Question

A microbiologist is preparing a medium on which to culture E. coli bacteria. She buffers the medium at pH 7.00 to minimize the effect of acid-producing fermentation. What volumes of equimolar aqeous solutions of K₂HPO₄ and KH₂PO₄ must she combine to make 600.0 mL of the pH 7.00 buffer?

Ka values for phosporic acid K_a1= 7.2x10^-3 K_a2= 6.3x10^-8 K_a3= 4.2x10-¹³

Answer 1

in this buffer  KH₂PO₄ is the weak acid

and  K₂HPO₄ is salt of weakacid and strong base KOH

according to hendersons equation pH = pKa + log[salt]/[acid]

given pH = 7 ; Ka is constant (pKa = -log Ka ); total volume =100

let the volume of salt be x

the volume of acid = 100-x

therefore

7 = pKa + logx/(100-x)          since it is given that salt and acid has sameconcentration

from the above equation we can calculate thevolume

suppose pKa = 6

log(x/100-x) = 1

or log (x/100-x) = log 10

x/(100-x) = 10

x = 1000/11 = 90.9ml (volume of salt)

100-90.9 = 9.1ml (volume of acid)