Acidity Constant for acid/base indicator

[gonelli]

I having a bit of trouble finding a way to work out a couple questions on a chemistry question sheet which involve using the acidity constant to solve the endpoint of an indicator.

 

First question involves methyl orange, and gives me Ka = 2 x 10^-4. It asks me to "Determine the pH of the endpoint for this indicator". But I'm unsure on how to do this? I know the Ka will equal [H3O+][conj. base] / [acid], does it involve using that equation?

 

And the second question is similar, this time involving bromophenol blue (Brb). It tells me the colour change that occurs in each type of solution and gives me Ka = 6.31 x 10^-5. The first part of this question asks to determine the magnitude of the ratio [brb-]/[HBrb] for bromophenol blue and the dominant species present in solutions of pH 3 and 8. And then it asks me to work out the endpoint as well.

 

Any help to point me in the right direction would great. Thanks.

[John Cuthber]

If your solution is much more acid than the indicator then the indicator will be entirely in the acid form. If your solution is much more alkaline then the indicator will be in the base form. (Roughly) how much of each is present when you are just at the end point?

From that and this

http://en.wikipedia.org/wiki/Henderson-Hasselbalch_equation

you should be able to calculate the answer you need.

[gonelli]

If the solution was moving from an acidic pH to a basic one, then at the endpoint there would be slightly more indicator in the base form, which is why you oberve a colour change. Is that right?

 

The Henderson-Hasselbalch equations involve the concentrations of both forms of the indicator. I haven't been given any concentrations in the question, so can I still use them?

[John Cuthber]

The equation involves the ratio of the concns. That ratio goes from (practically none : lots) to (lots : practically none) as you pass the endpoint. What's the ratio at the endpoint?

[gonelli]

At the endpoint, the ratio would be extremely large. Approaching infinity, since you are almost dividing by zero. Right?

[John Cuthber]

Before the endpoint the ratio is near infinite, after the endpoint it's near infinite the other way (ie near zero). Since the equation asks for the log of that ration it would be impossible to calculate it for either case.

When methyl orange is red it's acid, when it's yellow its basic. How do you make orange from red and yellow?

[gonelli]

So methyl orange will appear orange when you've got similar amounts of methyl orange in the acid and base form. Which would also be when the log of those equations is equal to zero, since the ratio of conc. is 1:1.

 

So is the point where the concentration ratio equals 1, where you work out your end point to be, since you couldn't calculate it when near infinity values appear?

[John Cuthber]

Bingo!

Where there's "exactly" as much of the acid form as the base form is where the colours mix and that's the endpoint.

 

I guess by now you have worked out the maths but here's a shortcut.

Log (x/x) = log(1) = zero

So adding it to pKa doesn't make any difference. The pH of the equivalence point is the same as the pKa of the indicator.

[gonelli]

Well, that makes sense. Thank you very much for all the help.

 

One quick question though. Usually with indicators you are given a range of pH values for which it will change colour over. Can this range be determined mathematically, or is it just found from experimental trial?

[John Cuthber]

The pH range for an indicator is generally determined experimentally. However they are generally a range of about 1 pH unit because that changes the ratio of, say, yellow to red by a factor of ten and that's a big enough change to see clearly.

[gonelli]

Okay. Thank you again.