The data in the question is incomplete and the question is unclear.
Assuming the problem statement as below:
What is the change in pH when ‘x’ L of ‘y’M NaOH solution is added to 1 L of a buffer solution which is 1 M in sodium acetate and 1 M in acetic acid.
Using the equation:
pH = pKa + log([salt] / [acid])
Here initially [salt] = [acid] = 1 M, so pH = pKa = 4.75 (for acetic acid)
Initial moles of salt = molarity * volume = 1*1 = 1 mole
Similarly initial moles of acid = 1 mole
Moles of NaOH added = x*y
After this addition, moles of acid decrease and moles of salt increase by the same amount
Above equation can also be written as :
pH = pKa + log([moles of salt] / [ moles of acid])
So after adding NaOH, equation becomes:
pH = 4.75 + log( (1+x*y) / (1- x*y) ) = z (say)
Thus the required answer is z-4.75
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