[Borek]

Wait, will this reaction be:

Na₂CO₃ + 2HCl --> 2NaCl + H₂CO₃?

No.

Several hours ago you checked that you don't have enough acid for this reaction:

No, because the ratio of HCl to Na₂CO₃ is 2:1 and we only have 50 ml of HCl which is only half the amount of Na₂CO₃

It even looked for a moment that you knew this is not a correct reaction:

So is it possible for the reaction to proceed as you wrote it

No.

But now we are back to the square one.

[spunkylulu]

No no I got it

Na₂CO₃ + HCl -->NaHCO₃ + NaCl

and then the second part of the reaction would be

NaHCO₃ +HCl --> NaCl + H₂O +CO₂

[Borek]

Na₂CO₃ + HCl -->NaHCO₃ + NaCl

OK

and then the second part of the reaction would be

NaHCO₃ +HCl --> NaCl + H₂O +CO₂

Would be, but we won't go there, as there is not enough acid, agreed?

Now, it seems like the problem can be reworded: we need to calculate pH of the solution of NaHCO₃, do you see it?

[spunkylulu]

Yes.

So we start with 0.01 mol of Na₂CO₃ and 0.005 mol HCl, right?  Then what?

[Borek]

We got to the point when we have a solution that is equivalent to the one prepared by mixing NaHCO₃ and NaCl, do you see it, or not?

Do you know how to calculate pH of the solution of an amphiprotic salt?

[spunkylulu]

Yes.  I think what gives me the most trouble is understanding the reaction and figuring out what reaction to use when calculating pH. 

[Borek]

http://www.chembuddy.com/?left=pH-calculation&right=pH-amphiprotic-salt

[spunkylulu]

That was helpful, thank you.

The only thing I continue to struggle with is knowing which Ka value to use in my calculation.  Since the reaction doesn't proceed to completion, I would think I would use the first Ka value, right?

The second reaction I have to do is NaHCO₃ and HCl (which, again, won't reach completion because there isn't enough HCl) and I would think to use Ka2 (since NaHCO3 comes from the second dissociation)

[Borek]

I have posted link to page that contains formula you need.

[spunkylulu]

So, based on what I have gathered, I'll use Ka2 for this reaction.  Is that correct?  (I think it's Ka2 because Ka2 relates to the dissociation of bicarbonate, and that's the product of this reaction)

[Borek]

Have you read the page I linked to? Derivation can be difficult to follow, but it yields a simple formula.