Aquatic Chemistry

# Introduction

This is a discussion on aquatic chemistry and precipitation.

# Background

Thermodynamic and kinetic model. Thermo is all about equilibrium, time goes to a large scale while kinetics is time based. For aqueous applications, we are concerned with two quantities:
Molarity of the solvent and molality.
$C_A = n_A/V$ and $m = n_A/(weight of solvent)$. If we have water close to ambient temperature, then $m=C_A$. To illustrate the difference between kinetics and thermodynamics, then the thermodynamic model will have an initial concentration of

(1)
\begin{equation} A kf-> <- B \end{equation}

CAo = CA + CB, CB/CA = k, and CA = CAO/1+K

While in kinetics, we deal with time dependent models and solve for the concentrations. (See page 18 in Chapter 2 for aqueous chemistry book).

Transport/Diffusion limited: reaction is infinitely fast, its the transport that limits you.

Reaction Limited: reaction is faster than transport, then it determines what goes on.

# Chemical Thermodynamics

If we have a closed system, we can define a state function of its internal energy,

(2)
\begin{align} \mathrm{d}U = \mathrm{d}Q - \mathrm{d}W \end{align}

The internal energy is the same based on the temperature, pressure, and composition. For the second law, we have another state function

(3)
\begin{align} \mathrm{d}S \geq \frac{\mathrm{d}Q}{T} \end{align}

The total entropy change is positive

(4)
\begin{align} \Delta S \geq 0 \end{align}

The third law states that there is an absolute temperature scale such that the entropy is zero at zero kelvin.

## Other Useful Functions

Enthalpy

(5)
\begin{equation} H = U + pV \end{equation}

Gibbs energy

(6)
\begin{align} G = H - TS; \quad \mathrm{d}G \leq 0 \end{align}

Suppose you have aragonite and calcite, the lowest dG is NOT enough to determine which reaction will take place. We have to look at the kinetics, and precipitation. If both have a dG<0, the fastest reaction will determine which precipitate will form.

## Chemical Potential of a System

Partial molar property:

(7)
\begin{align} M = \left( \frac{dM}{dn_i} \right)_{P,T,n_{i\neqj}} \end{align}

For Gibbs energy:

(8)
\begin{align} dG = \frac{\partial G}{\partial T} dT \cdots... \mathrm{See equation 40 in the aqueous Chemistry book} \end{align}
page revision: 2, last edited: 07 Dec 2010 21:13