Enthalpy of Mixing and Deviation from Raoult's Law: Screencasts

Illustrates the changes in state variables (V, H, U, S, G) when ideal solutions form.

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Describes how to use a diagram of enthalpy versus weight percent for a binary mixture to determine the final temperature when mixing is adiabatic.

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For nonideal solutions, positive or negative deviations from Raoult’s law correlate with whether the heat of mixing is positive or negative. Examples are presented for a binary mixture.

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Important Equations:

For an ideal solution: $H = x_AH_A + x_BH_B$ where $$H$$ is the enthalpy (kJ/mol) of the binary solution, $$x_A$$ and $$x_B$$ are mole fractions of the two components, and $$H_A$$ and $$H_B$$ are the molar enthalpies (kJ/mol) of the pure components at the same temperature as the enthalpy of the solution.

A non-ideal solution can be represented as: $H = x_AH_A + x_BH_B + \alpha x_Ax_B$ where $$\alpha$$ is a non ideal parameter. $\Delta H_{mix} = H – x_AH_A – x_BH_B = \alpha x_Ax_B$ where $$\Delta H_{mix}$$ is the heat of mixing at constant temperature. $\Delta H_{mix} = H^E$ where $$H^E$$ is the excess enthalpy.

Modified Raoult’s Law: $x_i\gamma_iP_i^{sat} = y_iP$ where $$x_i$$ is the liquid phase mole fraction of component $$i$$,

$$\gamma_i$$ is the activity coefficient of component $$i$$,

$$P_i^{sat}$$ is the saturation pressure of component $$i$$,

$$y_i$$ is the vapor phase mole fraction of component $$i$$, and

$$P$$ is pressure.