Lesson 7a: aqueous ammonium nitrate and sulphate at a fixed relative humidity |
1st Calculation |
|
Note: the above should be entered on the
"variable temperature" parametric calculations page of
Model II |
First we plot the moles of liquid water associated with the particle against temperature:
1st Graph: select the variables and enter the options as given below. | |
X Variable: "temperature" 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. |
There is about a 10% increase in the water content of the particle over this 25 K range, from about 12.3 to about 13.6 moles. What is the cause, keeping in mind that the relative humidity and therefore the water activity of the solution has remained constant? To answer this question, plot the water activity coefficient (fH2O):
2nd Graph: select the variables and enter the options as given below. | |
X Variable: "temperature" Range: leave blank Scale: linear (the default) |
Y Variable: "fH2O(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. |
Here we see about a 10% decrease in fH2O over the temperature range. Recall that:
water activity = xH2O × fH2O
Because the water activity coefficient falls as temperature increases the water mole fraction xH2O (and consequently the the amount of water in the particle) must rise to maintain a constant water activity. This confirms what we saw in the first graph.
2nd Calculation |
|
Note: the above should be entered on the
"variable temperature" parametric calculations page of
Model II |
3rd Graph: select the variables and enter the options as given below. | |
X Variable: "temperature" 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. |
The water content of the (NH4)2SO4 droplet also increases with temperature, but this time by only about 1.5% from 17.95 to 18.22 moles. We can see a similarly small change in the water activity coefficient:
4th Graph: select the variables and enter the options as given below. | |
X Variable: "temperature" Range: leave blank Scale: linear (the default) |
Y Variable: "fH2O(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 water activity coefficient has a value of about 1.049, and changes only by a very small amount. The deviations from the smooth curve are an artifact: the numerical output of the calculated activity coefficients is rounded to six digits.
We conclude from these calculations that, for simple salts at quite high relative humidities, the water content of a particle varies relatively little with temperature. Also, that individual salts have different water uptake properties – in this case (NH4)2SO4 showing the smaller variation.
Proceed to Lesson 7b to learn how water uptake varies with temperature for sulphuric acid particles, or return to the main page for this lesson.