Appendix I
Absorption
by Water and Henry's Law
Page 32 of DuPont's Hydrogen Cyanide: Properties, Uses,
Storage and Handling
^{1} contains a plot of the
partial pressure of HCN above aqueous solutions of HCN at various
concentrations and temperature. These values are equilibrium
values. That means that at these concentrations the rate of HCN
in the gas phase becoming absorbed into the solution is exactly
balanced by the rate of HCN leaving solution into the gas phase.
Because the plot shows equilibrium values, it contains implicitly the
value of partition coefficients, i.e., it is possible to obtain
the equilibrium concentration of HCN in solution in water exposed to HCN
in the gas phase as a given concentration and temperature. This
appendix extracts those values. In DuPont's plot liquid phase
concentration is expressed in weight percent and gas phase concentration
in millimeters of mercury (also known as Torr); this appendix derives
relationships in terms of molarity (M) and grams per cubic meter
(g/m^{3}).
These values are equilibrium values, which means that they are an upper
limit to the concentration that may be found in water exposed to HCN.
How fast such equilibrium establishes itself is a question of kinetics
and is a much more difficult problem.
By reading the values for a given temperature from the plot, one can
construct a plot of the weight percent HCN in water as a function of gas
phase concentration in Torr. The relationship is linear in the region
of interest; so intermediate values can be found by fitting the points
with a leastsquares linear regression. At 0 Torr, the concentration in
water should be 0%; therefore the fits have only one free parameter, the
slope. This linear relationship is known as Henry's Law and the slope
can be identified with the Henry's Law constant.
Figure I.1
Figure I.1 shows such a plot for a temperature of 30 degrees Celsius
(° C).
The points have been read by eye from DuPont's plot. Notice that the
fit to a line is excellent and is likely to average out slight
deviations in the estimates of values in DuPont's plot. The slope in
this case was found to be 0.029 percent/Torr.


Temperature Dependence
Similar plots were made for 0, 10, 20, 30, 40, and 50 degrees.
The values of the slope were:
Table I.1: Slope of the GasLiquid Partition
as a Function of Temperature. 
Temperature ° C 

Slope percent/Torr 
0   0.105 
10   0.066 
20   0.047 
30   0.029 
40   0.020 
50   0.013 
Unit Conversion
The problem is now essentially solved except for unit conversions.
DuPont's liquid phase concentration is expressed in weight percent, and
I wish to express that value in molarity (M). The first step is to
calculate what volume of water contains 1 mole of HCN. The
molar mass of HCN is 27.03 g. The mass of water
(M_{H2O}) can be expressed as:
(M_{H2O}) = (100/C 1) x 27.03
where C is the concentration in weight percent HCN.
The density of water is 1.0 g/mL and will be treated here as independent
from temperature. HCN density as a function of temperature was found by
a linear extrapolation of the densities found on page 2 of the same
DuPont document. The fit in g/mL yielded:
p_{HCN}=0.7150.00133 x T
where T is expressed in degrees Celsius (° C), and p_{HCN}
is the density of HCN. The volume of solution that contains 1 mole of
HCN can now be calculated, if one neglects the small effect of mixing on
changing the volume. Figure 11 on page 31 of DuPont's handbook displays
the specific gravity of HCN solutions as a function of the weight
percent HCN. Inspection of this figure is sufficient to show that
neglect of the volume of mixing is warranted. The volume of solution
in milliliters (mL)
that contains 1 mole HCN is therefore:
V= 27.03/p_{HCN} + M_{H2O}/1.0
I convert to molar concentration:
[HCN] = 1000/V
The gas phase concentrations of in the gas chamber were in the range of
816 g/m^{3}. I therefore chose an array from 120
g/m^{3} converted that array to Torr and calculated from the
above relationships the equilibrium water concentration at the given
Temperatures. Conversion from g/m^{3} is straightforward:
P=R x T x (C/27.03) x (760/101325)
Here P is the partial pressure of HCN in Torr. R is the universal gas
constant (8.31441 m^{3}Pa/mol K (SI units!). T is the temperature in
Kelvin (273.15 plus the temperature in Celsius); C is the concentration
of HCN expressed in g/m^{3}; 27.03 is the molar mass of HCN in
grams (not SI units, but grams cancel); there are 760 Torr in an
atmosphere and 101,325 Pascals (Pa).
Results
The results of these calculations are shown if Figure I.2. The
temperatures in the gas chambers were most likely between 20 and 40 °
C, but even if they got down to 10 ° C, and even if the higher
concentrations reported were used, the equilibrium concentration of HCN is
on the order of 0.10.2 M. In other words, these are the maximum
concentrations that could be achieved. More likely, the concentration was
limited by kinetics and never reached equilibrium.
Figure I.2
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