### Selectivity of Gases in an MOF

## by Patrick LePochat

Submitted : Fall 2013

We evaluated the selectivity of CO_{2} and N_{2} at a constant temperature of 298K and different pressures to establish a selectivity curve for these two substances in a specific Metal-Organic Framework (MOF) nicknamed SIFSIX-2-Cu-i. Using the Dual-Site Langmuir Freundlich equation we were able to take the anti-derivative and solve for the unknowns x_{1} and x_{2}. Because there are two unknowns it was especially tricky, the sum of the two x values must equal 1. All of this work was done with knowledge of calculus II and either by hand or using a calculator with accuracy to within 0.0000000002999% error. This MOF is practical because it absorbs a higher ratio of CO_{2} to its partial pressure than N_{2} to its partial pressure. Lastly we produced a graph and chart of our findings and using this information an equation for a line emerged to be used with the two compounds at any pressure.

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