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 solve this problem, we need to calculate the electrochemical potential for \( \text{Na}^+ \) and \( \text{Cl}^- \) ions using the Nernst equation, which describes the potential at which there is no net flow of ions across the membrane.

### Given Data:
- **Concentration of \( \text{Na}^+ \) inside (\( [\text{Na}^+]_{in} \))**: 10 mM
- **Concentration of \( \text{Na}^+ \) outside (\( [\text{Na}^+]_{out} \))**: 250 mM
- **Concentration of \( \text{Cl}^- \) inside (\( [\text{Cl}^-]_{in} \))**: 6 mM
- **Concentration of \( \text{Cl}^- \) outside (\( [\text{Cl}^-]_{out} \))**: 250 mM
- **Membrane potential (\( V_m \))**: -70 mV (negative inside)
- **Temperature**: 25°C

We’ll use the Nernst equation to find the equilibrium potential for each ion, and then determine the direction in which each ion will move based on the membrane potential.

### Step 1: Nernst Equation for Each Ion
The Nernst equation for a monovalent ion at a given temperature is:

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

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

The formula simplifies at 25°C to:

\[
E_{ion} = \frac{58 \, \text{mV}}{z} \log \left( \frac{[\text{ion}]_{out}}{[\text{ion}]_{in}} \right)
\]

#### For \( \text{Na}^+ \) (z = +1):
\[
E_{\text{Na}^+} = \frac{58 \, \text{mV}}{1} \log \left( \frac{250}{10} \right)
\]

Calculating:

\[
E_{\text{Na}^+} = 58 \, \text{mV} \times \log(25) \approx 58 \times 1.398 = 81.08 \, \text{mV}
\]

#### For \( \text{Cl}^- \) (z = -1):
\[
E_{\text{Cl}^-} = \frac{58 \, \text{mV}}{-1} \log \left( \frac{250}{6} \right)
\]

Calculating:

\[
E_{\text{Cl}^-} = -58 \, \text{mV} \times \log(41.67) \approx -58 \times 1.62 = -93.96 \, \text{mV}
\]

### Step 2: Compare Membrane Potential with Equilibrium Potentials
- **Membrane Potential (\( V_m \))**: -70 mV

Now, we can assess the direction of ion flow based on the calculated equilibrium potentials:

1. **For \( \text{Na}^+ \):**
   - \( V_m = -70 \, \text{mV} \), while \( E_{\text{Na}^+} = 81.08 \, \text{mV} \).
   - Since \( V_m < E_{\text{Na}^+} \), \( \text{Na}^+ \) ions will move **inward** (into the cell) to reach equilibrium.

2. **For \( \text{Cl}^- \):**
   - \( V_m = -70 \, \text{mV} \), while \( E_{\text{Cl}^-} = -93.96 \, \text{mV} \).
   - Since \( V_m > E_{\text{Cl}^-} \), \( \text{Cl}^- \) ions will move **outward** (out of the cell) to reach equilibrium.

### Summary:
- **\( \text{Na}^+ \)** ions will move **inward**.
- **\( \text{Cl}^- \)** ions will move **outward**.

### Explanation:
The movement of ions is driven by the difference between the membrane potential and each ion's equilibrium potential. Each ion will tend to move in the direction that brings the membrane potential closer to its own equilibrium potential.

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 for Na+ and Cl- ions across a muscle cell membrane with concentrations inside and outside the cell at 10 mM and 6 mM, respectively, and an external solution concentration of 250 mM NaCl. With a membrane potential of -70 mV at 25°C, determine the direction of ion movement using the Nernst equation. Ideal for undergraduate chemistry or biophysics students.

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