# 2.15: Gas Mixtures - Amagat's Law of Partial Volums

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Amagat’s law of partial volumes asserts that the volume of a mixture is equal to the sum of the partial volumes of its components. For a mixture of components $$A$$, $$B$$, $$C$$, etc., Amagat’s law gives the volume as

$V_{mixture}=V_A+V_B+V_C+\dots \nonumber$

For real gases, Amagat’s law is usually an even better approximation than Dalton’s law$${}^{6}$$. Again, for mixtures of ideal gases, it is exact. For an ideal gas, the partial volume is

$V_A=\frac{n_ART}{P_{mixture}} \nonumber$

Since $$n_{mixture}=n_A+n_B+n_C+\dots$$, we have, for a mixture of ideal gases,

\begin{align*} V_{mixture}&=\frac{n_{mixture}RT}{P_{mixture}} \\[4pt] &=\frac{\left(n_A+n_B+n_C+\dots \right)RT}{P_{mixture}} \\[4pt] &=V_A+V_B+V_C+\dots \end{align*}

Applied to the mixture, the ideal-gas equation yields Amagat’s law. Also, we have $$V_A=x_AV_{mixture}$$.

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