Gmtsing=AHmixing -TASmiring = 2ZAc{xA-xi}+ RT{x,Inx4+x,Inx,}
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![The image depicts a thermodynamic equation describing the Gibbs free energy change of mixing, \(\Delta \overline{G}_{\text{mixing}}\). The equation is shown as follows:
\[
\Delta \overline{G}_{\text{mixing}} = \Delta \overline{H}_{\text{mixing}} - T \Delta \overline{S}_{\text{mixing}}
\]
This expression can also be written in expanded form as:
\[
= 2Z \Delta \varepsilon \{ x_A - x_A^2 \} + RT \{ x_A \ln x_A + x_B \ln x_B \}
\]
Where:
- \( \Delta \overline{H}_{\text{mixing}} \) is the enthalpy change of mixing.
- \( T \Delta \overline{S}_{\text{mixing}} \) is the temperature multiplied by the entropy change of mixing.
- \( Z \) represents a coordination number.
- \( \Delta \varepsilon \) is the difference in interaction energies.
- \( x_A \) and \( x_B \) are the mole fractions of components A and B, respectively.
- \( RT \) is the product of the gas constant \( R \) and temperature \( T \).
- \( \ln \) refers to the natural logarithm.
This equation is used to determine the free energy change when two components are mixed, taking into account both enthalpic and entropic contributions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7fb77b93-067c-4e79-8948-ff1235e31cff%2F2a92c191-f838-40ab-af54-1a6c9c56d23c%2F9o5g5o_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The image depicts a thermodynamic equation describing the Gibbs free energy change of mixing, \(\Delta \overline{G}_{\text{mixing}}\). The equation is shown as follows:
\[
\Delta \overline{G}_{\text{mixing}} = \Delta \overline{H}_{\text{mixing}} - T \Delta \overline{S}_{\text{mixing}}
\]
This expression can also be written in expanded form as:
\[
= 2Z \Delta \varepsilon \{ x_A - x_A^2 \} + RT \{ x_A \ln x_A + x_B \ln x_B \}
\]
Where:
- \( \Delta \overline{H}_{\text{mixing}} \) is the enthalpy change of mixing.
- \( T \Delta \overline{S}_{\text{mixing}} \) is the temperature multiplied by the entropy change of mixing.
- \( Z \) represents a coordination number.
- \( \Delta \varepsilon \) is the difference in interaction energies.
- \( x_A \) and \( x_B \) are the mole fractions of components A and B, respectively.
- \( RT \) is the product of the gas constant \( R \) and temperature \( T \).
- \( \ln \) refers to the natural logarithm.
This equation is used to determine the free energy change when two components are mixed, taking into account both enthalpic and entropic contributions.
Transcribed Image Text:**Problem Statement:**
Derive the expression for the derivative of this expression with respect to \( x_A \) (i.e., \( \frac{d \left( \Delta \bar{G}_{\text{mixing}} \right)}{dx_A} \)).
*Note: There are no graphs or diagrams accompanying this text.*
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