Tritium Assay Analysis by PVT Mass Spectrometer

DOE-HDBK-1129-99

V = volume of the container in liters

z = compressibility factor (See Table C.1)

R = constant = 62.3631 (See below)

T = temperature ( K)

In the formula, the container volume (V) is determined ahead of time by measurement using a

volume measuring system, or, if no other means is available, it may be calculated from the

physical dimension of the container. The gas pressure (P) and temperature (T) are determined

by measurement with available instruments at the time of the mass spec sampling. R is a

constant, which is a function of the units of pressure and volume used in the equation and is

equal to 62.3631 for pressure in torr and volume in liters.

The compressibility factor (z) is a function of gas type, pressure, and temperature and is either

determined from a compressibility table for tritium or estimated using a standard equation such

z(T2) = 1 + [(P (torr) x 0.000832)/1000]

This equation is for a temperature of 295 K.

Most operating facilities have established methods for determining the compressibility factor.

For those facilities that do not already have these methods established, Table C-1,Table of

Tritium Compressibility Factors, may be helpful.

As an example, for a container with a volume of 22.414 L at a pressure of 760 torr and a

temperature of 273.15 K (Standard Temperature and Pressure (STP) conditions) the number of

moles is calculated as follows:

N = PV/zRT

= (760 x 22.414)/(1.000 x 62.3631 x 273.15)

= 1.0000 mole

Note: z(T2) at 273.15 K = 1.000.

The total moles of gas in the container at any time, t, is the sum of the moles of the individual

gases present in the mixture at that time or in equation form:

PV/zRT = n(Moles Total) = n(T2)+n(HT)+n(DT)+n(CT4)+n(qTw)+n(He-3)+n(N2)+ n(O2)+n(Ar)+n(etc.)

The n(qTw) represents a generic tritium-containing component. The "q" in, n(qTw), represents any

other element which may be present, and the "w" represents the number of tritium atoms in the

molecule. The n(etc.), represents any generic, non-radioactive, non-tritium component.

From this equation, it follows that

PV/zRT = n(Moles Total) = n(Total Moles of Tritium Containing Gases) + n(Total Moles of Non-tritium Gases)

where

n(Total Moles of Tritium Containing Gases) = n(T2) + n(HT) + n(DT) + n(CT4) + n(qTw) + etc.

and

n(Total Moles of Non-Tritium Gases) = n(He-3) + n(N2) + n(O2) + n(Ar) + n(etc.) + etc.

The number of moles of tritium in the container is the sum of the number of moles of tritium in

each tritium component. The number of moles of tritium in each tritium component is equal to

the number of moles of the component multiplied by the moles of tritium per mole of component.

C-2