Lesson 8b: solid/liquid equilibrium of (NH4)2SO4

### 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. Note:  the above should be entered on the variable "relative humidity, or total water" parametric calculations page of Model II (http://www.aim.env.uea.ac.uk/aim/model2/mod2rhw.php).

#### 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) Y Variable: "moles of H2O(aq)" Range: leave blank Scale: linear (the default) Click on the "Draw the Graph" button at the end of the page, and the plot will appear in the right frame.

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.