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phantomvommand
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Hi guys,
We have this very common graph where pV deviates from ideality.
May I know the equation for such a curve?
Secondly, if the x-axis were changed to V, what would the graph look like?
Mathematical equation for the deviation from ideality of real gases
- Thread starter phantomvommand
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In summary, the equation for the curve where pV deviates from ideality is represented by the compressibility factor Z, which is a function of reduced pressure, reduced temperature, and ascentric factor. Changing the x-axis to V would result in a graph of Z as a function of reduced volume. More information can be found in textbooks such as P.W. Atkins' physical chemistry.
Hi guys,
We have this very common graph where pV deviates from ideality.
May I know the equation for such a curve?
Secondly, if the x-axis were changed to V, what would the graph look like?
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BvU
Science Advisor
Homework Helper
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The vertical axis is labelled incorrectly. It should read $$\frac{PV}{RT}$$where V is the molar volume. This is called the compressibility factor Z. According to the Principle of Corresponding States, Z is a function of the reduced pressure ##P/P_C##, the reduced temperature ##T/T_C##, and the ascentric factor ##\omega##, where the subscript C indicates the value at the critical point and where ##\omega## varies with the specific gas. Graphs of Z as a function of reduced temperature, reduced pressure, and ascentric factor can be found in most thermo books.phantomvommand said:
1. What is the mathematical equation for the deviation from ideality of real gases?
The mathematical equation for the deviation from ideality of real gases is known as the Van der Waals equation. It is given by:
(P + a(n/V)^2)(V - nb) = nRT
Where P is the pressure, V is the volume, n is the number of moles, T is the temperature, a is a constant related to intermolecular forces, and b is a constant related to the volume of the gas molecules.
2. How is the Van der Waals equation different from the ideal gas law?
The Van der Waals equation takes into account the non-ideal behavior of real gases, while the ideal gas law assumes that gases behave ideally. The Van der Waals equation includes two additional parameters, a and b, which account for the attractive forces between gas molecules and the volume occupied by the gas molecules, respectively.
3. What does the constant 'a' represent in the Van der Waals equation?
The constant 'a' in the Van der Waals equation represents the strength of the intermolecular forces between gas molecules. It is a measure of how much the gas molecules attract each other, and it is different for each gas.
4. How does temperature affect the deviation from ideality of real gases?
As temperature increases, the deviation from ideality decreases for real gases. This is because at higher temperatures, gas molecules have more kinetic energy and are able to overcome the attractive forces between them, making them behave more ideally.
5. Can the Van der Waals equation accurately predict the behavior of all real gases?
No, the Van der Waals equation is an approximation and cannot accurately predict the behavior of all real gases. It is most accurate for gases at low pressures and high temperatures, and it becomes less accurate at high pressures and low temperatures.
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