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Some properties of a mixture can be calculated by using $X=\sum_{i=1}^n n_i X_i $, where X is a property of the mixture, $n_i$ and $X_i$ are mole fraction and property of the ith component.

The formula can be used to calculate mixture properties like density (an intensive property) and enthalpy (an extensive property) of the a mixture, but we cannot use the formula to calculate for example temperature of the mixture (intensive property).

Is there a rule to say the formula can be used for what kind of property of mixtures?

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  • $\begingroup$ The formula "perhaps" can be used to calculate mixture properties. But they often can't. One example is the Gibbs free energy of mixing, since the entropy of mixing decidedly cannot be represented in that way. $\endgroup$
    – Jon Custer
    Commented May 18, 2022 at 19:46
  • $\begingroup$ @JonCuster thanks for pointing out, it is enthalpy, corrected. $\endgroup$
    – Ebi
    Commented May 18, 2022 at 20:05
  • $\begingroup$ Enthalpy for an ideal solution, yes. For a regular solution, much less most real solutions, that form is no longer suitable. $\endgroup$
    – Jon Custer
    Commented May 18, 2022 at 20:07
  • $\begingroup$ Your equation can't be used for density, and, for an ideal solution, it can be used in terms of mole fractions for molar volume. $\endgroup$ Commented May 18, 2022 at 21:32

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Wikipedia article on Dalton's law lists several other "laws" for various quantities in gas mixtures: some of them simply add (like pressures in the Dalton's law), while the others add with proportionality coefficients.

The basic premise of most of these laws is that we are talking about a mixture of ideal gases, which do not interact among themselves. The idea ultimately traces to adding independent events in probability theory, and the validity for every quantity needs to be examined on the basis of what it means and how it is related to other quantities.

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  • $\begingroup$ thanks for your answer. What I would like to learn is the foormula is applicable to what kind of properties of ideal gas? $\endgroup$
    – Ebi
    Commented May 19, 2022 at 15:01

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