Difference between revisions of "Tutorial 2: entropy of mixing of methanol+water"

Revision as of 07:46, 20 April 2017

This tutorial is currently under construction

When two pure liquids are put in contact the new configurations that the molecules can adopt and the new molecular interactions will lead to a change in entropy. Typically, this change is positive because of disorder, although in principle specific molecular interactions can lead to a decrease in entropy in some cases. For ideal gases, the entropy of mixing has an analytical expression, and it depends only on the relative number of molecules of each component in the mixture. The total entropy of a mixture of ideal gases is:

[math]S_\text{mixture}^\text{ideal} = \sum\limits_\Lambda N_\Lambda \bar{S}_\Lambda - k_\text{B} \sum\limits_\Lambda N_\Lambda \ln{\left(\frac{N_\Lambda}{N}\right)},[/math]

where [math]N_\Lambda[/math] is the number of molecules of component [math]\Lambda[/math] and [math]N[/math] is the total number of molecules. [math]\bar{S}_\Lambda[/math] refers to the entropy per molecule in the pure component [math]\Lambda[/math]. For real mixtures, one defines the excess entropy of mixture [math]S_\text{mix}^\text{E}[/math] to account for the deviation of the mixing entropy with respect to what one would expect for ideal systems:

[math]S_\text{mix}^\text{E} = S_\text{mixture}^\text{real} - S_\text{mixture}^\text{ideal}[/math].

In this tutorial we will calculate [math]S_\text{mix}^\text{E}[/math] for a 1:1 mixture of water and methanol. More detailed information can be found in Ref.^[1]

Generating the trajectories