Lesson 7a: aqueous ammonium nitrate and sulphate at a fixed relative humidity

### Content

The liquid water contents of NH4NO3 and (NH4)2SO4 particles are examined as a function of temperature at a fixed ambient relative humidity. The water content is shown to be related to the water activity coefficient.

### Part 1

In the first calculation we look at aqueous NH4NO3 at a fixed high relative humidity:

 1st Calculation Select "Graph" as the form of output, and then enter the values and options under the following headings: Ambient Conditions (1) For temperature, enter: Start Value = 275, End Value = 300, Number of points = 25. (2) Select a fixed relative humidity (the default), and enter 0.90 (i.e., 90%). Ionic Composition in Moles Ammonium = 1.0, Nitrate = 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 temperature" parametric calculations page of Model II (http://www.aim.env.uea.ac.uk/aim/model2/mod2t.php).

#### Viewing and Interpreting the Results

A page will appear in the other browser window 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 drop down lists. Instructions, and details of the variables, are given in the right frame.

First we plot the moles of liquid water associated with the particle against temperature:

 1st Graph:  select the variables and enter the options as given below. X Variable: "temperature" 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.

There is about a 10% increase in the water content of the particle over this 25 K range, from about 12.3 to about 13.6 moles. What is the cause, keeping in mind that the relative humidity and therefore the water activity of the solution has remained constant? To answer this question, plot the water activity coefficient (fH2O):

 2nd Graph:  select the variables and enter the options as given below. X Variable: "temperature" Range: leave blank Scale: linear (the default) Y Variable: "fH2O(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.

Here we see about a 10% decrease in fH2O over the temperature range. Recall that:

water activity = xH2O × fH2O

Because the water activity coefficient falls as temperature increases the water mole fraction xH2O (and consequently the the amount of water in the particle) must rise to maintain a constant water activity. This confirms what we saw in the first graph.

### Part 2

Next, we do a similar calculation for the salt (NH4)2SO4. Use the back button on the other browser window to return to the data input page, or select this link. Fill in the E-AIM input form in the other browser window as follows:

 2nd Calculation Select "Graph" as the form of output, and then enter the values and options under the following headings: Ambient Conditions (1) For temperature, enter: Start Value = 275, End Value = 300, Number of points = 25. (2) Select a fixed relative humidity (the default), and enter 0.90 (i.e., 90%). 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 temperature" parametric calculations page of Model II (http://www.aim.env.uea.ac.uk/aim/model2/mod2t.php).

#### Viewing and Interpreting the Results

Again plot the moles of liquid water associated with the particle against temperature:

 3rd Graph:  select the variables and enter the options as given below. X Variable: "temperature" 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.

The water content of the (NH4)2SO4 droplet also increases with temperature, but this time by only about 1.5% from 17.95 to 18.22 moles. We can see a similarly small change in the water activity coefficient:

 4th Graph:  select the variables and enter the options as given below. X Variable: "temperature" Range: leave blank Scale: linear (the default) Y Variable: "fH2O(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.

The graph shows that the water activity coefficient has a value of about 1.049, and changes only by a very small amount. The deviations from the smooth curve are an artifact: the numerical output of the calculated activity coefficients is rounded to six digits.

We conclude from these calculations that, for simple salts at quite high relative humidities, the water content of a particle varies relatively little with temperature. Also, that individual salts have different water uptake properties – in this case (NH4)2SO4 showing the smaller variation.

Proceed to Lesson 7b to learn how water uptake varies with temperature for sulphuric acid particles, or return to the main page for this lesson.