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Relation of Separation Factor to Vapor Pressures
When only two isotopic compounds are present in the mixture being separated, such as a mixture of CH4 and CH3D or a mixture of H2160 and H2I80, the separation factor in distillation may be estimated with sufficient accuracy for survey purposes from the ratio of the vapor pressures 7г of the two compounds,
aAB = (13.2)
ffB
where A is the compound with higher vapor pressure. Measurements of the separation factor in liquid-vapor equilibrium of many isotopic mixtures have shown that In a (measured) is within 10 percent of In a [calculated from (13.2)] except for 3He-4He or H2-HD-D2 mixtures. With the same exceptions, measured lna’s vary less than 10 percent with isotopic composition at constant temperature or pressure.
For Eq. (13.2) to be strictly true, it is sufficient that the liquid and vapor phases form ideal solutions, which is usually very nearly the case for isotopic mixtures at pressures up to 1 atm.
When more than two isotopic compounds are present in the mixture being separated, such as H2, HD, and D2, or H2 0, HDO, and D2, the relation between separation factor and vapor pressures becomes more involved. The situation is complicated further when the vapor pressure of a mixed isotopic compound cannot be measured, because it cannot be isolated in pure form. HDO is such a compound, because it remains in equilibrium with H20 and D20:
2HD0=*H20 + D20
The approximate relation between separation factor for hydrogen from deuterium and the measurable vapor pressures of H20 and D2Ois
= I"*’0
The general rule is that in a mixture of isotopic compounds
ЛГАиДА^ВДА^Вї……………….. ХЪп
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n l*XA„ V *ХВП |
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a*(A, B) = The conditions required for this relation to be strictly true will be described later. |
the separation factor for isotopes A and В may be approximated by
Table 13 3 lists for a number of isotopic mixtures the separation factor computed from vapor pressures by this general formula. This table gives separation factors at the normal boiling point and at the triple point, the lowest temperature at which distillation is possible. As this table shows, the separation factor is greatest for compounds of elements of low atomic weight and increases as the temperature is reduced.
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Table 13.3 Separation factors in distillation estimated from vapor-pressure ratios
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Deuterium. The first part of Table 13.3 lists vapor-pressure ratio data for four compounds of hydrogen that are handled in large enough volumes to be possible feed materials for a plant to concentrate deuterium by distillation.
H2 + HD is the only mixture of compounds of hydrogen that has a separation factor as favorable as in conventional industrial distillation. In this case, however, the true separation factor is less favorable than here calculated from the vapor-pressure ratio, because of nonidealities in gaseous and liquid mixtures of hydrogen and HD. Moreover, it is desirable to operate above atmospheric pressure, to preclude in-leakage of air. Under practical conditions, at 1.6 atm, the relative volatility obtainable is around 1.6 [Nl]. This is the most favorable relative volatility for separation of deuterium by distillation.
Although water has a slightly less favorable relative volatility than ammonia, water makes the better working substance because it is available in unlimited quantities, whereas the amount of deuterium that could be extracted from ammonia is limited to the amount present in ammonia produced industrially.
Methane cannot be used as working substance in a distillation process because its relative volatility is so close to unity. This is regrettable in view of the large amount of natural gas that might be used as a source of deuterium.
Concentration of deuterium by distillation of hydrogen will be discussed in Sec. 4 and water in Sec. 5.
Noble gases. The second part of Table 13.3 lists vapor-pressure ratios for isotopes of the noble gases helium, neon, argon, and xenon. The vapor-pressure ratio is very high for helium, much smaller for neon, scarcely different from unity for argon, and precisely 1 for xenon. This illustrates the general rule that distillation is a possible separation method for isotopes of the lightest elements, but becomes useless at atomic weights much over 20. Distillation is the preferred method for separating helium isotopes.
Carbon, oxygen, and nitrogen. The only other compounds listed in Table 13.3 whose isotopic species have been concentrated to a significant degree by distillation are CO, NO, and H2 О (for oxygen isotope separation). Distillation becomes unattractive as a method for separating an isotope of low natural abundance when the vapor-pressure ratio is below 1.01, because the plant required for a given output becomes very large and the time required to bring the plant into steady production becomes very great. This is a consequence of the high holdup per unit separation capacity in this method in which the process fluid is liquid. Gas-phase separation processes such as gaseous diffusion are less subject to this difficulty.
Derivation of Eq. (13.3). The following derivation of Eq. (13.3) relating the deuterium separation factor in the distillation of water to the vapor pressure rr of H20 and D20 is similar to that given by Urey [Ul]. It is assumed that:
1. Liquid and vapor phases form ideal solutions.
2. The vapor pressure of НЕЮ is the geometric mean of the vapor pressures of H20 and D20.
3. Equilibrium in the reaction
H20 +D20 s* 2HDO
is maintained in the liquid phase.
4. The distribution of deuterium and hydrogen atoms among the three species of water is random, so that the equilibrium constant for this reaction has the value of 4.0. These assumptions are plausible, but are not subject to complete experimental confirmation because liquid НЕЮ cannot be isolated, because it disproportionates into H20 and D20. Values for the equilibrium constant calculated by statistical mechanics are around 3.8.
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ш Ahdo + 2*о2о^2^нго +>’hdo^ 2*h, o +*HDC |
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"*HDO + 2уСзо/ |
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Because of the ideal solution assumption 1, irx where p is the pressure. Because of assumption 4, *hdo = 2 V*H30*D30 With these substitutions in (13.5), (2ян20*Н30IP) + (2 V^HjO^DjO-^HjO^DjO/P) |
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f 2 V*h3o*d3o + 2jcd3o ‘ (2*h3o + 2 V*H3o*D2oy V^DjO V^HjO^HjO I ‘AhjO Wd3o*d3o V ^d3o |
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All mole fractions have canceled out, and a* is independent of composition. The general equation (13.4) may be derived in similar fashion from analogous assumptions. |
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Distillation of water. Combs et al. [Cl 1 ] have determined the deuterium separation factor in the distillation of water by measuring the H/D ratio in water liquid and vapor in equilibrium. The third and fourth columns of Table 13.4 compare their measured separation factors with values predicted by Eq. (133) from their values for the vapor pressures of pure H20 and D20. The agreement in the two sets of values of In a is within 6 percent. The agreement with Kirshenbaum’s vapor-pressure ratios [K2] is somewhat poorer. Rolston et al. [R8] have proposed the equation In a* = 0.0592 — &03/T + 25,490/Г2 to correlate ah data to 1976. |
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The agreement at this deuterium content is within experimental uncertainty. However, a small but significant trend of separation factor with deuterium content was observed, as indicated in Table 13.6. These results for water and ammonia suggest that Eq. (13.4) can be used to predict separation factors in distillation with an error in to a* no greater than 10 percent. |
Water contains the three molecular species H20, НЕЮ, and D20. In concentrating heavy water by distillation, the deuterium separation factor is defined as the ratio of the atomic ratio of deuterium to hydrogen in the liquid to the corresponding ratio in the vapor. In terms of the mole fractions of individual compounds in the liquid дг and vapor y, the separation factor a* is
Vapor-pressure ratio
V^HjO/^DjO Separation factor
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Table 13.4 Deuterium separation factors in distillation of water
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