# Problem: The protein hemoglobin (Hb) transports O2 in mammalian blood. Each Hb can bind 4 O2 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 4 O2(g) + Hb(aq) ⇌ [Hb(O2)4](aq) in a fetus, comparedto Kc for the same reaction in an adult.

###### FREE Expert Solution

4 O2(g) + Hb(aq) ⇌ [Hb(O2)4](aq)

Kp → equilibrium units in terms of pressure of gaseous species

${\mathbf{K}}_{\mathbf{p}}\mathbf{=}\frac{\mathbf{products}}{\mathbf{reactants}}\phantom{\rule{0ex}{0ex}}{\mathbf{K}}_{\mathbf{p}}\mathbf{=}\frac{\mathbf{1}}{{\left({P}_{{O}_{2}}\right)}^{\mathbf{4}}}$

Fetal hemoglobin:

Pfetal = 0.025 atm

Kp, fetal = 2.56x106

Kp and Kc are related to one another by the following equation below:

$\overline{){{\mathbf{K}}}_{{\mathbf{p}}}{\mathbf{=}}{{\mathbf{K}}}_{{\mathbf{c}}}{\left(\mathbf{RT}\right)}^{\mathbf{∆}\mathbf{n}}}$

R = gas constant = 0.08206 (Latm)/(molK)
T = temperature, K
Δn = moles of gas products – moles of gas reactants

Δn = 0 moles gas – 4 moles gas
Δn = –4 mol

$\overline{){{\mathbf{K}}}_{{\mathbf{p}}}{\mathbf{=}}{{\mathbf{K}}}_{{\mathbf{c}}}{\left(\mathbf{RT}\right)}^{\mathbf{∆}\mathbf{n}}}\phantom{\rule{0ex}{0ex}}\frac{{\mathbf{K}}_{\mathbf{p}}}{{\left(\mathbf{RT}\right)}^{\mathbf{∆}\mathbf{n}}}\mathbf{=}\frac{{\mathbf{K}}_{\mathbf{c}}\overline{){\left(\mathbf{RT}\right)}^{\mathbf{∆}\mathbf{n}}}}{\overline{){\left(\mathbf{RT}\right)}^{\mathbf{∆}\mathbf{n}}}}\phantom{\rule{0ex}{0ex}}\overline{){{\mathbf{K}}}_{{\mathbf{c}}}{\mathbf{=}}\frac{{\mathbf{K}}_{\mathbf{p}}}{{\left(\mathbf{RT}\right)}^{\mathbf{∆}\mathbf{n}}}}$

T = body temperature = 37°C + 273.15 = 310.15 K

###### Problem Details

The protein hemoglobin (Hb) transports O2 in mammalian blood. Each Hb can bind 4 O2 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 4 O2(g) + Hb(aq) ⇌ [Hb(O2)4](aq) in a fetus, compared
to Kc for the same reaction in an adult.