Textbook Question
(a) Based on the following energy profile, predict whether kf > kr or kf < kr. [Section 15.1]
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Ch.15 - Chemical Equilibrium
Chapter 15, Problem 4
A chemist at a pharmaceutical company is measuring equilibrium constants for reactions in which drug candidate molecules bind to a protein involved in cancer. The drug molecules bind the protein in a 1:1 ratio to form a drug–protein complex. The protein concentration in aqueous solution at 25 _x001F_C is 1.50 * 10^-6 M. Drug A is introduced into the protein solution at an initial concentration of 2.00 * 10^-6 M. Drug B is introduced into a separate, identical protein solution at an initial concentration of 2.00 * 10^-6 M. At equilibrium, the drug A–protein solution has an A–protein complex concentration of 1.00 * 10^-6 M, and the drug B solution has a B–protein complex concentration of 1.40 * 10^-6 M. Calculate the Kc value for the A–protein binding reaction and for the B–protein binding reaction. Assuming that the drug that binds more strongly will be more effective, which drug is the better choice for further research?
Verified step by step guidance1
Identify the reaction for the drug-protein binding: Drug + Protein ⇌ Drug-Protein Complex. This is a 1:1 binding reaction.
Write the expression for the equilibrium constant (Kc) for the reaction: Kc = [Drug-Protein Complex] / ([Drug][Protein]).
For Drug A, substitute the equilibrium concentrations into the Kc expression: [Drug-Protein Complex] = 1.00 * 10^-6 M, [Protein] = 1.50 * 10^-6 M - 1.00 * 10^-6 M, and [Drug] = 2.00 * 10^-6 M - 1.00 * 10^-6 M.
For Drug B, substitute the equilibrium concentrations into the Kc expression: [Drug-Protein Complex] = 1.40 * 10^-6 M, [Protein] = 1.50 * 10^-6 M - 1.40 * 10^-6 M, and [Drug] = 2.00 * 10^-6 M - 1.40 * 10^-6 M.
Compare the Kc values for Drug A and Drug B. The drug with the higher Kc value binds more strongly to the protein, indicating it is the better choice for further research.
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 reaction. It is calculated using the formula Kc = [products]/[reactants], where the concentrations are raised to the power of their coefficients in the balanced chemical equation. A higher Kc value indicates a greater tendency for the formation of products, which is crucial for determining the effectiveness of drug binding in this context.
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Equilibrium Constant Expressions
Binding Affinity
Binding affinity refers to the strength of the interaction between a drug molecule and its target protein. It is often reflected in the equilibrium constant; a higher Kc value suggests a stronger binding affinity. Understanding binding affinity is essential in pharmacology, as it helps predict how effectively a drug can inhibit or activate its target, which is particularly important in drug development for conditions like cancer.
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02:06Nuclear Binding Energy
Stoichiometry of Binding Reactions
Stoichiometry in binding reactions describes the quantitative relationship between the concentrations of reactants and products. In this case, the 1:1 binding ratio between the drug and protein means that one molecule of drug binds to one molecule of protein. This stoichiometric relationship is vital for calculating the equilibrium concentrations and ultimately determining the Kc values for the drug-protein interactions.
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Related Practice
Textbook Question
The following diagrams represent a hypothetical reaction A ¡ B, with A represented by red spheres and B represented by blue spheres. The sequence from left to right represents the system as time passes. Does the system reach equilibrium? If so, in which diagram(s) is the system in equilibrium? [Sections 15.1 and 15.2]
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Textbook Question
The following diagram represents a reaction shown going to completion. Each molecule in the diagram represents 0.1 mol, and the volume of the box is 1.0 L. (d) Assuming that all of the molecules are in the gas phase, calculate n, the change in the number of gas molecules that accompanies the reaction. [Section 15.2]
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Textbook Question
Ethene (C2H4) reacts with halogens (X2) by the following reaction:
C2H4(𝑔) + X2(𝑔) ⇌ C2H4X2(𝑔)
The following figures represent the concentrations at equilibrium at the same temperature when X2 is Cl2 (green), Br2 (brown), and I2 (purple). List the equilibria from smallest to largest equilibrium constant. [Section 15.3]