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- https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/DeVoes_Thermodynamics_and_Chemistry/11%3A_Reactions_and_Other_Chemical_Processes/11.09%3A_Effects_of_Temperature_and_Pressure_on_Equilibrium_PositionTo investigate this effect, we write the total differential of \(G\) with \(T\), \(p\), and \(\xi\) as independent variables \begin{equation} \dif G = -S\dif T + V\difp + \Delsub{r}G\dif\xi \tag{11.9....To investigate this effect, we write the total differential of \(G\) with \(T\), \(p\), and \(\xi\) as independent variables \begin{equation} \dif G = -S\dif T + V\difp + \Delsub{r}G\dif\xi \tag{11.9.1} \end{equation} and obtain the reciprocity relations \begin{equation} \Pd{\Delsub{r}G}{T}{p, \xi} = -\Pd{S}{\xi}{T,p} \qquad \Pd{\Delsub{r}G}{p}{T, \xi} = \Pd{V}{\xi}{T,p} \tag{11.9.2} \end{equation} We recognize the partial derivative on the right side of each of these relations as a molar diffe…
- https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/DeVoes_Thermodynamics_and_Chemistry/05%3A_Thermodynamic_Potentials/5.04%3A_Closed_Systems5.3.4–5.3.6 with \begin{equation} \dif U = T\dif S-p\dif V \tag{5.4.1} \end{equation} to obtain \begin{equation} \dif H = T \dif S + V \difp \tag{5.4.2} \end{equation} \begin{equation} \dif A = -S \di...5.3.4–5.3.6 with \begin{equation} \dif U = T\dif S-p\dif V \tag{5.4.1} \end{equation} to obtain \begin{equation} \dif H = T \dif S + V \difp \tag{5.4.2} \end{equation} \begin{equation} \dif A = -S \dif T - p \dif V \tag{5.4.3} \end{equation} \begin{equation} \dif G = -S \dif T + V \difp \tag{5.4.4} \end{equation} Equations 5.4.1–5.4.4 are sometimes called the Gibbs equations.
- https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/DeVoes_Thermodynamics_and_Chemistry/14%3A_Galvanic_Cells/14.02%3A_Electric_Potentials_in_the_Cell
- https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/DeVoes_Thermodynamics_and_Chemistry/07%3A_Pure_Substances_in_Single_Phases\( \newcommand{\ljn}{\hspace3pt\lower.3ex{\Rule{.6pt}{.5ex}{0ex}}\hspace-.6pt\raise.45ex{\Rule{.6pt}{.5ex}{0ex}}\hspace-.6pt\raise1.2ex{\Rule{.6pt}{.5ex}{0ex}} \hspace3pt} \) \( \newcommand{\lljn}{\hs...\( \newcommand{\ljn}{\hspace3pt\lower.3ex{\Rule{.6pt}{.5ex}{0ex}}\hspace-.6pt\raise.45ex{\Rule{.6pt}{.5ex}{0ex}}\hspace-.6pt\raise1.2ex{\Rule{.6pt}{.5ex}{0ex}} \hspace3pt} \) \( \newcommand{\lljn}{\hspace3pt\lower.3ex{\Rule{.6pt}{.5ex}{0ex}}\hspace-.6pt\raise.45ex{\Rule{.6pt}{.5ex}{0ex}}\hspace-.6pt\raise1.2ex{\Rule{.6pt}{.5ex}{0ex}}\hspace1.4pt\lower.3ex{\Rule{.6pt}{.5ex}{0ex}}\hspace-.6pt\raise.45ex{\Rule{.6pt}{.5ex}{0ex}}\hspace-.6pt\raise1.2ex{\Rule{.6pt}{.5ex}{0ex}}\hspace3pt} \)
- https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/DeVoes_Thermodynamics_and_Chemistry/06%3A_The_Third_Law_and_Cryogenics\( \newcommand{\ljn}{\hspace3pt\lower.3ex{\Rule{.6pt}{.5ex}{0ex}}\hspace-.6pt\raise.45ex{\Rule{.6pt}{.5ex}{0ex}}\hspace-.6pt\raise1.2ex{\Rule{.6pt}{.5ex}{0ex}} \hspace3pt} \) \( \newcommand{\lljn}{\hs...\( \newcommand{\ljn}{\hspace3pt\lower.3ex{\Rule{.6pt}{.5ex}{0ex}}\hspace-.6pt\raise.45ex{\Rule{.6pt}{.5ex}{0ex}}\hspace-.6pt\raise1.2ex{\Rule{.6pt}{.5ex}{0ex}} \hspace3pt} \) \( \newcommand{\lljn}{\hspace3pt\lower.3ex{\Rule{.6pt}{.5ex}{0ex}}\hspace-.6pt\raise.45ex{\Rule{.6pt}{.5ex}{0ex}}\hspace-.6pt\raise1.2ex{\Rule{.6pt}{.5ex}{0ex}}\hspace1.4pt\lower.3ex{\Rule{.6pt}{.5ex}{0ex}}\hspace-.6pt\raise.45ex{\Rule{.6pt}{.5ex}{0ex}}\hspace-.6pt\raise1.2ex{\Rule{.6pt}{.5ex}{0ex}}\hspace3pt} \)
- https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/DeVoes_Thermodynamics_and_Chemistry/13%3A_The_Phase_Rule_and_Phase_Diagrams\( \newcommand{\ljn}{\hspace3pt\lower.3ex{\Rule{.6pt}{.5ex}{0ex}}\hspace-.6pt\raise.45ex{\Rule{.6pt}{.5ex}{0ex}}\hspace-.6pt\raise1.2ex{\Rule{.6pt}{.5ex}{0ex}} \hspace3pt} \) \( \newcommand{\lljn}{\hs...\( \newcommand{\ljn}{\hspace3pt\lower.3ex{\Rule{.6pt}{.5ex}{0ex}}\hspace-.6pt\raise.45ex{\Rule{.6pt}{.5ex}{0ex}}\hspace-.6pt\raise1.2ex{\Rule{.6pt}{.5ex}{0ex}} \hspace3pt} \) \( \newcommand{\lljn}{\hspace3pt\lower.3ex{\Rule{.6pt}{.5ex}{0ex}}\hspace-.6pt\raise.45ex{\Rule{.6pt}{.5ex}{0ex}}\hspace-.6pt\raise1.2ex{\Rule{.6pt}{.5ex}{0ex}}\hspace1.4pt\lower.3ex{\Rule{.6pt}{.5ex}{0ex}}\hspace-.6pt\raise.45ex{\Rule{.6pt}{.5ex}{0ex}}\hspace-.6pt\raise1.2ex{\Rule{.6pt}{.5ex}{0ex}}\hspace3pt} \)
- https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/DeVoes_Thermodynamics_and_Chemistry/07%3A_Pure_Substances_in_Single_Phases/7.09%3A_Standard_Molar_Quantities_of_a_Gas7.8.14 to obtain a relation between the chemical potential, the standard chemical potential, and measurable properties, all at the same temperature: \begin{gather} \s{ \mu(p') = \mu\st\gas + RT\ln\fra...7.8.14 to obtain a relation between the chemical potential, the standard chemical potential, and measurable properties, all at the same temperature: \begin{gather} \s{ \mu(p') = \mu\st\gas + RT\ln\frac{p'}{p\st} + \int_0^{p'}\!\! \left( V\m - \frac{RT}{p} \right)\difp } \tag{7.9.2} \cond{(pure gas)} \end{gather} Note that this expression for \(\mu\) is not what we would obtain by simply integrating \(\dif\mu=V\m \difp\) from \(p\st\) to \(p'\), because the real gas is not necessarily in its sta…
- https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/DeVoes_Thermodynamics_and_Chemistry/06%3A_The_Third_Law_and_Cryogenics/6.01%3A_The_Zero_of_Entropy“If the entropy of each element in some crystalline state be taken as zero at the absolute zero of temperature: every substance has a finite positive entropy, but at the absolute zero of temperature t...“If the entropy of each element in some crystalline state be taken as zero at the absolute zero of temperature: every substance has a finite positive entropy, but at the absolute zero of temperature the entropy may become zero, and does so become in the case of perfect crystalline substances.”
- https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/DeVoes_Thermodynamics_and_Chemistry/zz%3A_Back_Matter/10%3A_Index
- https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/DeVoes_Thermodynamics_and_Chemistry/09%3A_Mixtures/9.05%3A_Activity_Coefficients_in_Mixtures_of_NonelectrolytesThis e-book will use various symbols for activity coefficients, as indicated in the following list of expressions for the chemical potentials of nonelectrolytes: \begin{equation} \tx{Constituent of a ...This e-book will use various symbols for activity coefficients, as indicated in the following list of expressions for the chemical potentials of nonelectrolytes: \begin{equation} \tx{Constituent of a gas mixture} \quad \mu_i = \mu_i\rf\gas + RT\ln\left(\phi_i\frac{p_i}{p}\right) \tag{9.5.13} \end{equation} \begin{equation} \tx{Constituent of a liquid or solid mixture} \quad \mu_i = \mu_i^* + RT\ln\left(\g_i x_i\right) \tag{9.5.14} \end{equation} \begin{equation} \tx{Solvent of a solution} \quad…
- https://chem.libretexts.org/Courses/Lebanon_Valley_College/CHM_312%3A_Physical_Chemistry_II_(Lebanon_Valley_College)/05%3A_Single_Component_Phase_Equilibrium/5.02%3A_Chemical_Potential_and_FugacityLet \(\mu'\) be the chemical potential and \(\fug'\) be the fugacity at the pressure \(p'\) of interest; let \(\mu''\) be the chemical potential and \(\fug''\) be the fugacity of the same gas at some ...Let \(\mu'\) be the chemical potential and \(\fug'\) be the fugacity at the pressure \(p'\) of interest; let \(\mu''\) be the chemical potential and \(\fug''\) be the fugacity of the same gas at some low pressure \(p''\) (all at the same temperature).
