[Edher]

Saludos,

        This IS a good homework problem,

If 535 mL of gaseous HCL, at 26.5 *C and 747mmHg, is dissolved in enough water to prepare 625 mL of solution, what is the pH of this solution?

I almost got the right answer,

n=PV/RT = 747 mmHg (0.535L) / 62.364 mmHg.mol-1.K-1 (299.65 K) = 0.0213858 moles

0.0213858 moles / 1 L   = 0.0213858 M

0.0213858 moles = X moles    
          1 L                0.625 L                                

X = 0.011441403 moles

0.011441403 moles  = 0.0183062448 M
          0.625 L

- (log 0.0183062448) = 1.7374 pH

However, the right answer is 1.466 pH. Where did I go wrong?

Edher

[Mitch]

This doesn't give the right answer, although its closer... But wouldn't the moles of HCl in the gas phase also equal the moles of HCl in the aqueous phase? So why did you make a mole ratio?

[Edher]

Saludos Mitch,

         Yeah, I tried exactly what you said before I came up with the ratio step, but since I didn't get the right answer I was just trying to add a few more steps to maybe somehow get the right answer.

If I leave out the ratio, and use the number of moles in the gas phase I get pH 1.66 rather than 1.466. Do you think perhaps there's a typo in my book?

Edher

[Mitch]

I think so.

[jdurg]

Nope, the book is just fine because I came up with an answer of 1.466 for the pH.  Let me show you where you went wrong.

Your first step is correct.  You need to figure out the number of moles of HCl you have from the temperature, pressure, and volume data.  You correctly came up with 0.0213858 moles.  In this next part is where you went wrong.

Once you have the number of moles of HCl gas, you have to calculate its concentration in the total volume of solution you were given.  This is done by taking your number of moles (0.0213858) and dividing it by your total volume (0.625 L).  This will give you a molarity of HCL of 0.03421728 M which is also the H+ concentration.  

For some reason, you tried to do a mole ratio when there was absolutely no need.  The units for the answer you came up with out of the n=(PV)/(RT) is simply moles.  Not moles per liter.

Anyway, now that you have the molarity of the H+ concentration, you just take the -log of that and you get a pH of 1.466.  

[Mitch]

woops nice catch.

[Edher]

Nope, the book is just fine because I came up with an answer of 1.466 for the pH.  Let me show you where you went wrong.

Your first step is correct.  You need to figure out the number of moles of HCl you have from the temperature, pressure, and volume data.  You correctly came up with 0.0213858 moles.  In this next part is where you went wrong.

Once you have the number of moles of HCl gas, you have to calculate its concentration in the total volume of solution you were given.  This is done by taking your number of moles (0.0213858) and dividing it by your total volume (0.625 L).  This will give you a molarity of HCL of 0.03421728 M which is also the H+ concentration.  

For some reason, you tried to do a mole ratio when there was absolutely no need.  The units for the answer you came up with out of the n=(PV)/(RT) is simply moles.  Not moles per liter.

Anyway, now that you have the molarity of the H+ concentration, you just take the -log of that and you get a pH of 1.466.  

Thank you jdurg,

        To think that I actually did exactly what you said but didn't bother to find the negative logarithm of that. Instead, I subtracted that from the ratio then look for the negative logarithm. But now I know how to solve it.

Thank You,
Edher