Textbook Question
In Section 11.5, we defined the vapor pressure of a liquid in terms of an equilibrium. (b) By using data in Appendix B, give the value of Kp for this reaction at 30 C.
Ch.15 - Chemical Equilibrium
Chapter 15, Problem 102
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 guidance1
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.
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.
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).
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.
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.
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Equilibrium Constant (Kc)
The equilibrium constant (Kc) is a numerical value that expresses the ratio of the concentrations of products to reactants at equilibrium for a given chemical reaction. It indicates the extent to which a reaction proceeds to form products. A higher Kc value signifies a greater tendency for the formation of products, while a lower Kc indicates a preference for reactants. In the context of hemoglobin, Kc reflects the affinity of hemoglobin for oxygen.
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Equilibrium Constant Expressions
P50 Value
The P50 value is a specific measure used to describe the oxygen-binding affinity of hemoglobin. It represents the partial pressure of oxygen at which 50% of the hemoglobin is saturated with oxygen. A lower P50 value indicates a higher affinity for oxygen, meaning that hemoglobin can bind oxygen more readily. In this case, fetal hemoglobin has a lower P50 than adult hemoglobin, suggesting it binds oxygen more effectively.
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Le Chatelier's Principle
Le Chatelier's Principle states that if a system at equilibrium is subjected to a change in concentration, temperature, or pressure, the system will adjust to counteract that change and restore a new equilibrium. This principle helps explain how changes in the environment, such as increased oxygen levels, can shift the equilibrium position of the hemoglobin-oxygen binding reaction. Understanding this principle is crucial for interpreting the differences in Kc values between fetal and adult hemoglobin.
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