Eckhard Worch - Hydrochemistry : basic concepts and exercises

Logarithmic quantities (e.g. log a , log c, log K ) are frequently used in hydrochemistry and, consequently, also in this textbook. Therefore, it seemed useful to compile the main definitions and rules that are needed to work with logarithms.

Definitions:

The logarithm of a number x is the exponent n of a basis b if x is expressed as power of b :

If the basis b is 10, the logarithm is referred to as decimal (decadic, common) logarithm:

Note that the decimal logarithm is often written simply as log x instead of log10 x . This simplified notation is also used in this book.

If the basis b is the number e (Euler number, e = 2.71828), the logarithm is referred to as natural logarithm, written as ln x :

The relationship between the decimal and the natural logarithm is given by:

p notation:

The p notation, often used in hydrochemistry, means the negative decimal logarithm of a quantity and is used for constants as well as activities (or concentrations):

Logarithm of a product:

Logarithm of a quotient:

Logarithm of the p-th power of a number x:

Inverse properties:

The following list is a compilation of the most important equations from the main text. The equations are arranged according to the chapters where they were introduced and where you can find a detailed interpretation.

Density, :

Dynamic () and kinematic ( v ) viscosity:

Molar heat capacity, c p :

Capillary rise, h , in a capillary with the inner radius r :

Vapor pressure of small droplets with the radius r , p (droplets):

c p molar heat capacity, g gravity of Earth, H enthalpy, h capillary rise, m mass, p (droplets) vapor pressure of small droplets, p 0 vapor pressure (bulk liquid), R gas constant, r radius, V Volume, V m molar volume, T absolute temperature, dynamic viscosity, kinematic viscosity, contact angle, density, surface tension

Mass concentration, *:

Molar concentration (molarity), c :

Substance amount (number of moles), n :

Equivalent concentration, c (1/ z X):

Molal concentration (molality), b :

Mass fraction, w :

Mole fraction, x :

Note: For gaseous mixtures, y is used as symbol for the mole fraction.

Partial pressure, p :

Relationship between partial pressure, p i , and molar concentration, c i , in the gas phase:

Ionic strength, I :

Ion balance, condition of electrical neutrality:

Activity, a :

Activity coefficient, z :

(Debye-Hckel equation)

(Gntelberg equation)

a activity, b molality, c molar concentration, I ionic strength, M molecular weight (molar mass), m mass, n substance amount (number of moles), p i partial pressure, p total total pressure, R gas constant, T absolute temperature, V volume, w mass fraction, x mole fraction, y mole fraction (gas phase), z ion charge (absolute value), activity coefficient, * mass concentration