Lesson 4a: aqueous mixtures at fixed relative humidities

### Content

The uptake of water by a system containing two salts is compared to the uptake by each salt individually.

### Part 1

We first examine the amount of water associated with a single salt, ammonium nitrate, at a very high relative humidity (99%). Fill in the E-AIM input form in the other browser window as follows:

 1st Calculation Enter the values and select the options under the following headings: Ambient Conditions Relative humidity = 0.99 (i.e., 99%). Ionic Composition in Moles Ammonium = 1.0, Nitrate = 1.0. 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 "simple" calculations page of Model III (http://www.aim.env.uea.ac.uk/aim/model3/model3a.php).

From the output we see that the aqueous phase concentrations are 0.3197 mol kg-1 of NH4+(aq) and NO3(aq), and the total water uptake is 173.64 moles or 3128 g.

Next, we do a similar calculation, but for a 1:1 mixture of NH4NO3 and NaNO3 in which the total amount of material is now 2 moles:

 2nd Calculation Enter the values and select the options under the following headings: Ambient Conditions Relative humidity = 0.99 (i.e., 99%). Ionic Composition in Moles Ammonium = 1.0, Sodium = 1.0, Nitrate = 2.0. 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 "simple" calculations page of Model III (http://www.aim.env.uea.ac.uk/aim/model3/model3a.php).

#### Interpreting the Results

Again, there are no gas phase species, because we used the simplest of the E-AIM models, which suppresses the gas phase partitioning. No solids form because the humidity is high. Notice that the molalities are 0.1586 mol kg-1 of NH4+(aq) and Na+(aq). In this calculation we also find that the NO3(aq) molality is 0.3173 mol kg-1, which is very similar to that for NH4NO3 on its own (0.3197 mol kg-1 in the first calculation). The water uptake is now 349.91 moles, close to double that for NH4NO3 alone, which reflects the fact that we now have twice as much salt - in moles - as before.

This approximate doubling of the amount of water uptake with the moles of salt, even though the salts are different, is clearly an important relationship if it applies more generally. We will explore this further in the next section.

### Part 2

Here the molalities and water content of NH4NO3/NaNO3 particles are determined at two lower relative humidities, and compared with those for NH4NO3 alone. Return to the data input page in the right hand browser window, and do the following two calculations:

 3rd and 4th Calculations Enter the values and select the options under the following headings: Ambient Conditions Relative humidity = 0.90 (90%, first calculation); then relative humidity = 0.80 (80%, second calculation). Ionic Composition in Moles Ammonium = 1.0, Nitrate = 1.0 (for both calculations). 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 "simple" calculations page of Model III (http://www.aim.env.uea.ac.uk/aim/model3/model3a.php).

For this single salt aerosol particle at 90% relative humidity the ion molalities are 4.094 mol kg-1, and at 80% they have increased to 10.05 mol kg-1.

Next, return to the 1:1 NH4NO3/NaNO3 mixture and repeat the above calculations. Make sure you record the nitrate molality for both relative humidities.

 5th and 6th Calculations Enter the values and select the options under the following headings: Ambient Conditions Relative humidity = 0.90 (90%, first calculation); then relative humidity = 0.80 (80%, second calculation). Ionic Composition in Moles Ammonium = 1.0, Sodium = 1.0, Nitrate = 2.0 (for both calculations). 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 "simple" calculations page of Model III (http://www.aim.env.uea.ac.uk/aim/model3/model3a.php).

#### Interpreting the Results

At 90% relative humidity the salt mixture has an NO3(aq) molality of 3.864 mol kg-1 compared to 4.094 mol kg-1 for the NH4NO3 alone. These molalities are still similar, but are not as close as was found at 99% relative humidity (0.3197 and 0.3173 mol kg-1, in Part 1 above).

At 80% relative humidity the mixed salt solution has an NO3(aq) molality of 8.905 mol kg-1, whereas for NH4NO3 alone the molality is rather higher at 10.05 mol kg-1. The total water differs correspondingly, with 6.2335 moles (= 12.467 / 2) for 1 mole of the salt mixture compared to 5.5234 moles of water for 1 mole of NH4NO3. There is a departure from the simple sum that applied at at 99% relative humidity, and the differences increase at lower relative humidities where the solutions are more concentrated. It is at these higher concentrations that the behaviour and characteristics of the individual ions, and their interactions both with each other and with water, become more important. Consequently the thermodynamic properties of the two solutions diverge, and simple additive relations that ignore the differing properties of the solutes do not hold.

Continue to Lesson 4b to learn about an empirical relationship for water uptake of mixed solutions, or return to the main page for this lesson.