Abstract:
The present study has consisted primarily of an investigation
of the rates of isotopic sulfur exchange between sulfur dioxide and
various sulfur (VI) solutions, both 100% H₂SO₄ and, in particular,
related ammonia-containing sulfur (VI) solutions. One of the main
objects of the work was to obtain a comparison between exchange
rates in such systems and those previously observed in aqueous
acid systems. The exchange was studied at temperatures from
167.5°C to 225.3°C, the sulfur (VI) systems examined including:
(1) 100% H₂SO₄; (2) fused ammonium bisulfate; (3) mixtures of ammonium
bisulfate and 100% H₂SO₄; and (4) a 1:1 mixture of ammonium bisulfate and 84.5% H₂SO₄. The observed rates were all conveniently
measurable throughout the indicated temperature range.
Previous studies of exchange rates between sulfur dioxide and
either concentrated sulfuric acid solutions or fused ammonium bisulfate
have shown in both cases the reaction to be first order in the amount of sulfur dioxide and proportional to the fraction of it
dissolved in the solution, viz.: Rate = k (SO₂) (1) where (SO₂) represents dissolved sulfur dioxide concentration. The
results showed, however, a wide variation of the rate constants for
different types of solutions. In an attempt to account for this wide
variation, an effort has now been made to interpret both the present
results as well as previous data in terms of sulfur dioxide activities
rather than concentrations. To this end equation (1) has been rewritten
in the form Rate = k[subscript a] γ (SO₂) (2) where γ is the activity coefficient of sulfur dioxide in the solutions.
In order to calculate the rate constants based on sulfur dioxide
activities (k[subscript a]), the concentration rate constants (k) and activity
coefficients (γ) were first calculated. The latter quantities were
computed from the relationship: γ = P/P' (3) where P is the actual partial pressure of solute SO₂ over a solution
at the composition of interest and P' is the calculated ideal
solution (Raoult's law) partial pressure at the same composition.
Values of P in equation (3) were calculated directly from sulfur
dioxide distribution coefficients between gas phase and solution on the basis of the ideal gas equation, Henry's law having been found
valid in these systems. The distribution coefficients were either
obtained from the present exchange results or, for some of the previous
data, were estimated by interpolation or extrapolation from
data measured under slightly different conditions.
A comparison between the two types of rate constants, k and
k[subscript a], shows that, while the constants, k, vary drastically from one solution to another, the activity constants, k, vary among themselves to only a modest degree. A striking example of this feature
is provided by comparison of exchange rates at 225.3°C in fused
ammonium bisulfate and in the 1:1 mixture of ammonium bisulfate
with 84.5% H₂SO₄. Here the constants k differ by a factor of 32
while the k[subscript a] values differ by only a factor of two. This comparison
shows clearly the merits of interpreting the rate as first order in
sulfur dioxide activity rather than concentration.
Apparent activation energies, frequency factors and activation
entropies, both for k values and k[subscript a] values, have been calculated
for the systems: (1) fused ammonium bisulfate; (2) 100% H₂SO₄;
and (3) 1:1 ammonium bisulfate and 84.5% H₂SO₄. It was found that,
even though the k values themselves showed good accord among
themselves as compared to the k values, these related kinetic
parameters failed to reflect this accord. Thus important variations
among the k based parameters appear to persist with the k[subscript a] based parameters. It is suggested that the basis for this lack of concordance
among the latter parameters may be related to the fact that
the activity coefficients of the sulfur (VI) exchanging species and of
the activated complexes have not been adequately taken into account.
Since the sulfur (VI) concentration in the solutions varied but
little from case to case, it was not possible to test the rate dependence
on this factor. However, previous work has demonstrated a
first order dependence of rate on bisulfate ion in aqueous acid, and
it has been assumed the same dependence prevails in the present
solutions. If this assumption is valid, the relative constancy of k[subscript a]
values observed, as the ratio of bisulfate ion concentration to unionized
H₂SO₄ concentration changes drastically from one solution to
another, implies that the rate must be approximately first order in
both of these sulfur (VI) species and must have, for exchange with
either, approximately the same specific rate constant. Hence it is
tentatively proposed that the exchange rate may be, at least approximately,
described, for all the solutions here examined by the rate
law Rate = k₂ γ (SO₂)[(HSO₄⁻) + (H₂SO₄)]