Can the Volatility of HCl be Ignored?
The analysis presented in the manual ignores the involvement of HCl. As is easily detected from its pungency, solutions of HCl are accompanied by significant concentration of HCl in the vapor phase. Indeed, while the Henry's Law constant for CO2 in water at 25 oC is 0.032 mol/L-atm, the constant for HCl and water is estimated* to be 19.0 mol/L-atm
i.e., Molarity of HCl = 19.0 PHCl .
So the vapor pressure of HCl in equilibrium with a 1.0 M solution of HCl is 1 / 19.0 = 0.053 atm. (~5% of 1 atm)
If both the temperature and the concentration of HCl remained constant during the experiment, we could simply include the contribution of HCl vapor with the "air" that fills the gaseous volume of the apparatus before the reaction proceeds, as we assume in the lecture and lecture notes..
However, unlike the water, some HCl is necessarily consumed by its reaction with the unknown. We use 10 mL of 1.0 M HCl (= 10 mmol) of acid. The unknown samples weigh approximately 200 mg and contain 50% - 90% NaHCO3. Therefore, the samples contain between 100 and 180 mg of NaHCO3 (Molar Mass = 82.0 mg/mmol) or between 1.2 - 2.4 mmol. The same number of mmol of HCl are consumed in the reaction. So, the final amount of HCl in the solution is only between 7.6 - 8.8 mmol. The volume remains 10 mL, so the final concentrations of HCl are reduced from 1.0 to 0.76 - 0.88 mmol/mL.
From Henry's Law for HCl, the vapor pressure of such solutions of HCl will be between 0.76/19.0 and 0.88/19.0 or,
PHCl = 0.040 - 0.046 atm.
So, the contributions of HCl to the pressure in the initial (PHCl = 0.053 atm) and final systems (PHCl = 0.040 - 0.046 atm) are not constant. The change is between 0.007 - 0.013 atm.
For the typical experimental conditions in this exercise, the partial pressure of CO2 in the gas phase after the reaction is 0.33 ± 0.07 atm. As noted in the lecture, we include the initial HCl contribution as part of the air in the system, so only the change in HCl concentration and consequent partial pressure due to the consumption of HCl would affect our results.
Therefore, the percent error that is introduced in the partial pressure of CO2 by ignoring the change in HCl concentration, and its consequential partial pressure, ranges from:
100 X 0.007 / (0.33 ± 0.07) to 100 X 0.013 / (0.33 ± 0.07)
1.7 % - 5.0 %
For some unknowns, this could be comparable to the error in measuring the intial and final syringe and system volumes.
We choose to ignore this correction in our analysis.
The truly astute student will note that the above analysis remains incomplete in that it ignores the amounts of HCl that are lost from the solution to the vapor phase before and after the reaction. A more complete analysis is left to the student..
* The Henry's Law constant for HCl is strongly temperature dependent
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Last Update: RFS 2015-09-18