Question

What is the total volume of the solution when an indicator, HIn, first changes color if the Ka = 3.4 x 10^-6 and 30.0 mL solution of 0.40 M Ba(OH)2 is titrated with 0.25 M HCl using this indicator. Show work.

Answer 1

Hi, the indicator HIn ionized in the solution as follows:

If we assume that HIn is colorless and In- has a colour such as phenolphthalein, the first colour change occurs immediately after HIn = In-. Since you are adding base a miniscule amount of base causes the equilibrium to shift towards In- and colour change occurs. According to Henderson Hasselbalch equation, we have

since at colour change HIn = In-

so

and log1 = 0

since the Ka is given as and and

So, we need pH = 5.47

now and

Now that we have the amount of H+ in the solution, we can say that this amount of hydrogen ions in the solution comes from HCl solution. An amount equivalent to the millimoles of barium hydroxide is also required.

millimoles of barium hydroxide = 30.0 mL x 0.40 M = 12 mmol

since 1 mol barium hydroxide produces two hydroxide ions, = 24 mmol

since there should be H+ at the end (total volume = 30+x), the millimoles of H+ =

since we are using 0.25 M HCl and x mL of it are required the millimoles of HCl are 0.25x.

Now

millimoles of HCl = millimoles of OH- + millimoles of H+ in the solution

solving this equation for x gives us the volume of HCl which is 96.0 mL

so we need 96 mL of HCl to bring this change and the total volume of the solution is 30+96 = 126 mL

I hope this helps, if you need more information, please do not hesitate to ask.