PH of solution containing HCl and bicarbonate

[kmichel1985]

This should be an easy one for some of you, but it's difficult to me because of my lack of chemistry knowledge. This is not a homework problem, but a calculation I need to do for my research.

I need to calculate the pH of a 1 Liter solution containing 0.000077 M HCl and 0.03 M Na-HCO3.
(not necessary to read --->) I started with 10 mL of 25% HCl, which has a concentration of 7.7 M HCl. I diluted this in 1 Liter of water bringing the concentration of HCl down to 0.077 M. I then take 1 mL of this solution and dilute it again in 1 L bringing the concentration of HCl down to 0.000077 M. To this solution I add 2.52 grams of sodium bicarbonate. This has a concentration of 0.03 M (2.52 g) x (1 mol / 84 g) x (1/L). The pKa for bicarbonate/carbonic acid, or HCO₃ / H₂CO₃ is 6.4. The pKa for carbonate/bicarbonate, or CO₃/HCO₃ is 10.3. Bicarbonate, a buffer, reacts with HCl, as follows:

NaHCO₃ + HCl <--> H₂CO₃ + NaCl

If you don't want to do calculations, could you tell from just looking at the concentrations that I will have a near neutral pH? I'm growing microorganisms.

 

[Borek]

If you want to know pH, it is better to measure it.

Amount of HCl you added is three orders of magnitude lower than the amount of bicarbonate, so it is not able to substantially change the pH of the solution - which means you are close to the pH of the bicarbonate ($\frac{pK_{a1}+pK_{a2}}{2}$, see derivation here). pH calculator shows pH changes just by a few hundredths.

 

[kmichel1985]

Thanks for the help. I just used the calculator and got the same result. Someone else told me I could use Henderson-Hasselbach, but in that equation do I also use the intermediate pKa? This person told me to:

1.) assume that all the HCl is reacted with the bicarbonate to form H2CO3
2.) assume that initially HCO3 and H2CO3 are equimolar
3.) add the concentration of HCl lost to H2SO3 and subtract it from HCO3.

 

[Borek]

Thanks for the help. I just used the calculator and got the same result. Someone else told me I could use Henderson-Hasselbach, but in that equation do I also use the intermediate pKa? This person told me to:

1.) assume that all the HCl is reacted with the bicarbonate to form H2CO3
2.) assume that initially HCO3 and H2CO3 are equimolar
3.) add the concentration of HCl lost to H2SO3 and subtract it from HCO3.

That's also a correct approach. Yes, you need to use pK_a1 here, as it will be about equilibrium between H₂CO₃/HCO₃^-.

Note that HH equation has its limitations, especially when the pH calculated is far from the pKa value, pr when the pKa is small or too high.