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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)].

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Answer:

The equilibrium constant of Fetal hemoglobin is 4 times larger than that of Adult hemoglobin

Explanation:

From the question we are told that

The P50 value for Fetal hemoglobin is [tex][P_{O_2}]_F = 19 torr [/tex]

The P50 value for Adult hemoglobin is [tex] [P_{O_2}]_A = 26.8 torr [/tex]

The chemical reaction for the binding process is

[tex]4O_2_{(g)}+Hb_{(aq)}\to [Hb(O_2)_4_{{(aq)}}][/tex]

Considering Fetal hemoglobin

Generally the equilibrium constant is mathematically represented as

[tex]K_c_F = \frac{[P_{[Hb(O_2)_4}]}{ [P_{O_2}]_F^4 * [P_{Hb}]}[/tex]

Here [tex][P_{[Hb(O_2)_4}] [\tex] and [P_{Hb}] will be 1 because both substances are aqueous

So

[tex]K_c_F = \frac{1}{ 19^4 *1 }[/tex]

=> [tex]K_c_F = \frac{1}{ 19^4 }[/tex]

Considering Adult hemoglobin

Generally the equilibrium constant is mathematically represented as

[tex]K_c_A = \frac{[P_{[Hb(O_2)_4}]}{ [P_{O_2}]_A^4 * [P_{Hb}]}[/tex]

=> [tex]K_c_A = \frac{1}{ 26.8 ^4 *1 }[/tex]

=> [tex]K_c_A = \frac{1}{ 26.8 ^4}[/tex]

So the ratio of the equilibrium constant of Fetal hemoglobin to that of Adult hemoglobin is mathematically represented as

[tex]Z = \frac{K_c_F}{K_c_A}[/tex]

=>       [tex]Z = \frac{\frac{1}{19^4}}{\frac{1}{26.8^4}}[/tex]  

=>     [tex]Z =  4 [/tex]

So the equilibrium constant of  Fetal  hemoglobin is 4 times larger than that  of Adult hemoglobin

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