Soluble Gasses

what is the pH of DI water left to stand in 10 (ppmv) ammonia gas and exposed to atmospheric carbon dioxide?

Keywords: ammonia carbon dioxide, NH3, CO3,

Some gasses dissolve in water, then behave like acids or bases. Ammonia and carbon dioxide are good examples.

I am going to show you how to use the equiligraph to estimate the total of dissolved gas species as a function of pH and how to estimate the relative fraction of each species.

We are going to use a set of tools described on the  DIY Chemistry Hero Kit page. If you haven’t been there, please at least take a quick look now.

Basics first!

The solubility of gasses is described by Henry’s law.  In essence, the solubility of a gas in a liquid is proportional to the partial pressure of the gas over the liquid. The proportionality constant is called the ‘Henry’s law constant’ and it is a function of temperature.

[X]aq  = PX * KH(T)

Where:

[X]aq is the concentration of gas species X in aqueous solution. (mole/L) or (mole/Kg)

PX  is the partial pressure of gas X (bar)

KH(T) is the Henry’s law constant (mole/(kg*bar)) or  (mole/(L*bar))

A good source for Henry’s law constants is the NIST Chemistry Webbook.

For Ammonia at room temperature, the Henry’s law constant is 27 (mole Kg-1 bar-1).

The concentration of free ammonia distilled water with 10 (ppmv) NH3 partial pressure is:

1) (ppmv) to (bar)

PNH3 = 1.0x10-5  (atm) * (760 torr/atm )/ (750 torr / bar)

= 1.01x10-5 (bar)

The concentration of free ammonia is then:

[NH3] = 27 (mole Kg-1 bar-1) * 1.0x10-5  (bar) = 2.7x10-5  (mole Kg-1 )

NOTE: for our purposes, we will ingore the difference between (m and ole Kg-1 ) and (mole L-1 ).

Now that we know the concentration of free ammonia, this should be simple.

Get the ammonia transparency and a fresh photocopy graph for a background. set the CTotal line at log10(2.7x10-5 ) = -3.6.

This is shown in figure 1.  The problem with figure 1 is that it is WRONG, because it shows the total concentration is fixed at all pH. This would be a good chart if we’d just made a solution of ammonia from a concentrated aqueous solution.

Figure 1 shows that the free ammonia concentration will drop as the pH drops below the pKa!

However, the partial pressure of ammonia gas actually holds the free ammonia concentration constant. As the pH drops, free ammonia, NH3,  is converted to ammonium ion, NH+4 . As the free ammonia is converted, more gas dissolves into the solution, keeping the free ammonia concentration constant.

The as a result, the total concentration CTotal = [NH3] + [NH+4 ] increases as the pH drops. Figure 6. Equiligraph showing ammonia with CTotal = 2.7x10-4 (M). The typical configuration is shown.  This is not a correct representation of the ammonia gas dissolved in water with PNH3 = 10 (ppmv). Figure 2. Plot showing correct concentration of ammonia and CTotal as a function of pH for 10 (ppmv) ammonia gas. The line labeled CTotal increases as the pH decreases because free ammonia is converted to ammonium ion.

In order to correct this problem, all we have to do is recognize that the free ammonia line  α1 line represents CTotal * α1 , and α1  is the fraction of the total present at any given pH.  This means that for a fixed free ammonia concentration:

[NH3] / α1   = CTotal

Basically, all we have to do is divide the fixed ammonia concentration by α1 to get a line representing CTotal .

We do this by inverting the graph, because on a log scale, division is represented by subtraction.

Figure 2 shows this inversion. For a solution buffered at pH =7.0, the total concentration of all ammonia species, CTotal,  is slightly less than 0.1 (M), which mostly in the form of ammonium NH+4. at pH =8, the concentration of ammonium ion is about 0.01 (M).

Of course, Figure 2 is still WRONG!  We are not accounting for atmospheric carbon dioxide, CO2.  Figure 2 would be valid if we had a controlled atmosphere that excluded  CO2.

Now we know the concentration of carbonate species as a function of pH for atmospheric CO2 levels.  This is a very useful graph, but it is a bit busy.  I am going to transfer only the [H2CO3] line to a photocopy, so I can use it for other analyses.

We now can look at the equilibrium between NH3 and CO2 gasses dissolved in an aqueous solution held artificially at a fixed pH (buffered solution).

Take the NH3 transparency, overlay the graph with only [H2 CO3] on it and we get figure 5, which immediately gives us the answer we wanted:

The total concentration of ammonia species in a solution with 10 (ppmv) ammonia gas  standing over a solution saturated with carbon dioxide at atmospheric levels.

The red circle in figure 5 highlights the desired answer:

H2CO3 + NH3  <-->  NH4+ + HCO3-

with the condition that:

[NH4+] = [HCO3-]

Atmospheric carbon dioxide,CO2, levels are currently around 380 (ppmv)

For carbon dioxide at room temperature, the Henry’s law constant is 0.035 (mole Kg-1 bar-1).

The concentration of free CO2 in distilled water with 380 (ppmv) CO2 partial pressure is:

380 (ppmv) to (bar)

PCO2 = 380 x10-6  (atm) * (760 torr/atm )/ (750 torr / bar)

= 3.85 x10-4 (bar)

The concentration of free ammonia is then:

[CO2] = 0.035 (mole Kg-1 bar-1) * 3.8x10-4  (bar)

= 1.35 x10-5  (mole Kg-1 )

log10(1.35 x10-5 ) = -4.87 Figure 3. Plot of carbonic acid, with the free carbon dioxide set equal to [H2CO3] at log10(1.35 x10-5 ) = -4.87

Get the CO2 transparency and a fresh photocopy graph for a background. Set the CTotal line at log10(1.35 x10-5 ) = -4.87. This is shown in figure 3. Figure 4 shows the inverted graph, with the [H2CO3] now representing the CTotal.

[H2CO3] / α0   = CTotal

At this point a little clarification is needed.

CO2 + H2O <--> H2CO3.

The assumption made here is that [H2CO3.] is equal to [ CO2 ]aq.  The first equilibrium constant accounts for this assumption.

H2CO3 <---> H+ + HCO3-

HCO3- <----> H+ + CO32-

These equilibria imply that if the pH is artificially held higher than the pH of a pure acid solution, then the solution will continue to dissolve CO2 and convert it to both HCO3-  and CO32- . This is similar to the case for ammonia described above. Figure 4. Inverted plot of carbonic acid, with the free carbon dioxide set equal to [H2CO3] at log10(1.35 x10-5 ) = -4.87. The [H2CO3] now represents CTotal Figure 5. Plot of  total concentration of ammonia species with 10 (ppmv) NH3 gas and atmospheric CO2 standing over the solution. The resulting equilibrium solution will have a pH near 8.6 and a concentration of [NH4HCO3]  near 10-2.6 = 2.5 x 10-3 (M). The red circle highlights  the intersection of the [NH4+] and [HCO3-] lines. This is the result we wanted.

Why this works....

The ammonia equilibrium, in terms of the ammonia partial pressure:  Note that for a given ammonia pressure, the [NH4+] is proportional to [H+].

For our system, the dominant species in the carbon dioxide system is bicarbonate ion, HCO3-  Setting [NH4+] equal to [HCO3-] Rearranging: Solving the last equation for [H+], we get a pH of 8.4. This compares very well with the value of 8.6 we took from the graphic solution in figure 5. The  computed ammonium bicarbonate concentration, [NH4HCO3] is 10-2.7 = 2.0 x10-3 (M), which is very close to the value 10-2.6 = 2.5 x10-3 (M) we read from the graph in figure 5.

Of course, this physics model only works for over the range, pK1,CO2 + 0.7 pH < pKNH3-0.7 (6.3+0.7 < pH < 9.24 - 0.7), because this is the valid range where our assumption that [HCO3-] is the dominant CO2 species.

For pH outside of this range we need to account for [CO32-].   Solving an equation that is cubic in [H+] gets messy, but we can plot the the two sides of the equation [HCO3-] + 2 [CO32-]. vs [NH4+], as shown in figure 6.  This is an exact solution. Figure 6 shows the result for PNH3 of 10 and 100 (ppmv)

The graph shown in figure 5 is an approximate solution, where we assume that the [NH4+] dominates the total concentration of ammonia species, CTotal, NH3 = [NH4+] + [NH3].  This only holds at pH < ( 9.24 - 0.7).

Figure 7 shows us the error in these estimate for 10 and 100 (ppmv) ammonia with atmospheric CO2. Figure 7 graph also gives us a better understanding of how the result will vary if either the PNH3 or PCO2 changes .

Note that above the pKNH3, additional alkalinity is required and that the allowed [NH4+] drops below the free [NH3].  The extra alkalinity will eventually be neutralized by the [H2 CO3], so these graphs do not represent equilibrium for pH > pKNH3.

You also can use this method to predict the partial pressure of either CO2 or NH3, simply by assuming a starting concentration of ammonium carbonate!

I think it would be safe to say that most chemists, with a 4 year degree in chemistry, would find this problem easier to solve by measuring the pH in the lab. This approach would not measure the resulting [NH4HCO3].

Unfortunately, this is often not possible. In this case, getting EHS to approve a supply of ammonia gas in the building would be a major hurdle.

I have used a very similar analysis to set up test chambers where a known vapor pressure of ammonia gas was required.   I did not need EHS approval because I was only storing solutions of ammonium phosphate.  I did not need to buy equipment to monitor and control ammonia gas. I knew each part being tested was exposed to the same ammonia level because I used the same solution. Figure 6. Plot [NH4+] vs [HCO3-] + 2[CO32-] for ammonia pressures of 10 and 100 (ppmv) and a normal atmospheric CO2 pressure of 380 (ppmv). Figure 7. Plots similar to figure 5, showing the inverted [H2CO3] and [NH3} lines, which estimate CTotal for both species.  As expected, the error increases when pH > 8.5 (pKNH3 - 0.7).

Tutorials / Interpretation:

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Software / Apps:

Titration:    Apple AppStore

Equiligraph, buffer capacity and titration curve. Fizz:

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A calculator showing CaCO3 solubility as a function of atmospheric CO2 Solubility:

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Equiligraph showing solubility as function of pH