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Given an extracellular [Pi-2] of 4mM and an intracellular [Pi-2] of 40 mM, what is the equilibrium potential of a plasma membrane permeable only to Pi-²?

Given an extracellular [Pi-2] of 4mM and an intracellular [Pi-2] of 40 mM, what is the equilibrium potential of a plasma membrane permeable only to Pi-²?

Human Anatomy & Physiology (11th Edition)
Human Anatomy & Physiology (11th Edition)
11th Edition
ISBN:9780134580999
Author:Elaine N. Marieb, Katja N. Hoehn
Publisher:Elaine N. Marieb, Katja N. Hoehn
Chapter1: The Human Body: An Orientation
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### Understanding Equilibrium Potential of a Plasma Membrane **Problem Statement:** Given an extracellular \([Pi^{-2}]\) of 4mM and an intracellular \([Pi^{-2}]\) of 40 mM, what is the equilibrium potential of a plasma membrane permeable only to \(Pi^{-2}\)? (Hint— you do *not* need a calculator to solve this question.) **Answer Options:** - +305 mV - -61 mV - +61 mV - +30.5 mV - 0 mV - -30.5 mV #### Explanation: To understand this problem, let's break down the concepts required to find the equilibrium potential. The equilibrium potential for an ion across a plasma membrane can be determined using the Nernst equation. However, with the hint indicating that a calculator is not needed, this implies that the answer can be derived by logical comparison or an understanding of typical values. Given: - **Extracellular \(Pi^{-2}\)**: 4 mM - **Intracellular \(Pi^{-2}\)**: 40 mM By noting that intracellular concentration is 10 times higher than the extracellular concentration (*40 mM / 4 mM = 10*), we know from standard chemistry that a tenfold concentration difference typically corresponds to an equilibrium potential shift of around -60 mV, due to the logarithmic nature of the Nernst equation. Additionally, because the ion in question has a charge of -2, the equilibrium potential will be more negative compared to a monovalent ion. Hence, it will move towards a more negative value consistent with established electrochemical principles. Among the given options, the most appropriate and equivalent estimate of the equilibrium potential would thus be **-30.5 mV** due to the increased complexity of divalent ions compared to the standard -60 mV seen in monovalent contexts. Therefore, the correct option is: - **-30.5 mV**
Transcribed Image Text:### Understanding Equilibrium Potential of a Plasma Membrane **Problem Statement:** Given an extracellular \([Pi^{-2}]\) of 4mM and an intracellular \([Pi^{-2}]\) of 40 mM, what is the equilibrium potential of a plasma membrane permeable only to \(Pi^{-2}\)? (Hint— you do *not* need a calculator to solve this question.) **Answer Options:** - +305 mV - -61 mV - +61 mV - +30.5 mV - 0 mV - -30.5 mV #### Explanation: To understand this problem, let's break down the concepts required to find the equilibrium potential. The equilibrium potential for an ion across a plasma membrane can be determined using the Nernst equation. However, with the hint indicating that a calculator is not needed, this implies that the answer can be derived by logical comparison or an understanding of typical values. Given: - **Extracellular \(Pi^{-2}\)**: 4 mM - **Intracellular \(Pi^{-2}\)**: 40 mM By noting that intracellular concentration is 10 times higher than the extracellular concentration (*40 mM / 4 mM = 10*), we know from standard chemistry that a tenfold concentration difference typically corresponds to an equilibrium potential shift of around -60 mV, due to the logarithmic nature of the Nernst equation. Additionally, because the ion in question has a charge of -2, the equilibrium potential will be more negative compared to a monovalent ion. Hence, it will move towards a more negative value consistent with established electrochemical principles. Among the given options, the most appropriate and equivalent estimate of the equilibrium potential would thus be **-30.5 mV** due to the increased complexity of divalent ions compared to the standard -60 mV seen in monovalent contexts. Therefore, the correct option is: - **-30.5 mV**
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