A membrane permeable only by Na^+ is used to separate the following two solutions: α 0.1

step 1 The voltage difference between the membranes when the sodium ions are allowed to move is plus 20

A membrane permeable only by Na^+ is used to separate the...

A membrane permeable only by $\mathrm{Na}^{+}$ is used to separate the following two solutions: \[ \begin{array}{ll} \alpha & 0.10 \mathrm{mol} \mathrm{kg}^{-1} \mathrm{NaCl}, 0.05 \mathrm{mol} \mathrm{kg}^{-1} \mathrm{KCl} \\ \beta & 0.05 \mathrm{mol} \mathrm{kg}^{-1} \mathrm{NaCl}, 0.10 \mathrm{mol} \mathrm{kg}^{-1} \mathrm{KCl} \end{array} \] What is the membrane potential at $25^{\circ} \mathrm{C}$, and which solution has the highest positive potential?

A membrane permeable only by $\mathrm{Na}^{+}$ is used to separate the following two solutions:
\[
\begin{array}{ll}
\alpha & 0.10 \mathrm{mol} \mathrm{kg}^{-1} \mathrm{NaCl}, 0.05 \mathrm{mol} \mathrm{kg}^{-1} \mathrm{KCl} \\
\beta & 0.05 \mathrm{mol} \mathrm{kg}^{-1} \mathrm{NaCl}, 0.10 \mathrm{mol} \mathrm{kg}^{-1} \mathrm{KCl}
\end{array}
\]
What is the membrane potential at $25^{\circ} \mathrm{C}$, and which solution has the highest positive potential?

Key Concepts

Electrochemical Gradient

The electrochemical gradient combines the effects of the chemical concentration gradient and the electrical potential difference across a membrane. It is the driving force for ion movement, as ions move in response to both their concentration differences and the electrical forces acting on them, which is essential in understanding how equilibrium is reached in systems with selective permeability.

Nernst Equation

The Nernst equation is a key tool used to relate the concentration gradient of a permeable ion across a membrane to the equilibrium electrical potential (membrane potential) that balances this gradient. By incorporating factors such as temperature, ion charge, and ion concentrations on either side, the equation provides a quantitative method to calculate the potential difference resulting from selective ion permeability.

Membrane Potential

Membrane potential is the electrical potential difference across a biological or synthetic membrane, which arises due to differences in ion concentrations between the two sides of the membrane. It is a fundamental concept in electrochemistry and cell physiology, as it influences ion transport, electrical signaling, and the overall equilibrium state of charged species.

Selective Permeability

Selective permeability refers to the property of a membrane that allows certain ions or molecules to pass through while blocking others. This characteristic is crucial for establishing and maintaining ion concentration gradients, as it determines which species contribute to the creation of membrane potential by being able to traverse the membrane.

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