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)].

Answer 1

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

Step-by-step explanation:

From the question we are told that

The P50 value for Fetal hemoglobin is
`[P_(O_2)]_F = 19 torr`

The P50 value for Adult hemoglobin is
`[P_(O_2)]_A = 26.8 torr`

The chemical reaction for the binding process is

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

Considering Fetal hemoglobin

Generally the equilibrium constant is mathematically represented as

`K_c_F = ([P_([Hb(O_2)_4)])/( [P_(O_2)]_F^4 * [P_(Hb)])`

Here
`[P_([Hb(O_2)_4)] [\tex] and [P_(Hb)] will be 1 because both substances are aqueous</p><p>So</p><p> [tex]K_c_F = (1)/( 19^4 *1 )`

=>
`K_c_F = (1)/( 19^4 )`

Considering Adult hemoglobin

Generally the equilibrium constant is mathematically represented as

`K_c_A = ([P_([Hb(O_2)_4)])/( [P_(O_2)]_A^4 * [P_(Hb)])`

=>
`K_c_A = (1)/( 26.8 ^4 *1 )`

=>
`K_c_A = (1)/( 26.8 ^4)`

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

`Z = (K_c_F)/(K_c_A)`

=>
`Z = ((1)/(19^4))/((1)/(26.8^4))`

=>
`Z =  4`

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