Lesson 8a: solid/liquid equilibrium of NH4NO3

### Content

The model is used to determine the deliquescence relative humidity of NH4NO3 for a series of different temperatures.

### Part 1

The deliquescence point is obtained by calculating the water uptake of NH4NO3 as a function of relative humidity at a series of fixed temperatures. First, for 273.15 K:

 1st Calculation Select "Graph" as the form of output, and then enter the values and options under the following headings: Ambient Conditions (1) Temperature = 273.15 (2) Select "Relative humidity" as the variable. Start Value = 0.45 (i.e., 45%), End Value = 0.80 (i.e., 80%), Number of points = 50. Ionic Composition in Moles Ammonium = 1.0, Nitrate = 1.0. Trace Gases Check the NH3 and HNO3 boxes to prevent the model from trying to partition these gases 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 II (http://www.aim.env.uea.ac.uk/aim/model2/mod2rhw.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 H2O(aq)" to find out at what relative humidity the salt first begins to take up water, i.e., deliquesces:

 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 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.

At this rather low temperature we see that the deliquescence point lies at about 76% relative humidity. The amount of water taken up at this relative humidity is 3.8 moles, giving a salt molality of (1/3.8) × 1000/18.0152 = 14.6 mol kg-1.

### Part 2

Next, repeat the calculation and plot from Part 1 at both 298.15 K and 323.15 K and determine the deliquescence points and salt concentrations at these higher temperatures.

At 298.15 K the deliquescence relative humidity and water uptake are about 62% and 2.1 moles, respectively. The molality of the salt in the saturated solution is therefore (1/2.1) × 1000/18.0152 = 26.4 mol kg-1.

At the highest temperature, 323.15 K, the deliquescence relative humidity is only 47%; and the 1.3 moles of water taken up give a solution molality of (1/1.3) × 1000/18.0152 = 42.7 mol kg-1.

#### Interpreting the Results

From these results we see, first of all, that the deliquescence relative humidity of NH4NO3 decreases very rapidly with increasing temperature, more so than for any other common atmospheric compound. Why is this? We recall first of all that the deliquescence point corresponds to the solid salt being in equilibrium with its saturated aqueous solution. Consequently, the concentrations we calculated above are the same as the solubilities of solid NH4NO3(s) in water at the three temperatures. These vary greatly: from only 14.6 mol kg-1 at 273.15 K to 42.7 mol kg-1 at 323.15 K. The equilibrium relative humidity (equivalent to the water activity) above a salt solution decreases with concentration. That is why the deliquescence relative humidity is so low at 323.15 K compared to 273.15 K: the solubility of the salt is much higher and the concentration of the saturated aqueous solution almost 3× greater.

Also, remember from Lesson 7 that the water activity coefficient of aqueous NH4NO3 solutions has only a small dependence upon temperature. This confirms that the effects of solution non-ideality are small for a single strong electrolyte, and that the primary influence controlling the deliquescence relative humidity is the variation of the solubility of the solid salt with temperature.

Proceed to Lesson 8b to learn how the deliquescence properties of ammonium sulphate vary with temperature, or return to the main page for this lesson.