Lesson 2b: deliquescence of a dry salt aerosol

### Content

The system containing ammonium (NH4+) and nitrate (NO3) is equilibrated over a range of relative humidities, and the deliquescence point of solid ammonium nitrate is determined.

### Entering the Data

In Lesson 1 we saw that ammonium nitrate was in the aqueous phase for relative humidities greater than about 70%, while in the previous part of this lesson we found that the salt exists as a solid at 50% relative humidity. Is there a smooth or sudden transition between the two states, and where does this transition occur?

To answer this question we calculate the amount of solid NH4NO3 in the system across a range of relative humidities. 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), and 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 = 0.50 (i.e., 50%), End Value = 0.70 (i.e., 70%), Number of points = 60. Ionic Composition in Moles Ammonium = 1.0, Nitrate = 1.0. Trace Gases Click on "HNO3" and "NH3" to prevent these gases being partitioned into the vapour phase. 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 moles of solid NH4NO3 against relative humidity:

 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 NH4NO3" 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.

Notice that the moles of solid salt in the system drops to zero at about 61% relative humidity in a sharp transition. This is called the deliquescence point, and the value of the relative humidity at this point is the Deliquescence Relative Humidity or "DRH".

Next, plot the amount of liquid water in the system:

 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 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.

As expected, we see that there is no liquid water below about 61% relative humidity where the system contains only solid NH4NO3(s). Immediately above 61% relative humidity we see that there are about 2.1 moles of liquid water. Here system exists as a completely aqueous solution, because we saw in the previous graph that there is no solid NH4NO3 above the deliquescence point. The moles of liquid water increase at higher relative humidities, showing that the ammonium nitrate solution is becoming more dilute, as we would expect.

The deliquescence relative humidity of a single salt is the relative humidity at which the salt takes up water and dissolves into it. This quantity is a function only of temperature for a single salt, but not for mixtures of salts, as will be shown in a later lesson.

The DRH can be looked at in another way: it is the equilibrium relative humidity above an aqueous solution that is saturated with respect to the solid it contains. Thus the concentration of the solution at the deliquescence point is the same as the solubility of the salt at that temperature. In this example the molality of the NH4NO3 at that point is - by inspection of the graphs - equal to 1.0/2.1 × (1000/18.0152) = 26.4 mol kg-1. You can verify this by plotting the molality of NH4+ or NO3 ions in the system against the relative humidity.