"what's the new pH" challenge question

[beastmaster]

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You have 100mL of 0.01M acid at pH of 2.

What volume of H2O is needed to raise the pH by a tenth?

 

[Will Hunting]

You have 100mL of 0.01M acid at pH of 2.

What volume of H2O is needed to raise the pH by a tenth?

26.5 ml?

 

[SpyPuts]

58.4 mL (give or take) will get you to a pH of 2.2.

Question is kind of sketchy since pH can exceed 14 and drop below 0.

 

[PneoDr]

NM, I meant 58mL =(

 

[EndSong]

If by a tenth you mean .1 then its ~26 mL
If by a tenth you mean raise the value by a tenth of a the original value then 58.4 mL

 

[Will Hunting]

If by a tenth you mean .1 then its ~26 mL
If by a tenth you mean raise the value by a tenth of a the original value then 58.4 mL

Haha yea, i just assumed tenth =.1 and not .2, it's probably the latter so 58.4 ml.

 

[beastmaster]

Boy you guys are sharp (~26mL is correct by my calculation), even picked up on the ambiguity in my wording! I thought of the question on my way to work, imagining drinking large volumes of water and what it would do to a small pool of stomach acid. I should have solved it before labeling it a 'challenge' to people preparing for the MCAT!! I should have asked how much antacid you'd need!


[The solution, for the curious: a concentration of 0.01M means you have 0.1 moles of HCl sitting in ~100mL water. Basic multiplication will give you a total of ~126mL water if you switch 0.01 with 0.008 (the reverse log of 2.1, a tenth increase). 26mL is the difference in volume. Le Chatelier's principle means you don't have to run to the messy Hasselbach for this one!]

 

[rs76]

How do you solve this one. SInce its a stong acid all of the HCl disassociates. Therefore you have .1 M H+ and pH=-log(.01)=2

A tenth increase means that the pH means that the new pH will be 2.2. How do you solve for the volume now?

Your fellow dumb MCAT'er!

 

[SpyPuts]

Find out what concentration of H+ corresponds to a pH of 2.2. This requires a calculator. Since the moles of acid does not change, you know that moles acid initially is equal to the moles of acid after the dilution, allowing you to use M(1)*V(1)=M(2)*V(2)

Solve as such:

M(i)*V(i)=M(f)*V(f)

The only unknown now is final volume. You know initial conc., initial volume, and final concentration.

 

[Righty123]

You have 100mL of 0.01M acid at pH of 2.

What volume of H2O is needed to raise the pH by a tenth?

Just a quick note:

A 0.01M acid (assumed to be HCl) does not give you a pH of 2 when the volume is 100mL (0.1L), since the moles comes out to 0.001mol of H+ ( 10^-3), which is a pH of 3. The initial molarity would have to be 0.1 for the pH to be 2.

 

[Nooro]

not to sound like a jerk, and I realize this is SUPER trivial, but i'm curious as to how people got around 26ml when i'm getting exactly 25? The reason i ask, is, if perhaps i'm doing it the wrong way but just coming close out of luck?

.01 x 100 ml = .008 x (new volume)

which comes out to 125 ml, therefore a difference of 25 ml?

Sorry

 

[pballer66]

Yep got 25 ml here. start out by finding what concentration of acid gives you a pH of 2.1 which somes out to ~.008M then you use the equation M1V1=M2V2 so 100(.01)=.008V2 and V2 = 125 so then 125-100 equals 25 ml.

 

[Will Hunting]

Yep got 25 ml here. start out by finding what concentration of acid gives you a pH of 2.1 which somes out to ~.008M then you use the equation M1V1=M2V2 so 100(.01)=.008V2 and V2 = 125 so then 125-100 equals 25 ml.

We didn't round. .01*100=.00794 =126.58-100=26.58. if u use .008 then u get 25. In this case the sig figs make a difference.

 

[Nooro]

wow, yeah I wold delete my question if I could, just wasnt thinking all there, thanks guys.

 

[Will Hunting]

Just a quick note:

A 0.01M acid (assumed to be HCl) does not give you a pH of 2 when the volume is 100mL (0.1L), since the moles comes out to 0.001mol of H+ ( 10^-3), which is a pH of 3. The initial molarity would have to be 0.1 for the pH to be 2.

I'm pretty sure pH is equal to the concentration of H+ which is the molarity. in this case it's says you have 100ml of .01M Acid. You're right in that M=moles/liters so .01M * .1L =.001 moles, but pH doesn't ask for the number of moles it asks for concentration.

 

[beastmaster]

Just a quick note:

A 0.01M acid (assumed to be HCl) does not give you a pH of 2 when the volume is 100mL (0.1L), since the moles comes out to 0.001mol of H+ ( 10^-3), which is a pH of 3. The initial molarity would have to be 0.1 for the pH to be 2.

That's an incorrect analysis.

pH deals with concentration of H+ (molarity) rather than absolute content (moles). Volume is irrelevant to pH. I can extract 10mL out of the 100mL solution and it will still be pH of 2 because the concentration of H+ remains the same.