Lesson 3c: evaporation of a liquid aerosol

### Content

The model is used to examine how the existence of a liquid aerosol depends on the amounts of material present and the relative humidity, for a system containing HNO3 and NH4NO3.

### Part 1

We first determine the relative humidities for which a particle phase exists, for the same amounts of ions as in the previous part of this lesson. Select this link to open the data input page for variable "relative humidity, or total water" calculations using Model III (http://www.aim.env.uea.ac.uk/aim/model3/mod3rhw.php). Fill in the input form as follows:

 1st Calculation Select "Graph" as the form of output, and then enter the values and options under the following headings: Ambient Conditions Select "Relative humidity" as the variable. Start Value = 0.70 (i.e., 70%), End Value = 0.95 (i.e., 95%), Number of points = 60. Ionic Composition in Moles Hydrogen = 1E-7, Ammonium = 1E-7, Nitrate = 2E-7. 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 III (http://www.aim.env.uea.ac.uk/aim/model3/mod3rhw.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.

First, plot the number of moles of aqueous phase NO3(aq) to determine how this varies with relative humidity, and at what point the aqueous phase ceases to exist:

 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 NO3-(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.

As the relative humidity decreases from 95%, so also does the moles of aqueous phase NO3(aq). This is because the lowering of the relative humidity requires the equilibrium aqueous phase to have a lower water activity, and therefore higher ion concentrations. These in turn result in higher equilibrium partial pressures of HNO3(g) and NH3(g) and consequently the transfer of material to the gas phase. You can verify this, if necessary, by plotting the molality of NO3(aq) present in the aqueous phase ("mNO3-" as Y axis variable), or HNO3 in the gas phase ("moles of HNO3(g)" as Y axis variable).

At about 86% relative humidity the number of moles of aqueous NO3 reaches zero. This is the transition point between gas phase NH3 and HNO3 existing alone at lower relative humidities and the same compounds in equilibrium with an aqueous phase in more humid atmospheres.

### Part 2

The relative humidity of transition depends on the amount of material in the system, and we will investigate this next. Return to the data input page in the right hand browser window, and repeat the previous calculation, but with the ion amounts increased by a factor of 10:

 2nd Calculation Select "Graph" as the form of output, and then enter the values and options under the following headings: Ambient Conditions Select "Relative humidity" as the variable. Start Value = 0.70 (i.e., 70%), End Value = 0.95 (i.e., 95%), Number of points = 60. Ionic Composition in Moles Hydrogen = 1E-6, Ammonium = 1E-6, Nitrate = 2E-6. 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 III (http://www.aim.env.uea.ac.uk/aim/model3/mod3rhw.php).

#### Viewing and Interpreting the Results

First, plot the number of moles of aqueous phase NO3(aq):

 2nd 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 NO3-(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 moles of NO3(aq) is not just larger than before, as you would expect, but now remains greater than zero at all relative humidities between 70% and 95%. This is because the additional amount of material in the system is enough for the aqueous phase to release the amounts of HNO3 and NH3 required to produce the equilibrium partial pressures at each relative humidity.

### Part 3

We expect from the above that input amounts of the ions intermediate between the "base" and the "×10" calculations will yield a transition relative humidity somewhere below 86%. Similarly, for total amounts of material less than the "base" calculation we expect the transition relative humidity to be increased. To investigate this, run the following problem:

 3rd Calculation Select "Graph" as the form of output, and then enter the values and options under the following headings: Ambient Conditions Select "Relative humidity" as the variable. Start Value = 0.70 (i.e., 70%), End Value = 0.95 (i.e., 95%), Number of points = 60. Ionic Composition in Moles Hydrogen = 0.75E-7, Ammonium = 0.75E-7, Nitrate = 1.5E-7. 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 III (http://www.aim.env.uea.ac.uk/aim/model3/mod3rhw.php).

#### Viewing and Interpreting the Results

This time, plot the molality of NO3(aq):

 3rd Graph:  select the variables and enter the options as given below. X Variable: "relative humidity" Range: leave blank Scale: linear (the default) Y Variable: "mNO3-(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 transition relative humidity below which no aqueous phase particle exists (and molality is therefore zero) has now increased to about 90%. This is what we would expect: the aqueous phase becomes more dilute with increasing relative humidity, and the partial pressures of trace gases at equilibrium with it become lower. Therefore, when the total amounts of ions in the system are small a aqueous phase will exist only at relative humidities for which the amounts of HNO3(g) and NH3(g) are also small. In contrast, as the total amount of material increases the relative humidity of transition falls as there are then enough ions to sustain the higher equilibrium partial pressures of HNO3(g) and NH3(g) over the more concentrated solutions.

In summary, there is a transition relative humidity above which a aqueous phase exists, and below which the ions are present only as the gases HNO3(g) and NH3(g). This transition relative humidity depends on the total amount of material in the system. In general, the transition will be dependent upon the system composition and also the temperature, but we have not investigated these effects here.

Proceed to Lesson 3d to examine equilibrium between trace gases and solid particles, or return to the main page for this lesson.