#### Gas-Phase Chemical Equilibrium: Screencasts

Explains why the equilibrium constant is dimensionless and why it is independent of pressure.

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Derives the Van’t Hoff equation that shows how the equilibrium constant changes as temperature changes and simplifies for the case that the heat of reaction is constant.

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Discusses the effect of adding an inert gas at constant temperature to a chemical reaction at equilibrium at either constant pressure or constant volume.

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##### Important Equations:

Change in Gibbs free energy of a reaction at standard conditions:

$\Delta G^{\circ} _T = \sum _i \nu _i \Delta G^{\circ} _{f,i}$

where $$\Delta G^{\circ} _T$$ = change in Gibbs free energy at standard conditions (ideal gas at 1 bar pressure for gases) at temperature $$T$$,

$$\nu _i$$ = stoichiometric coefficient for component $$i$$

$$\Delta G^{\circ} _{f,i}$$ = Gibbs free energy of formation of component $$i$$ at the same temperature $$T$$.

$exp \left( -\frac{\Delta G^{\circ} _T}{RT} \right) = K_a$

where $$R$$ = ideal gas constant,

$$T$$ = absolute temperature

$$K_a$$ = equilibrium constant, which is dimensionless.

The pure component fugacity at 1 bar for an ideal gas is 1 bar.

For ideal gases:

$K_a = \prod _i (y_iP)^{\nu _i}$

where $$y_i$$ = gas-phase mole fraction.

$\frac{\partial (\Delta G^{\circ} _T/RT)}{\partial T} = \frac{\partial (-lnK_a)}{\partial T} = -\frac{\Delta H^{\circ} _T}{RT^2}$

where $$\Delta H^{\circ} _T$$ = heat of reaction at standard conditions at temperature $$T$$.

If the heat of reaction is assumed independent of temperature (a reasonable assumption for many reactions if the temperature range is not too large):

$ln \left( \frac{K_2}{K_1} \right) = \frac{\Delta G^{\circ} _1}{RT_1} – \frac{\Delta G^{\circ} _2}{RT_2} = -\frac{\Delta H^{\circ} _{rxn}}{R} \left( \frac{1}{T_2} – \frac{1}{T_1} \right)$

where $$K_1$$ and $$K_2$$ are equilibrium constants at absolute temperatures $$T_1$$ and $$T_2$$ respectively

$$\Delta H^{\circ} _{rxn}$$ = heat of reaction, which is independent of temperature.

$K_a = P\hat{a}^{\nu_i} _i$

where $$\hat{a} _i = \hat{f}_i /f^{\circ} _i$$ which is the thermodynamic activity,

$$\hat{f} _i$$ = fugacity of component $$i$$ in the mixture

$$f^{\circ} _i$$ = fugacity of the pure component $$i$$ at standard pressure (1 bar) and the temperature of the system.