Lesson 8b: solid/liquid equilibrium of (NH4)2SO4
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Content
The model is used to determine how the deliquescence relative humidity of
another important atmospheric salt, (NH4)2SO4,
varies with temperature.
Part 1
Use the back button on the other browser window to return to the
data input page for variable "relative humidity, or total water" calculations
using Model II,
or select this link.
As before, the deliquescence point is obtained by calculating the water uptake
of (NH4)2SO4 as a function of relative
humidity at a series of fixed temperatures. First, for 273.15 K:
1st Calculation |
- Select "Graph" as the form of output, and then enter the values
and options under the following headings:
- Ambient Conditions
- (1) Temperature = 273.15
- (2) Select "Relative humidity" as the variable. Start Value
= 0.75 (i.e., 75%), End Value = 0.85 (i.e., 85%),
Number of points = 50.
- Ionic Composition in Moles
- Ammonium = 2.0, Sulphate = 1.0.
- Trace Gases
- There are no entries under this heading.
- Solid Phases
- There are no entries under this heading.
- Click on the "Run" button at the end of the page to do the
calculation.
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Note: the above should be entered on the
variable "relative humidity, or total water" parametric calculations page of
Model II (https://www.aim.env.uea.ac.uk/aim/model2/mod2rhw.php).
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Viewing and Interpreting the Results
A page will appear which enables you to plot various quantities
against each other, by choosing the X and Y variables, their ranges, and scales (linear or log10)
from the lists on the left hand side. Instructions, and details of
the variables, are given in the right frame.
Plot the number of "moles of H2O(aq)" to find out at what relative humidity
the salt deliquesces:
1st Graph: select the variables and enter
the options as given below. |
X Variable: "relative humidity"
Range: leave blank
Scale: linear (the default)
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Y Variable: "moles of H2O(aq)"
Range: leave blank
Scale: linear (the default)
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Click on the "Draw the Graph" button at the end of the
page, and the plot will appear in the right frame.
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At this temperature we see that the deliquescence point
lies at about 81.5%, roughly 5% higher than for NH4NO3.
The amount of water taken up at this relative humidity is 10.5 moles, giving
a salt molality of (1/10.5) × 1000/18.0152 = 5.3 mol kg-1.
Part 2
Next, repeat the calculations and plots from Part 1 at
298.15 K and 323.15 K and determine the deliquescence points and salt
concentrations at these higher temperatures.
At 298.15 K the deliquescence relative humidity and water uptake are little
changed at about 80% and 9.75 moles, respectively. The molality of the salt
in the saturated solution is therefore (1/9.75) × 1000/18.0152 =
5.7 mol kg-1.
At the highest temperature, 323.15 K,
the deliquescence relative humidity is 78.5%; and the 8.8 moles of water
taken up give a solution molality of (1/8.8) × 1000/18.0152 = 6.3
mol kg-1.
Interpreting the Results
From these results we see, first of all, that the deliquescence relative humidity
of (NH4)2SO4 changes very little
with temperature, in contrast to what we saw for NH4NO3
in Lesson 8a. However, we can again explain this in terms of the variation with
temperature of the solubility of the solid salt in water: this increases from
5.7 mol kg-1 to only 6.3 mol kg-1
which is a comparatively small change over a 50 K range in temperature.
As was the case for NH4NO3,
the water activity coefficient of aqueous NH4SO4 solutions
has only a small dependence upon temperature. Consequently, as the
variation of the salt solubility with temperature is the primary
influence controlling the deliquescence relative humidity, it is no suprise
that the change is very small in this case.
You should now review the conclusions on the
main page of this lesson.