A neuron with an intracellular Cl concentration of 20 mM is placed in a solution that contains 125 mM CI at 25°C. The membrane potential of the neuron is -70 mV. Assuming the neuronal cell membrane has channels that allow facilitated diffusion of Cl', do you expect Cl' to flow into the cell? Explain your answer
A neuron with an intracellular Cl concentration of 20 mM is placed in a solution that contains 125 mM CI at 25°C. The membrane potential of the neuron is -70 mV. Assuming the neuronal cell membrane has channels that allow facilitated diffusion of Cl', do you expect Cl' to flow into the cell? Explain your answer
Human Anatomy & Physiology (11th Edition)
11th Edition
ISBN:9780134580999
Author:Elaine N. Marieb, Katja N. Hoehn
Publisher:Elaine N. Marieb, Katja N. Hoehn
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![### Problem 7 Analysis: Chloride Ion (Cl-) Diffusion in Neurons
**Problem Statement:**
A neuron with an intracellular Cl⁻ concentration of 20 mM is placed in a solution that contains 125 mM Cl⁻ at 25°C. The membrane potential of the neuron is -70 mV. Assuming the neuronal cell membrane has channels that allow facilitated diffusion of Cl⁻, do you expect Cl⁻ to flow into the cell? Explain your answer and provide quantitative support for your answer (i.e., show calculations).
**Approach and Calculations:**
To determine whether Cl⁻ will flow into the neuron, we need to consider the electrochemical gradient, which is the combined effect of the concentration gradient and the electrical potential across the membrane.
We'll use the Nernst equation to find the equilibrium potential for Cl⁻ (\(E_{\text{Cl}}\)):
\[ E_{\text{Cl}} = \frac{RT}{zF} \ln{\left(\frac{[Cl^-]_{\text{outside}}}{[Cl^-]_{\text{inside}}}\right)} \]
Where:
- \(R\) is the universal gas constant (8.314 J/(mol·K))
- \(T\) is the temperature in Kelvin (25°C = 298 K)
- \(z\) is the valence of the ion (-1 for Cl⁻)
- \(F\) is Faraday's constant (96485 C/mol)
- \([Cl^-]_{\text{outside}}\) and \([Cl^-]_{\text{inside}}\) are the extracellular and intracellular concentrations, respectively.
Plugging in the values:
\[ E_{\text{Cl}} = \frac{8.314 \times 298}{-1 \times 96485} \ln{\left(\frac{125}{20}\right)} \]
First, calculate the natural logarithm:
\[ \ln{\left(\frac{125}{20}\right)} = \ln{6.25} \approx 1.83 \]
Next, input this value into the Nernst equation:
\[ E_{\text{Cl}} = \frac{8.314 \times 298}{-96485} \times 1.83 \]
\[ E_{\text{Cl}} = \frac{2476.172}{-96485} \times 1.83 \]
\[ E](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd2932a05-99f3-41c1-989e-7dbca32c3377%2Fc9a2960b-bbd0-46a4-81d5-4da0b113ee77%2F475zil_processed.png&w=3840&q=75)
Transcribed Image Text:### Problem 7 Analysis: Chloride Ion (Cl-) Diffusion in Neurons
**Problem Statement:**
A neuron with an intracellular Cl⁻ concentration of 20 mM is placed in a solution that contains 125 mM Cl⁻ at 25°C. The membrane potential of the neuron is -70 mV. Assuming the neuronal cell membrane has channels that allow facilitated diffusion of Cl⁻, do you expect Cl⁻ to flow into the cell? Explain your answer and provide quantitative support for your answer (i.e., show calculations).
**Approach and Calculations:**
To determine whether Cl⁻ will flow into the neuron, we need to consider the electrochemical gradient, which is the combined effect of the concentration gradient and the electrical potential across the membrane.
We'll use the Nernst equation to find the equilibrium potential for Cl⁻ (\(E_{\text{Cl}}\)):
\[ E_{\text{Cl}} = \frac{RT}{zF} \ln{\left(\frac{[Cl^-]_{\text{outside}}}{[Cl^-]_{\text{inside}}}\right)} \]
Where:
- \(R\) is the universal gas constant (8.314 J/(mol·K))
- \(T\) is the temperature in Kelvin (25°C = 298 K)
- \(z\) is the valence of the ion (-1 for Cl⁻)
- \(F\) is Faraday's constant (96485 C/mol)
- \([Cl^-]_{\text{outside}}\) and \([Cl^-]_{\text{inside}}\) are the extracellular and intracellular concentrations, respectively.
Plugging in the values:
\[ E_{\text{Cl}} = \frac{8.314 \times 298}{-1 \times 96485} \ln{\left(\frac{125}{20}\right)} \]
First, calculate the natural logarithm:
\[ \ln{\left(\frac{125}{20}\right)} = \ln{6.25} \approx 1.83 \]
Next, input this value into the Nernst equation:
\[ E_{\text{Cl}} = \frac{8.314 \times 298}{-96485} \times 1.83 \]
\[ E_{\text{Cl}} = \frac{2476.172}{-96485} \times 1.83 \]
\[ E
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