Lesson 1c: reducing the relative humidity

### Content

The effects of reductions in the ambient relative humidity on water uptake, aqueous phase activities, and equilibrium gas partial pressures above NH4NO3 and HNO3 particles are examined.

### Part 1

Now we consider an ammonium nitrate (NH4NO3) particle containing 1 mole of salt, but at two relative humidities lower than the 99% examined earlier. Return to the data input page in the right hand browser window, and fill in the form as follows:

 1st Calculation Enter the values and select the options under the following headings: Ambient Conditions Relative humidity = 0.98 (i.e., 98%). 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).

#### Interpreting the Results

The results appear broadly similar to those for the first run in Lesson 1a at 99% relative humidity. However, looking in the "Aqueous Phase" section, we see that the amount of liquid water has approximately halved from 3138 g to 1503 g, and as a consequence the ammonium and nitrate concentrations have doubled from 0.3197 mol kg-1 at 99% relative humidity to 0.6655 mol kg-1 in the current calculation.

The change in concentrations of the ions also, of course, entails a change in the activities. The mole fraction activities of NH4+(aq) and NO3(aq) are both equal to 0.01171 × 0.5667 = 0.006636 (compared to 0.005694 × 0.6402 = 0.0036453 for the 99% relative humidity case). The activity coefficients have decreased slightly from 99% to 98% relative humidity.

In the "Gases" section the equilibrium partial pressures 1.6848E-12 atm (HNO3), and 2.8718E-07 atm (NH3), are both larger than at 99% relative humidity. Thus, as the solution becomes more concentrated the equilibrium partial pressures of these gases increase.

In the "Solids" section we now have an entry that was not present at 99% relative humidity: the saturation ratio of solid NH4NO3 is 0.01111. This quantity is related to the equilibrium constant for the dissolution of NH4NO3(s), Ks(NH4NO3), as follows:

NH4NO3(s) = NH4+(aq) + NO3(aq)

Ks(NH4NO3) = aNH4+ × aNO3 = (xNH4 fNH4) × ( xNO3 fNO3)

where Ks(NH4NO3) is equal to the activity product of the ions NH4+ and NO3 in a solution saturated with respect to solid NH4NO3(s). Equilibrium constants Ks for all solids are functions of temperature, but not the composition of the system. The activity of the pure solid phase does not appear as a denominator in the equation above as it is unity by definition. The saturation ratio, given in the model output, is equal to the actual value of the activity product in a solution (0.0066362 in the present example) divided by Ks(NH4NO3). A saturation ratio of unity (1.0) would mean that the solution was completely saturated with respect to the salt, and that any further increase in concentration would result in the precipitation of the solid.

### Part 2

Now repeat the calculation from Part 1, but for a lower relative humidity of 0.65 (65%):

 2nd Calculation Enter the values and select the options under the following headings: Ambient Conditions Relative humidity = 0.65 (i.e., 65%). 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).

#### Interpreting the Results

The aqueous phase now has only 2.4679 moles of water, a factor of 34 less than was the case at 98% relative humidity. The mole fractions and molalities of the ammonium and nitrate ions are correspondingly higher, though their activity coefficients have decreased further to 0.2627. We note that the changes in solute activity coefficients with concentration are very dependent on the nature of the the solute – in many cases values become very large at high concentrations, which is the opposite of what we find here.

In the "Gases" section the equilibrium partial pressure of NH3 is 4.6063E-07 atm, and that of HNO3 is 8.2501E-11 atm. This shows that the equilibrium partial pressures of these gases rise steeply as the solution becomes more concentrated.

In the "Solids" section we see that the saturation ratio of solid NH4NO3 is 0.8724 at this relative humidity. This is quite close to unity (complete saturation), and suggests that an aqueous solution of NH4NO3 will become saturated with respect to the solid at a relative humidity not too far below 65%. This behaviour will be examined further in a later lesson.

### Part 3

Here we repeat the previous calculation, but for a pure HNO3 particle in order to illustrate how differently the two solutes behave. (You might also wish to try the same calculation for NaCl and HCl.) Follow the instructions in the box below:

 3rd Calculation Enter the values and select the options under the following headings: Ambient Conditions Relative humidity = 0.65 (i.e., 65%). Ionic Composition in Moles Hydrogen = 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).

#### Interpreting the Results

The aqueous phase for this HNO3 particle contains 6.5637 moles of water, which is almost three times as much as the same number of moles of NH4NO3 at the same relative humidity. The activity coefficients of the ions (2.018) are also many times greater. This illustrates how different the water uptake properties of different soluble electrolytes can be.

In the "Gases" section the equilibrium partial pressure of HNO3 is given as 0.6509E-4 atm, which is more than three orders of magnitude greater than that at 99% relative humidity (Lesson 1a). We would therefore expect that an aqueous HNO3 droplet would be unlikely to survive in an atmosphere at low relative humidity: its very high equilibrium HNO3 partial pressure would cause it to evaporate.

This result also illustrates the important general principle that gas/aerosol partitioning varies strongly with relative humidity, tending towards the aerosol phase at high relative humidities and the gas phase at low ones.

You should now proceed to Lesson 1d, or return to the main page for this lesson.