The indicator methyl red has a pKHIn = 4.95. It changes from red to yellow over the pH range from 4.4 to 6.2.What colour would you expect the solution in question 13 above to most look like?

Question

PLS ANSWER THE QUESTION.

Answer 1

First, the notation, since it is what has been blocking this thread.

HIn is the standard symbol for an acid-base indicator: "H" for the acidic proton and "In" for the rest of the indicator molecule (short for indicator). It dissociates like any weak acid:

HIn + H2O gives H3O+ + In-

The two forms have different colours. For methyl red, HIn is red and In- is yellow.

KHIn is just the acid dissociation constant of that indicator, and pKHIn = -log KHIn = 4.95. It is Ka under a name that says which acid you mean.

The rule that answers the question

Rearranged Henderson-Hasselbalch for an indicator:

pH = pKHIn + log([In-]/[HIn])

So the ratio of the two coloured forms is fixed entirely by how far the pH sits from 4.95:

pH = 3.95 (one unit below): ratio 1:10, about 91% HIn - looks red
pH = 4.95 (equal to pKHIn): ratio 1:1 - looks orange, the midpoint of the change
pH = 5.95 (one unit above): ratio 10:1, about 91% In- - looks yellow

That is where the quoted transition range comes from. Roughly pKHIn plus or minus 1 gives 3.95 to 5.95; the observed 4.4 to 6.2 differs a little because the eye is not equally sensitive to both colours, which is normal for real indicators.

How to finish it

Your "question 13" was not included in the post, so I cannot tell you the pH of that solution. But once you have it, read the answer straight off:

pH below 4.4 - fully red
pH between 4.4 and 6.2 - an orange blend, redder near 4.4 and more yellow near 6.2, with an even 50:50 mix at pH 4.95
pH above 6.2 - fully yellow

If question 13 was a strong-acid titration or an acidic salt, expect red; if it was a buffer near pH 5, expect orange; if it was neutral or basic, expect yellow.

Why this matters beyond the colour

An indicator is chosen so its transition range straddles the pH at the equivalence point of the titration you are running. Methyl red changing between 4.4 and 6.2 makes it right for titrating a weak base with a strong acid, where the equivalence point is acidic - and wrong for a weak acid with a strong base, where the equivalence point is basic and you would reach for phenolphthalein instead. Picking the indicator is really just matching its pKHIn to the pH you expect at the endpoint.