Schwarzenbach - Environmental organic chemistry

1. A.1 The Normal Distribution
2. A.2 The Error Function

The one-dimensional normal (or Gaussian) distribution along the x-axis is defined by:

(17-3)

where is the standard deviation and 2 is the variance of the distribution. p(x) has the following properties:

(1)

(2)

(3)

Integrals within finite boundaries have the following values:

(4)

(5)

Figure A.1 The normal distribution where each band on the x-axis has a width of one standard deviation ().

The Error Function erf(y) along the y-axis is defined by:

(1)

The Complementary Error Function is:

(2)

Symmetry properties and integral:

(3)

(4)

Special values:

Figure A.2 (a) The Error Function erf(y) for y = 3 to y = + 3. (b) One-sided diffusion from a boundary at y = 0 (Eq. 17-9) is given by the Complementary Error Function erfc(y) for y > 0.

Table A.1 The Error Function and its Complement

1. B.1 Some Useful Constants (IUPAC)
2. B.2 Dimension and Units of Physical Quantities
3. B.3 Specific Properties of Water at 20C
4. B.4 Specific Properties of Dry Air

Atomic mass	mu	1.66054021027 kg
Avogadro's number	NA	6.02213671023 mol1
Boltzmann's constant	k	1.3806581023 J K1
Elementary charge	e	1.602177331019 C
Faraday's constant	F	9.6485309104 C mol1
Gas (molar) constant	R	= k N = 8.314510 J mol1K1
0.083145 L bar mol1K1
Gravitational acceleration	g	= 9.80665 m s2
Molar volume of an ideal gas at 1 bar and 25C		= 24.465 L mol1
Permittivity of vacuum	o	8.8541871012 C V1m1
Planck's constant	h	6.62607551034 J s
Zero of Celsius scale	0C	= 273.15 K

Dimensions are: M = mass; L = length; T = time; I = current

Density	w	998.205	kg m3
Thermal expansivity