In Chaps. 12, 13, and 14, dealing with isotope separation, the composition of a mixture may be expressed in terms of the weight (or mass) fraction of each component, the mole fraction of

each component, or the atom fraction of each isotope. The relations among these three measures of composition may be illustrated by the example of water containing 0.79 weight fraction HjO (molecular weight 18), 0.19 weight fraction HDO (molecular weight 19), and 0.02 weight fraction Dj О (molecular weight 20). The procedure to obtain mole fractions from these weight fractions is shown below:

The atom fraction of deuterium is the ratio of the number of atoms of deuterium to the number of atoms of deuterium plus hydrogen in the mixture, or

(0.182 X 1) +(0.018X2)

———————— ~ = 0.109 (12.5)

The symbol z will be used to represent the fraction of a component in the feed stream to a unit, stage, or cascade; у the fraction in the enriched stream leaving a unit, stage, or cascade; and x the fraction in the depleted stream leaving a unit, stage, or cascade. The context will indicate whether weight, mole, or atom fractions are being dealt with. In the case of compounds containing a single atom of a polyisotopic element, such as UF6, atom fractions and mole fractions are identical.

For mixtures of two isotopes, the symbol z, y, or x refers to the fraction of desired isotope (for example, 235 U in the case of uranium or D in the case of hydrogen). For mixtures of three or more isotopes, the first subscript following z, y, or x indicates the specific isotope.

The location of a stream in a unit, stage, or cascade is also designated by a subscript, standing alone for a two-component system, or standing second after a comma for a multicomponent one. For example, z^p is the fraction of the ith isotope in feed.

Some relations for isotope separation plants are simpler when expressed as weight, mole, or atom ratios, defined as the ratio of the fraction of one component to the fraction of a second. These ratios are denoted by Greek letters f, £, or »j for feed, depleted, or enriched stream, corresponding to z, x, or y. In a two-component mixture, these ratios are defined as the ratio of the fraction of the desired component to that of the other component. For example, in a tails stream, the weight, mole of atom ratio for a two-component mixture is

(12-6>

For a multicomponent mixture the two components entering the ratio are designated by a double subscript, without comma, for example,

(»4 (ил)

x»

The ratio of atom fractions is frequently termed the abundance ratio. For example, the abundance ratio of 235 U to 238 U in natural uranium containing 0.007205 atom fraction 235 U and 0.99274 atom fraction 238U is 0.007205/0.99274 = 0.007258.