Thermodynamics about mixtures of ideal gases and vapors

In summary, to determine the mole fraction of each component in a gaseous mixture with different volume and pressure from the components, you can use the Ideal Gas Law and the equation Xa = na/n.
  • #1
ppoorrttee
2
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My question:
For gaseous mixture say gas A, B, and C:

I knew that X or the mole fraction is equivalent to volumetric fraction, when those gases have pressure and temperature the same with the mixture, and for dalton's law, the summation of the pressure of gases is equivalent to that of the mixture when volume and temperature are the same.

Now, let say the volume and pressure of the components of the mixture is not equal with the mixture at the same time, how can I determine it? Can Xa=Va/Vm and Xa=Pa/Pm be equal at the same time?

Thank you.
 
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  • #2
Answer: Xa=Va/Vm and Xa=Pa/Pm cannot be equal at the same time unless the gas mixtures have the same volume and pressure as the components. However, you can use the Ideal Gas Law to calculate the mole fraction for each component in a gaseous mixture. The equation is PV = nRT, where P is the total pressure of the mixture, V is the total volume of the mixture, n is the total number of moles of all components, R is the universal gas constant, and T is the temperature of the mixture. Then you can calculate the mole fraction of each component using the equation Xa = na/n, where na is the number of moles of component A.
 

1. What is the ideal gas law and how does it relate to mixtures of gases and vapors?

The ideal gas law is a fundamental equation in thermodynamics that describes the relationship between pressure, volume, and temperature for an ideal gas. In mixtures of gases and vapors, the ideal gas law still applies, but it must be modified to account for the presence of multiple components. This is done by using the partial pressure of each component, which is the pressure that the component would exert if it were the only gas present in the mixture.

2. How are the properties of mixtures of gases and vapors calculated?

The properties of mixtures of gases and vapors can be calculated using Dalton's law of partial pressures, which states that the total pressure of a mixture of gases is equal to the sum of the partial pressures of each component. Additionally, the mole fraction of each component in the mixture can be used to calculate the overall properties, such as the average molecular weight and specific heat capacity.

3. What is the difference between an ideal gas and a real gas?

An ideal gas is a theoretical concept that follows the assumptions of the ideal gas law, such as having no intermolecular forces and occupying no volume. Real gases do not necessarily follow these assumptions and may deviate from the ideal gas law at high pressures or low temperatures. However, mixtures of ideal gases and vapors can still be used to approximate the behavior of real gases in many cases.

4. How does the concept of entropy apply to mixtures of ideal gases and vapors?

Entropy is a measure of the disorder or randomness in a system, and it plays a crucial role in thermodynamics. In mixtures of ideal gases and vapors, the total entropy of the system is the sum of the individual entropies of each component. This can be used to calculate the change in entropy during processes involving mixtures of gases and vapors.

5. Can mixtures of ideal gases and vapors undergo phase changes?

Yes, mixtures of ideal gases and vapors can undergo phase changes, such as condensation or evaporation, just like pure substances. However, the behavior of each component in the mixture must be considered, as they may have different boiling points and vapor pressures. The composition and partial pressures of the components can also change during these phase changes.

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