Knowledge Revolution

Norrish

## Norrish Equation

For a single solute, the Norrish equation reduces to:    aw = Xw * exp(-ki * Xi^2)

where:

aw        = water activity

Xw        = mole fraction of water
Xi          = mole fraction of solids in ingredient i
ki          = Norrish constant for ingredient i

## Raoult's Law

Raoult's Law is very accurate within the range of 0.95 to 1.0 water activity, whereas the Norrish equation is reasonably accurate down to about 0.55.

aw = A nH2O /(nH2O+ nsolute)

where:

A          = activity coefficient

nH2O     = moles of water in solution (assumed to be 1 for solutions with aw >0.95)
nsolute   = moles of solute

This program uses a modified Norrish equation.  The author has found that by applying an activity coefficient (A) to the molecular weight (mwt), a more accurate water activity estimation is possible.  When calculating the solute mole fraction Xi, mwt is replaced with mwt/A.   A is generally less than 1, and is calculated by this program, as well as the value of the Norrish constant k.

Dissociation:
The Norrish equation and Raoult's Law depend on the number of moles of solute. Therefore, solutes which dissociate in solution contribute twice as many moles as solutes which do not dissociate.

eg:        Dissociation species = 2

Input requirements:

Solute name

Molecular weight

Number of dissociation species (generally 1 or 2)

Temperature

Data points of water activity vs solute concentration (g. solute/100g total)