# Entropy Changes in Mixing Ideal Gases

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In this Demonstration, ideal gases and are mixed isothermally by keeping the total volume constant (remove barrier option) or by adding gas to gas so the final volume is the same as the initial volume of (select "compress right"). Click the play button next to "mix gases" to initiate mixing. For "remove barrier", the entropy change of each gas is the same as that of a gas expanding into a vacuum. When the partial pressure decreases, entropy increases. For "compress right", if the partial pressure of a gas does not change, its entropy does not change, even when mixed with another gas. The total entropy change is the sum of the entropy changes of each gas. Gas is colored red and gas is colored blue, and when the gases mix, different shades of purple result, depending on the ratio of moles of each species. As the pressures increase, the color becomes more intense. When the initial pressures of and are equal and the "remove barrier" is selected, which corresponds to mixing at constant pressure, the entropy of mixing is , where and are the mole fractions of and in the final mixture.

Contributed by: Derek M. Machalek (June 2015)

Additional contributions by: John L. Falconer and Rachael L. Baumann

(University of Colorado Boulder, Department of Chemical and Biological Engineering)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

The total volume of the container is 2

,

,

,

or

,

,

where represents the number of moles, is the gas constant (J/[K mo]), is the entropy change (J/K), is the pressure (bar), is the volume (), the subscripts and represent the gases used, and the subscripts and represent the final and initial pressures.

The screencast video at [1] explains how to use this Demonstration.

Reference

[1] *Entropy Changes in Mixing Ideal Gases*. www.colorado.edu/learncheme/thermodynamics/EntropyChangesMixingIdealGases.xhtml.

## Permanent Citation