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Chemistry Forums for Students => High School Chemistry Forum => Topic started by: Rutherford on March 01, 2013, 10:37:10 AM

Title: Determine pKa1 of carbonic acid
Post by: Rutherford on March 01, 2013, 10:37:10 AM
Problem: When saying ''the solution of carbonic acid'', it is actually meant "the solution of carbon-dioxide in water". Most often, the pKa1 of this acid is said to be 6.4, which is not expected from its structure. If you know that in a soda-water, whose pH is 5.65, only 0.2% of the dissolved carbon-dioxide is present in the form of the undissociated acid, how much is the real first constant of acidity of H2CO3?

Attempt: I mark the number of moles of the dissolved CO2 at the beginning with x. 0.002x is the number of moles of carbonic acid. I have two reactions:
1° CO2+H2O ::equil:: HCO3- + H+      pKa1=6.4
  0.998x              y    2.24*10-6

y=0.177x

2° H2CO3 ::equil:: HCO3- + H+        pKa1=z
  0.002x       0.177x   2.24*10-6

z=3.70 while the answer is 3.77. Where am I wrong?
Title: Re: Determine pKa1 of carbonic acid
Post by: Borek on March 01, 2013, 12:47:16 PM
Quote from: Raderford on March 01, 2013, 10:37:10 AM
1° CO2+H2O ::equil:: HCO3- + H+      pKa1=6.4
  0.998x              y    2.24*10-6

Why 0.998x? pKa=6.4 was calculated assuming there is NO free CO2 present.

I would start calculating total concentration of carbon dioxide from known pH and pKa (assuming it is 100% converted into carbonic acid).
Title: Re: Determine pKa1 of carbonic acid
Post by: Rutherford on March 01, 2013, 12:57:46 PM
How do you mean NO CO2? The first pKa was calculated assuming that this reaction represents carbonic acid:
CO2+H2O ::equil:: HCO3-+H+

"I would start calculating total concentration of carbon dioxide from known pH and pKa (assuming it is 100% converted into carbonic acid)."

How would I do that? I need the concentration of HCO3-?
Title: Re: Determine pKa1 of carbonic acid
Post by: Borek on March 01, 2013, 01:53:06 PM
Quote from: Raderford on March 01, 2013, 12:57:46 PM
How do you mean NO CO2? The first pKa was calculated assuming that this reaction represents carbonic acid:
CO2+H2O ::equil:: HCO3-+H+

No FREE CO2. All is present in the form of H2CO3, and the reaction taking place is

H2CO3 ::equil:: H+ + HCO3-

Thats the definition of Ka, isn't it?

Quote
How would I do that? I need the concentration of HCO3-?

Stoichiometry of dissociation.
Title: Re: Determine pKa1 of carbonic acid
Post by: Rutherford on March 01, 2013, 03:09:36 PM
Quote from: Borek on March 01, 2013, 01:53:06 PM
No FREE CO2. All is present in the form of H2CO3, and the reaction taking place is

H2CO3 ::equil:: H+ + HCO3-

I calculated H2CO3 when assumed that [H+]=[HCO3-] then the actual [H2CO3]=0.002*the one I calculated earlier. Then again, I get the same pKa, 3.7  ???.
Title: Re: Determine pKa1 of carbonic acid
Post by: Borek on March 02, 2013, 06:19:06 AM
Wording is slightly ambiguous. I took

Quote
only 0.2% of the dissolved carbon-dioxide is present in the form of the undissociated acid

to mean 0.2% of the carbon dioxide is converted to carbonic acid (and dissociation follows), while it is intended to mean "in the equilibrium mixture concentration of carbonic acid is 0.2% of the total analytical concentration of CO2".

And with this approach I got 3.77.

Which is kind of stupid - final answer is given with three sigfigs, while the least number of sigfigs in the input data is one.
Title: Re: Determine pKa1 of carbonic acid
Post by: Rutherford on March 02, 2013, 06:35:38 AM
Got the same.
Calculated the concentration of CO2 from the first reaction, then added the amount that dissociated (2.24*10-6) to get the analytical concentration and I multiplied it by 0.002 to get the concentration of carbonic acid. Then the answer is really 3.77.

Thanks for the help.