[Halogen876]

I have an electrochemistry problem I've been having some trouble with. Here is is:

The voltage of a hydrogen electrode at 25°C was measured as -0.645V vs. an SCE reference electrode while immersed in a 0.00100F solution of a weak acid. At this electrode, H₂ was bubbled through the solution into the open atmosphere. Atmospheric pressure was measured as 748.0 mm Hg. The vapor pressure of water at 25°C is 23.8 mm Hg. Calculate the pKa of the weak acid.

I started off and converted the voltage vs the SCE to what it would be if it were measured vs an SHE so 0.242V-0.645V=-0.403V.

I converted the atmospheric pressure from mm Hg to atm so 0.9842 atm.

I'm not sure how the vapor pressure of water comes into it though...obviously I can convert it to atm to so 0.03132atm and I know Raoult's Law often is used when you're dealing with vapor pressure but I'm not sure how to incorporate that with the electrochemistry...

The answer in the book is 10.88. If anyone could help me get more of a start on this question, I'd really appreciate it! Thanks!

[Borek]

Apparently you are expected to assume (not a bad assumption I admit) that pressure inside of the bubbles is a sum of hydrogen and water partial pressures...

[Halogen876]

Ok thanks, that makes sense and I know the partial pressure of water since it's given in the question. I know E and E° (which is zero since we're dealing with a hydrogen electrode) but I'm not sure how to fill everything else into the Nernst equation since water is not involved in the reaction we're dealing with and I'm not sure how to find the partial pressure of hydrogen so I'm not quite sure where to go with it from here...any more help would be appreciated

[Borek]

What is the pressure inside of the hydrogen bubble?

[Halogen876]

Well the only thing I can think of is to assume that we're at standard conditions since we're dealing with a hydrogen electrode and we're not given any other information that I can see would lead to thinking something else but I could be mistaken...if I'm right though, then the pressure of hydrogen gas in the bubble would be 1 atm but I'm not sure

[Borek]

You were given atmospheric pressure (as measured during the experiment) for a purpose.

[Halogen876]

Yes, I figured that was there for a reason - i just wasn't quite sure what that reason was! I think I remember learning somewhere though that the pressure inside and outside a bubble is equal, which, in this case, is atmospheric pressure. So could I find the pressure of hydrogen in the bubble by subtracting the water vapor pressure from the atmospheric pressure?

[Borek]

So could I find the pressure of hydrogen in the bubble by subtracting the water vapor pressure from the atmospheric pressure?

Exactly.

[Halogen876]

That's great! Thank you so much! I was able to use that information and finish the question and come out with the correct answer! I really appreciate all of your *delete me*

[Halogen876]

That last message was supposed to say "help" not "delete me"! I don't know how that happened...