Question

The pH of blood serum is maintained by a proper balance of H2CO3 and NaHCO3 concentrations. Calculate the volume of 5M NaHCO3 solution that should be mixed with a 10 mL of sample of blood which is 2M in H2CO3 in order to maintain a pH of 7.4 . Given Ka1 and Ka2 for H2CO3 in blood are 4.3 x 10-7 and 5.6 x 10-11 .

Answer 1

Given that

Ka1 and Ka2 for H2CO3 in blood are 4.3 x 10-7 and 5.6 x 10-11 .

The 1st dissociation of carbonic acid is given by:

H2CO3⇌HCO−3+H+

For which:

K(a1)=[ / [H2CO3]

= 4.0×10−7mol/l at 25∘C.

Rearranging gives:

[H+]=K(a1)×[ / [HCO−3]

∴[H2CO3] / [HCO−3]=H+/ K(a1)

Given that ;

pH=7.4

there [H+]=10^-Ph

= 10^-7.4

= 4.0×10−8mol/l

Then;

∴ / [HCO−3]=4.0 / 4.0×10−7

=0.1

If the volume of buffer for both [H2CO3 ] and [HCO−3] is common and Molarity = numbe of moles / volume ;

then

nH2CO3 / nHCO−3=0.1

n = the number of moles.

We know that c=nv so the number of moles is given by:

n=c×v

number of moles of H2CO3= 2*10/1000

= 0.02 moles

Therefore;

nH2CO3 / nHCO−3=0.1

0.02 moles / 0.1 = nHCO−3

nHCO−3= 0.2 moles,

and volume in L= number of moles / Molarity

= 0.2 /5

= 0.04 L

= 40 ml