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(aq) + Hb(aq) ⇌ Hb(O2)4(aq) in a fetus, compared to Kc for the same reaction in an adult.

Verified step by step guidance

1. Step 1: Understand the relationship between P50 and the equilibrium constant (Kc). The P50 value is inversely related to the affinity of hemoglobin for oxygen, which means a lower P50 value indicates a higher affinity and a larger Kc.
2. Step 2: Recognize that the equilibrium constant Kc for the reaction 4 O2(aq) + Hb(aq) ⇌ Hb(O2)4(aq) can be related to the P50 value using the Hill equation, which describes the saturation of hemoglobin as a function of oxygen partial pressure.
3. Step 3: Use the given P50 values for fetal (19 torr) and adult (26.8 torr) hemoglobin to set up a ratio of the equilibrium constants. Since Kc is inversely proportional to P50, the ratio of Kc for fetal to adult hemoglobin can be expressed as (P50_adult / P50_fetal).
4. Step 4: Substitute the given P50 values into the ratio: (26.8 torr / 19 torr). This will give you the factor by which Kc for fetal hemoglobin is larger than that for adult hemoglobin.
5. Step 5: Simplify the ratio to find the relative increase in Kc for fetal hemoglobin compared to adult hemoglobin. This will provide an estimate of how much larger the equilibrium constant is for fetal hemoglobin.