation dp / dT = L / (TΔv) describing the phase equilibrium. Although the law of ideal gas was discovered by Klaberon, the equation of state of ideal gas is not called the Klaberon equation internationally.
Mathematically speaking, when an equation contains only one unknown, the unknown can be calculated. Therefore, of the four quantities of pressure, volume, temperature, and the amount of the contained substance, the fourth quantity can be calculated by knowing only three of them. This equation can be converted into the following 4 equivalent formulas according to the different calculation goals:
Find the pressure: p = nRT / v
Find the volume: v = nRT / p
Find the amount of substances: n = pv / RT
Find the temperature: T = pv / nR
Computing chemical equilibrium problems
According to the ideal gas state equation, it can be used to calculate the chemical equilibrium problem of gas reaction.
According to the ideal gas state equation, the following inference can be obtained:
When the temperature and volume are constant, the ratio of the gas pressure to the amount of the contained substance is the same, so that P flat / P start = n flat / n start
When the temperature and pressure are constant, the ratio of the volume ratio of the gas to the amount of the substance contained in the gas is the same, that is, V flat / V start = n flat / n start
By combining the equations of chemical reactions, it is easy to determine the conversion rate of a substance after the chemical reaction reaches equilibrium.