# 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

\[V_{mixture}=V_A+V_B+V_C+\dots\]

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

\[V_A=\frac{n_ART}{P_{mixture}}\]

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 \(V_A=x_AV_{mixture}\).