Lesson 5b: deliquescence of ammonium/sodium/nitrate mixtures

### Content

The deliquescence point, and water uptake, of mixtures of NH4NO3 and NaNO3 are studied for different ratios of the two salts.

### Part 1

In the first calculation we will determine the behaviour of a 1:1 molar mixture of the salts. Use the back button on the right hand browser window to return to the data input page for "variable relative humidity, or total water" calculations using Model III, or select this link. 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 = 0.45 (i.e., 45%), End Value = 0.65 (i.e., 65%), Number of points = 40. Ionic Composition in Moles Ammonium = 1.0, Sodium = 1.0, Nitrate = 2.0. 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

A page will appear in the other browser window 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 drop down lists. Instructions, and details of the variables, are given in the right frame.

Plot moles of liquid phase water 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 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.

Notice the sharp transition at 0.5 (50%) relative humidity where the salt mixture begins to take up water, and an inflection in the curve at about 62% relative humidity. The transition at 50% is the deliquescence point for the mixture and is called the mutual deliquescence relative humidity. Notice that this relative humidity is lower than the deliquescence points of either of the single salts (61% for NH4NO3, and 73.75% for NaNO3). This is always the case.

Next, we will determine the molalities of Na+(aq) and NH4+(aq) at the mutual deliquescence point by plotting the molalities of the ions (on two separate graphs) and noting the values at 50% relative humidity.

 2nd and 3rd Graphs:  select the variables and enter the options as given below. X Variable: "relative humidity" Range: leave blank Scale: linear (the default) Y Variable: "mNH4+(aq)", and then "mNa+(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.

We see from the graphs that the molality of NH4+(aq) at the mutual deliquescence point is about 26 mol kg-1, and the molality of Na+(aq) is 10.5 mol kg-1.

A further feature worth investigating is the inflection in the curve of moles of H2O(aq) near 61% relative humidity. To find the cause, we next plot moles of the solid NaNO3(s) against relative humidity.

 4th 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 NaNO3" 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.

Between the mutual deliquescence point at 50% relative humidity and the inflection at 62% some solid NaNO3(s) exists. However, the amount decreases as relative humidity rises and more salt dissolves into the increasingly dilute solution. At 62% relative humidity the last of the NaNO3(s) dissolves and it is this transition to a completely liquid system that causes the inflections we observed in the previous graphs.

### Part 2

The solid that exists at the mutual deliquescence point is not always the one with the lower deliquescence point, but is dependant on the mole ratio of the salts in the mixture. We will next study the deliquescence behaviour of a second NH4NO3/NaNO3 mixture, this time with a mole ratio of 1:3 of NH4+ to Na+:

 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 = 0.45 (i.e., 45%), End Value = 0.65 (i.e., 65%), Number of points = 40. Ionic Composition in Moles Ammonium = 1.0, Sodium = 3.0, Nitrate = 4.0. 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, we plot the moles of liquid water in order to determine the mutual deliquescence point of this mixture:

 5th 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.

We see that in this very different mixture the uptake of water begins at the same relative humidity of 50%. In fact, this is true for all mole ratios of the two salts at constant temperature.

Next we plot the molalities of NH4+(aq) and Na+(aq) to check the composition of the liquid solution at the mutual deliquescence point.

 6th and 7th Graphs:  select the variables and enter the options as given below. X Variable: "relative humidity" Range: leave blank Scale: linear (the default) Y Variable: "mNH4+(aq)", and then "mNa+(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.

We see from the graphs that the molality of NH4+(aq) at the mutual deliquescence point is 26 mol kg-1, and the molality of Na+(aq) is 10.5 mol kg-1. This is the same as for the 1:1 salt mixture studied in Part 1.

The fact that the eutectic composition of the aqueous phase, and the mutual deliquescence relative humidity, are constant for all ratios of salt can most easily be understood by taking a liquid mixture of some arbitrary composition as a starting point, and then considering what happens as the relative humidity is reduced. As this occurs the concentration of the solution increases until it becomes saturated with respect to one of the salts. Which salt depends on both the relative amounts of the two salts in solution and their thermodynamic properties. As relative humidity decreases further some of first salt precipitates (otherwise the solution would become supersaturated with respect to it), and the remaining solution becomes more concentrated with respect to the second salt as it is not being removed from solution. Eventually, at even lower relative humidities the solution also becomes saturated with respect to the second salt. This is the eutectic point, and the relative humidity is the mutual deliquescence relative humidity.

If we had started with a different initial ratio of salts then the path taken to the eutectic point would have been different – perhaps the other salt would have precipitated first – but the endpoint would have been the same: saturation with respect to both salts, which can only occur at one solution composition and equilibrium relative humidity for any given temperature.

Mutual deliquescence of two salts can also be looked at in terms of Gibbs' phase rule:

Degrees of freedom = (No. of components) – (No. of phases) + 2

At the eutectic point there are two solid salts in equilibrium with a saturated aqueous phase, hence there are three phases in total. There are also three components: two salts plus water. This leaves two degrees of freedom. Hence, if we also specify the temperature and pressure there are zero degrees of freedom and the composition of the eutectic is fixed and invariant irrespective of the total amounts of salt present.

It is worth noting that, for salts with high deliquescence relative humidities, the mutual deliquescence point is close to the product of the individual deliquescence relative humidities of the salts. However, for salts such as those examined here, which deliquesce at quite low relative humidities, this approximate rule no longer holds. Here the product is 45% (61% × 73.75%) relative humidity; not at all close to the actual value of 50%.

You should now review the conclusions on the main page of this lesson.