THERMODYNAMICS OF SOLUTIONS, MIXTURES AND ELECTROCHEMISTRY

Definiton of a solution

A homogenous mixture

Define solvent in terms of in a solution

Component in excess

Define solutes in terms of in a solution ?

Minor components in solution

Definition of Molality

Molar mass

$$m_{a}=\frac{n_{A}}{n_{B}M_{B}}$$

Where

$m_{A}$ - molar mass, $molkg^{-1}$

Denominator is mass of solute in solvent

Look at units and convert molar mass accordingly

Define Mole fraction of a species A

Molar fraction, unit less

$$x_{A}=\frac{n_{A}}{\sum n_{i}}$$

Total moles of A over all total mass in the solution

Definition of molarity

Molar concentration

$$c_{A}=\frac{n_{A}}{V}$$

What is the equation for IDEAL gas, in terms of chemical potential

$$\mu=\mu^{o}+RT\ln\frac{p}{p^{o}}$$

What is the change in gibbs reaction, at equillibrium, and why?

=0 at equilibrium

No net driving force

Forward and Backwards rates are constant

System is at minimum free energy

What is the Change in gibbs reaction when ideal gases are mixing

$\Delta G_{\operatorname{mi}x}=nRT\left(x_{A}\ln x_{A}+x_{B}\ln x_{B}\right)$

x_{i}\ln x_{i}<0 hence, mixing of ideal gas will always be spontaneous

What is the change in entropy of ideal gases mixing?

At equilibrium $\Delta H=0$ always for ideal gases

Hence using change in Gibbs energy equation

$$\Delta S_{\operatorname{mi}x}=-nRT\left(x_{A}\ln x_{A}+x_{B}\ln x_{B}\right)$$

What is fugacity

‘Effective’ pressure, correcting for non-ideality, resulting from intermolecular forces between gas molecules

$$f=\phi p$$

What is the equation for a REAL gas, in terms of chemical potential

$$\mu\left(T\right)=\mu^{o}\left(T\right)+RT\ln\frac{f}{p}$$

What is Raoults law

States that effective Vapor pressure of mixtures can be reduce the pure phase by its mole fraction in the actual solution

$$p_{A}=x_{A}p_{A}^{\ast}$$

What is the chemical potential of a component in an ideal solution (use Raoults law)

$$\mu_{A}=\mu_{H2O}^{\ast_{}}+RT\ln x_{H_2O}$$

What is an ideal solution

All intermolecular interactions are the same, so mixing causes no change in enthalpy or volume

All components of solution obey Raoults law

So interactions A-A = B-B = A-B

$$\Delta H_{\operatorname{mi}x}=0$$

$$\Delta V_{\operatorname{mi}x}=0$$

What is an ideal-dilute solution

Solute is present but is very diluted (solvent is major component)

Solvent obeys Raoults law (hence still ideal)

Solute obeys Henry’s law (ideal only at infinite dilution)

This is because solute-solvent interaction are NOT equal to solute-solute interactions

Henry’s Law

Rule that is made to describes the solute- solute interactions

$$p_{B}=x_{B}K_{B}$$

Boiling point elevation equation

$$\Delta T_{b}=x_{B}K_{B}$$

Where

$$K_{B}=\frac{RT^{\ast2}}{\Delta H_{vap}}$$

Depression of freezing point equation

$$\Delta T_{f}=x_{B}K_{B}$$

Where

$$K_{f}=\frac{RT^{\ast2}}{\Delta H_{fus}}$$

Van Hoffs osmotic pressure equation

$$\Pi=c_{B}RT$$

What is change in Gibbs energy of solvation

Required energy to solvate 1 mole of gaseous ions into 1 mole of aqueous ions

Gibbs energy of solvation equation

$$\Delta G_{solvation}=N_{A}\left(\frac{z_{i}^2e_{i}^2}{8\pi\epsilon_0r_{i}}\right)\left(\frac{1}{\epsilon_{r}}-1\right)$$

Ohm’s Law for voltage

V=IR

V - voltage applied to to cell

I - current flows, A

R - resistance, Ohms $\Omega$

Definition of conductance

How easily a material allows electric current to flow

Definition of resistance

How strongly a material opposes the flow of electric current, always present when there’s conducatnce

Conductance equations

$$G=\frac{I}{R}$$

Where

I - current flow

R - resistance

Or

$$G=\frac{kA}{l}$$

k - intrinsic conductance of solution at a given T

A - area of cell

L - length of cell

Definition of molar conductivities

The conductivity of a ions in a solution per mole

Equation of molar conductivity, including concentration

$$\Lambda=\frac{k}{c}$$

Definition of standard molar conductivity (at infinite dilution)

Molar conductivity of an electrolyte when the solution is so dilute that all the ions are separated and do not interact with each other

Debye huckle equation for molar conductivity equation

Only valid for strong electrolytes at LOW conc

$$\Lambda=\Lambda^{o}-k\sqrt{c}$$

Last term accounts for ion-ion interactions which reduce $\Lambda$

What is activity

‘Effective’ molality of species in a solution

Corrects for non ideality

$a_{B}=\frac{\gamma_{B}m_{B}}{m^{o}}$ , activity of solute B

What is the mean activity 

For electrolytes that dissociate into multiple ions, it’s hard to isolate and identify the activity of individual ions

DH law tells us to how activity coefficients deviate from ideality due to electrostatic interaction between ions, valid at low ionic strength, and only valid for non ideal solutions, as there is an excluded volume effect

$$\gamma_{\pm}=10^{-A\vert z_{+}z_{-}\vert\sqrt{I}}$$

Equation for ionic strength

$$I=\frac12\sum z_{i}^2\frac{m}{m^{o}}$$

Definition of eletrochemical potential

In terms of ion, the total driving force of an ion

$$\mu_{i}\left(bar\right)=\mu_{i}+z_{i}\phi$$

Where

z - charge of ion

$\mu_{i}$ - chemical potential which depended on conc or activity

$\phi$ - electrical potential of the phase

What is the nerst equation?

$$E=E^{o}-\frac{RT}{nF}\ln K$$

Where

$$K=\frac{a_{ox}}{a_{r}}$$

This allows us to know the electrode potential which is the difference between $\phi$ of metal and $\phi$ of the solution

Fundamentally, how much energy an electron gain or electron loss from metal to sol or vice versa

Equation for electrode potential of a cell

$$E_{cel}=E_{redb}-E_{oxn}$$

Definition of pH

$$pH=-\log_{10}\left(a_{H^{+}}\right)$$

Note this is activity not conecentration of protons

What is the Fermi energy!

can be equated with chemical potential or the electros in the solid

illustrated as the “top” of the valence band which is the energy level where the probability of occupation is ½

energy of electrons can be changed by applying a n external potential, $\phi$

Equation for ion transfer potential that shows distribution if a specific ion in electrode phases

$$\Delta\phi=\frac{RT}{zF}\ln\frac{a_{i,an}}{a_{i,ref}}$$

Highlights distribution of a specific ion in reference solution and analyse solution

What is the faradaic efficiently equation

$\epsilon=$ charge used to form P / totak charge passed x100

Or

$$\epsilon=\frac{znF}{Q}$$

Where

n - no. of moles which formed P

z - no. of electrons per mole of product made

F - faradsic constant

A - total charge passed

What is the faradaic efficiency equation