what volume of HCl was added if 20 mL of 1 M NaOH is titrated with 1 M HCl?

[Smooth Operater]

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

the answer is....20.4 mL

but how would you get it? Thanks!

 

[wvupredent]

forgive me if i'm simplifying it too much. i'm not trying to insult you. just want to make sure it's explained well.

you have one-to-one acid:base ratio. you know 20 ml NaOH was added and you want a pH of 2, which is acidic, so you know right away the HCl you add will be more than 20. The first 20 mL of HCl cancel out the NaOH, so you need to find the concentration of H+ in the solution to give a pH of 2.

pH= -log10[H+] --- [H+] is molar concentration

2 = -log10 [x/0.04] ---0.04 is total volume of solution and x is moles of H+

10^-2 = x/0.04

x= 0.0004

original 0.02 liters + 0.0004 liters = 0.0204 liters or 20.4 mL 👍

 

[wvupredent]

also note that x is in moles, but because it's a 1M solution, you can directly take that to liters.

you have to be careful if you're working with a concentration other than 1M. it just so happens this question given doesn't present the possibility for that mistake.

i hope this helps.

 

[Smooth Operater]

i am just wondering how come we need to use 0.04 L, the total volume of solution in the equation. THanks for you continous help! 🙂

 

[wvupredent]

You need to add 0.04 L more of HCl to make it an acidic solution with a pH of 2. If you simply added 20 mL, you'd have a neutral solution. Anything over 20 mL will be H+ ions floating around in the solution...the more H+ ions, the stronger the acidity, and the lower the pH value.
And since pH is a logarithmic value using concentration of H+ ions in the solution, you can simply solve for the number of moles you need to get that pH of 2. I set the equation up in my first post and solved for the number of moles of H+ (in the 40 mL of TOTAL solution). Since the molarity is 1 (1 mol/1 liter), then you know it is already in liters, as well as moles.

The first 20 mL are simply getting you to the equivalence point. After that, it begins becoming acidic, and they're asking you to find out how much of the acid you have to add to reach the specified pH.

Hope this help! Let me know if you have any other questions!

 

[wvupredent]

i just read your question again and realize what i just posted did not answer it. the reason we have to use 0.04 L of the total solution in the equation is [H+] is the MOLAR concentration of ions. So, you change [H+] to equal: x moles/L solution

I hope that answers the question you actually asked. 😀