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Problem with buffers in A2 Chemistry

I don't understand why for some questions I have to multiply the concentration by the total volume of both the acid and the alkali whereas in others I have to multiply by just the volume of the acid or alkali individually.

For example, in the question telling me to calculate the pH of a buffer solution by mixing weak acids with their salts.

50cm^3 of 1.00 mol/dm^3 methanoic acid (Ka = 1.78 x 10^-4) mixed with 20.0 cm^3 of 1.00 mol dm^-3 sodium methanoate

In this question, the mark scheme says to multiply 1.00 by 50/70 and 1.00 by 20/70 as I deduced how the 70 value is the combination of the two volumes. However usually I would multiply 1 by 20 and 50 respectively and then subtracting these values to obtain 30 and converting this to dm^3 I would get 0.030. This method has worked several times for exam questions us I don't understand how my method isn't viable here.
(edited 3 months ago)
Reply 1
I suspect your issue is down to the fact that there are two ways of making a buffer.

Your quoted Q has the conjugate base (salt solution) directly being added to the weak acid solution. BOTH the HA and the A- are diluting each other. There are two ways of dealing with this - the way you've said the MS deals with it, but multiplying the concs by the volume of each divided by the new total volume (the quick way). The slower way would be to work out how many mol of HA and A- there are (n = cv) and then dividing each by the new Vtot.

The other way of making a buffer would be to add an alkali to your HA. n(HA) goes down by n(OH-) added and n(A-) made = n(OH-) added - which I think is the bit where you mention 0.030.

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