The concentration of Na+ and Cl- inside a muscle cell are 10 mM and 6 mM, respectively. The membrane potential is -70 mV, negative inside. In one experiment the cell is submerged in a large container filled with a solution of 250 mM NaCl. The temperature is 25 •C and remains constant.
a) calculate the electrochemical potential and explain which direction (inward or outward) will Na+ and Cl ions move.

To determine the electrochemical potential for each ion and predict their movement direction, we need to consider both the concentration gradient and the electrical membrane potential. We’ll use the Nernst equation to calculate the equilibrium potential for each ion and compare it with the membrane potential to decide the direction of ion flow.

### Given Data:
- **Intracellular concentration of Na⁺ ([Na⁺]_in):** 10 mM
- **Extracellular concentration of Na⁺ ([Na⁺]_out):** 250 mM
- **Intracellular concentration of Cl⁻ ([Cl⁻]_in):** 6 mM
- **Extracellular concentration of Cl⁻ ([Cl⁻]_out):** 250 mM
- **Membrane potential (Vm):** -70 mV (inside of the cell is more negative)
- **Temperature (T):** 25 °C or 298 K

### Step 1: Calculate the Equilibrium Potential Using the Nernst Equation
The Nernst equation is:

\[
E_{\text{ion}} = \frac{RT}{zF} \ln \left( \frac{[\text{ion}]_{\text{out}}}{[\text{ion}]_{\text{in}}} \right)
\]

Where:
- \( R \) is the gas constant, approximately \( 8.314 \, \text{J/mol·K} \)
- \( T \) is the temperature in Kelvin (298 K at 25 °C)
- \( F \) is the Faraday constant, approximately \( 96485 \, \text{C/mol} \)
- \( z \) is the charge of the ion (+1 for Na⁺ and -1 for Cl⁻)

We can simplify this to:

\[
E_{\text{ion}} = \frac{61.5 \, \text{mV}}{z} \ln \left( \frac{[\text{ion}]_{\text{out}}}{[\text{ion}]_{\text{in}}} \right)
\]

#### a) Calculating the Equilibrium Potential for Na⁺:
For Na⁺ (\( z = +1 \)):

\[
E_{\text{Na}^+} = \frac{61.5 \, \text{mV}}{1} \ln \left( \frac{250 \, \text{mM}}{10 \, \text{mM}} \right)
\]

1. Calculate the ratio: \( \frac{250}{10} = 25 \)
2. Take the natural logarithm: \( \ln(25) \approx 3.2189 \)
3. Multiply by 61.5 mV: \( E_{\text{Na}^+} = 61.5 \times 3.2189 \approx 198 \, \text{mV} \)

So, \( E_{\text{Na}^+} \approx +198 \, \text{mV} \).

#### b) Calculating the Equilibrium Potential for Cl⁻:
For Cl⁻ (\( z = -1 \)):

\[
E_{\text{Cl}^-} = \frac{61.5 \, \text{mV}}{-1} \ln \left( \frac{250 \, \text{mM}}{6 \, \text{mM}} \right)
\]

1. Calculate the ratio: \( \frac{250}{6} \approx 41.67 \)
2. Take the natural logarithm: \( \ln(41.67) \approx 3.73 \)
3. Multiply by 61.5 mV: \( E_{\text{Cl}^-} = -61.5 \times 3.73 \approx -229 \, \text{mV} \)

So, \( E_{\text{Cl}^-} \approx -229 \, \text{mV} \).

### Step 2: Predicting the Direction of Ion Movement
Now, compare each equilibrium potential with the membrane potential (-70 mV):

- **For Na⁺:**
  - The equilibrium potential for Na⁺ is +198 mV, which is more positive than the membrane potential (-70 mV).
  - Na⁺ will move **inward** because it is attracted to the negative interior and has a concentration gradient driving it into the cell.

- **For Cl⁻:**
  - The equilibrium potential for Cl⁻ is -229 mV, which is more negative than the membrane potential (-70 mV).
  - Cl⁻ will tend to move **outward** since the cell interior is less negative than its equilibrium potential, and it will follow its concentration gradient outward.

### Summary:
- **Na⁺ ions will move inward** to bring the membrane potential closer to their equilibrium potential.
- **Cl⁻ ions will move outward** for the same reason.

Would you like further clarification on any part of this solution?

---

### Follow-up Questions:
1. What is the impact on membrane potential if Na⁺ and Cl⁻ reach their equilibrium potentials?
2. How would changing the external NaCl concentration affect the movement of Na⁺ and Cl⁻?
3. What would happen if the temperature were increased or decreased significantly?
4. How would adding

The concentration of Na+ and Cl- inside a muscle cell are 10 mM and 6 mM, respectively. The membrane potential is -70 mV, negative inside. In one experiment the cell is submerged in a large container filled with a solution of 250 mM NaCl. The temperature is 25 °C and remains constant. a) calculate the electrochemical potential and explain which direction (inward or outward) will Na+ and Cl ions move.

Learn how to calculate the electrochemical potential and predict the direction of ion movement for Na+ and Cl- in a muscle cell submerged in a NaCl solution. This detailed solution uses the Nernst equation and explains how membrane potential influences ion flow. Suitable for students in Grades 11-12 studying cell physiology or biophysics.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation