Buffer capacity is a measure of a buffer solution\'s resistance to changes in pH

Question

Buffer capacity is a measure of a buffer solution's resistance to changes in pH as strong acid or base is added. Suppose that you have 195 mL of a buffer that is 0.340 M in both hydrofluoric acid (HF) and its conjugate base (F). Calculate the maximum volume of 0.480 M HCI that can be added to the buffer before its buffering capacity is lost. Number mL, Previous O Next Exit Give Up & View Solution Check Answer Hint An ideal buffer has equal concentrations of acid and conjugate base for a [base] to [acid] ratio of 1 A buffer has lost its capacity when the ratio of [basel to [acid] is less than 0.10 or greater than 10.

Explanation / Answer

we know that

moles = molarity x volume (L)

so

moles of (HF + F-) = 0.34 x 0.195 = 0.0663

now

an ideal buffer has equal conc of both

so

moles of HF = 0.066/2 = 0.03315

also

moles of F- = 0.03315

let the volume of HCl added be V

we know that

moles = molarity x volume

so

moles of HCl added = 0.48 x V = 0.48V

now

when HCl is added

the reaction becomes

F- + H+ ---> HF

so

moles of F- reacted = moles of H+ added = 0.48V

moles of F- remaining = 0.03315 - 0.48 V

moles of HF formed = moles of H+ added = 0.48V

new moles of HF = 0.03315 + 0.48V

now

ratio of moles of base to acid = moles of F- / moles of HF

= ( 0.03315 - 0.48V) / ( 0.03315 + 0.48V)

so this should not be less than 0.1

so

( 0.03315 - 0.48V) / ( 0.03315 + 0.48V) > 0.1

0.03315 - 0.48V > 0.003315 + 0.048V

0.029835> 0.528V

V<0.0565

so

max volume of HCl = 0.0565 L = 56.5 ml

so

56.5 ml of HCl can be added

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