Top Score GC question

[TXpredent]

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What volume of HCl was added if 20 mL of 1 M NaOH is titrated with 1 M HCl to produce a pH = 2?

I know since the concentrations of the strong acid and strong base are the same, they will cancel each other out with a 1:1 ratio. So I know it's got to be just over 20 mL but how much HCl will give me a pH of 2?

I figured it would've been 1 x 10^-2 moles of HCl which with 1 M solution would be 1 x 10^-2 L which is 10 mL so 30 mL of HCl was titrated but the answer is 20.4. Their solution is really confusing and I can't figure out what's going on in it. Any ideas on how to do this problem?

 

[njohns24]

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[Member 8586]

if its 1M NaOH and 1M HCL both around 20 mL, how is the pH 2? - shouldn't it be around 7 (the equivalence point) b/c you're titrating a strong base with a strong acid?

 

[TXpredent]

Since the pH is 2 we know [H+] = 1e^-2. Set up as follows and solve for x.
1e^-2= x / 40 + x.....where 40 is the total volume (solved via MV=MV) and the x on the denominator is minute so can be ignored here. x = .4. Add that to the 20 that you added for neutralization. Bam!

ok, that makes much more sense, i was kinda close lol! I didn't understand Top Score's explanation but this makes much more sense. How did you know 'x' in the denominator was going to be minute? Also, what does 'x' represent here? The [H+] ions needed in a 40 mL solution to get a total concentration of 1 x 10^-2?

 

[csafizadeh]

I believe that X represents the number of moles of H+ ions needed since molarity which can also be viewed as concentration is equal to the number of ( moles / liters ).