Is the pH of the equivalence point equal to the pKa of the indicator?

[garytse86]

quote from http://www.chem.ubc.ca/courseware/pH/section15/content.html


Intuition may suggest that the endpoint of the titration will occur at the equivalence point if we choose an indicator whose pKa is equal to the pH of the equivalence point. If such an indicator was chosen, the colour change would be half complete at the equivalence point. Unfortunately, it is very difficult to tell when the colour change is precisely half complete, making it difficult to precisely identify the equivalence point. Since it is easiest to tell when the colour first starts to change, we want the equivalence point to occur then.

quote from http://www.teachmetuition.co.uk/Chemistry/Acids_and_Bases/acids_and_bases.htm#Selecting%20a%20Suitable%20Indicator

The equilibrium constant can be expressed as follows:

Kind = [H+][Ind-] / [HInd]

At the end point of the titration, when the colour of the indicator changes, the concentrations of Ind- and HInd are equal, so

Kind = [H+]

Taking the log of both of the terms in the above equation gives

pKind = pH (Since log of Kind = pKind and log of [H+] = pH)

So the indicator that you choose for a reaction must have a pKind value at the pH of the end point of the reaction.




Is the information from the first quote wrong?

Because endpoint is when the indicator is half way between its two extremes.

You want this half way position to coincide with the equivalence point of the titration because you want the intermediate colour to coincide with equivalence point

Therefore, you want: pH of the equivalence point = pKa of the indicator.
(surely you want pKa of the indicator to match the vertical section of the titration).

Something different:

I think the first site means:

pH of titration = pKa of the titration when reaction is half complete.



Can someone please help... I am seriously confused.

 

[Borek]

You are not the only one to be confused. The truth is there is no a one easy answer to the question about indicator selection.

At the end point color change is usually very fast. In most cases you will be not able to see continuous change of color. Due to the fact that you have to add full drop of the titrant to the solution - as long as the pKa is reasonably close to the end point pH error due to the selection of indicator is neglectable.

Let's say you are titrating 40 mL of 0.01M HCl with 0.01M NaOH. 40mL is selected so that you are in the best range for 50mL burette. Titrant is added dropwise. Each drop is about 0.05mL. These are rather standard conditions for titration (in practice you will probably use more concentrated titrant, but it will only result in larger pH differences then these presented below):

Drop before the endpoint pH = 3.92. At the endpoint pH = 7.00. Drop later pH is 8.79. The difference - in two drops - is almost 5 pH units. Thus every indicator with pKa between 3.79+1 and 8.79-1 will be able to completely change its color when two drops are added. Error that can be introduced by indicator iwth pKa <> 7 will be smaller than error introduced by the drop size.

Play with my BATE to check pH changes for other acids. Once you will understand what is going on in the solution and how the pH changes, you will be able to decide by yourself which indicator should work best.

The only practical answer to the question is - check which answer is expected by your teacher

Chemical calculators at

 

[garytse86]

the problem is i don't have access to teachers.

Can you answer my question though:

so you DO want the pKa of the INDICATOR to match the Equivalence pH of the titration?

btw i understand that you use methyl orange for strong acid / weak base, and phenolphthlain for weak acid / strong base.

Can you explain in more details for my original question please?

 

[BenGoodchild]

I know you NEVER use Universal indicator! Yey my chemistry GCSE was worth while!

 

[Borek]

the problem is i don't have access to teachers.

In this case that's good for you

so you DO want the pKa of the INDICATOR to match the Equivalence pH of the titration?

IMHO - the closer the better, but it is not a thing to die for. Remember there are several other sources of errors - titrant is added in drops, burette reading is with some error, CO2 from the air can change molarity of the base (either titrated or used as a titrant) and so on. All these add to the expected error value. As long as endpoint shown by indicator differs from the real endpoint by no more than 0.1% I doubt you will be able to do such precise titration that this error will show up.

btw i understand that you use methyl orange for strong acid / weak base, and phenolphthlain for weak acid / strong base.

In every case you should take a look at the titration curve and judge for yourself, if the error induced by the wrong indicator selection will be significant. In most cases the decisions made will boil down to the rule of thumb similar to the one you posted. You can use it as long as you understand what you are doing.

Chemical calculators at

 

[garytse86]

So can you tell me whether in my first post the first quote is wrong or not?

 

[Borek]

It is not an integer multiplication, that two times two is always four

Both approaches have their pros and cons. None is wrong. The second is in my humble opinion better.

Chemical calculators at

 

[garytse86]

k thanks :):)