Indicators Phenolphthalein is a commonly used indicator that is colorless in the
ID: 705165 • Letter: I
Question
Indicators Phenolphthalein is a commonly used indicator that is colorless in the acidic form (pH 10.0). It is a weak acid with a pKa of 8.7. What is the ratio of the conjugate base concentration to the acid concentration, that is, [B-???] when the indicator switches to the acidic color? Hint given in feedback. Answer: Use the result to the above question to determine what percent is in the acidic form when the acid color is first apparent? Answer: What is [B VHB] when the indicator switches to the basic color? Answer: Use the result to the above question to determine what percent is in the basic form when the base color is first apparent Answer:Explanation / Answer
The pka of phenolpthalein =8.7
pka=-log Ka , where Ka=acid dissociation constant of weak acid like phenolpthalein(say of the form HB)
HB <--->B-+H+ , ka=equilibrium constant=[B-][H+]/[HB]
HB form or acidic form of phenolpthalein is colorless,B- or basic form is pink
1) Using Henderson-hasselbach equation,
pH=pka +log [B-]/[HB]
It switches to acidic color at pH<8.3,
8.3=8.7+log [B-]/[HB]
or, log [B-]/[HB]=8.2-8.7=-0.4
or, [B-]/[HB]=10^-0.4=0.398
[B-]/[HB]=0.398
2) [B-]/[HB]=0.398
Add 1 to both sides,
[B-]/[HB]+1=0.398+1
or, [B-]+[HB]/[HB]=1.398
or,taking inverse of both sides,
[HB]/([B-]+[HB])=1/1.398
or, acid concentration/total concentration of acid and conjugate base=[HB]/([B-]+[HB])=0.715
percent acid=100*0.760=71.5%
3)Base color is first apparant at pH>10.0
Using Henderson-hasselbach equation,
pH=pka +log [B-]/[HB]
10.0=8.7+log [B-]/[HB]
or, log [B-]/[HB]=10.0-8.7=1.3
or, [B-]/[HB]=10^1.3=19.952
[B-]/[HB]=19.952
2) [B-]/[HB]=19.952
taking inverse of both sides,
[HB]/[B-]=1/19.952=0.0501
Add 1 to both sides,
[HB]/[B-]+1=0.0501+1
or, [B-]+[HB]/[B-]=1.0501
or,taking inverse of both sides,
[B-]/([B-]+[HB])=1/1.0501=0.952
or, base concentration/total concentration of acid and conjugate base=[B]/([B-]+[HB])=0.952
percent acid=100*0.952=95.2%
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