The protein hemoglobin (Hb) transports O2 in mammalian blood. Each Hb can bind 4

Question

The protein hemoglobin (Hb) transports O2 in mammalian blood. Each Hb can bind 4O2 molecules. The equilibrium constant for the O2-binding reaction is higher in fetal hemoglobin than in adult hemoglobin. In discussing protein oxygen-binding capacity, biochemists use a measure called the P50 value, defined as the partial pressure of oxygen at which 50%of the protein is saturated. Fetal hemoglobin has a P50 value of 19 torr, and adult hemoglobin has a P50 value of 26.8 torr. Use these data to estimate how much larger Kc is for the aqueous reaction 4O2(g)+Hb(aq)->[Hb(O2)4(aq)]

Express your answer using two significant figures.

KcF / KcA = ???

Explanation / Answer

1) first consider Fetal hemoglobin

the given reaction is

402 (g) + Hb (aq) ---> [Hb(02)4]

let the initial conc of Hb be y

now

50% of the protein is saturated

so

at equilibrium

[Hb] = 0.5y

[Hb(02)4] = 0.5y

at this point

given pressure of 02 is 19 torr

but we need the conc of 02

so

P= CRT

C = P / RT

so

conc of 02 = Pf/ RT

now

402 (g) + Hb (aq) ---> [Hb(02)4]

KcF = [ Hb(02)4] / [ Hb] [ 02]^4

so

KcF = 0.5 y / 0.05y [ Pf / RT]^4

KcF = ( RT/Pf)^4

now

similarly

KcA = ( RT / Pa )^4

now

KcF / KcA = (RT/Pf)^4 / ( RT / Pa)^4

KcF / KcA = ( Pa / Pf)^4

given

Pa = 26.8

and

Pf = 19

so using these values

KcF / KcA = ( 26.8 / 19)^4

KcF / KcA = 3.96

so

the value of KcF / KcA = 3.96

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