Questions: The resting potential of a cell is negative because at rest there is an excess of K+ inside the cell, and the membrane is permeable chiefly to K+.

The answer is the first one: at rest there is an excess of $\mathrm{K}^+$ inside the cell, and the membrane is permeable chiefly to $\mathrm{K}^+$.

Explanation:

1. At rest there is an excess of $\mathrm{K}^+$ inside the cell, and the membrane is permeable chiefly to $\mathrm{K}^+$.

   • Correct. The resting potential is primarily due to the high permeability of the cell membrane to $\mathrm{K}^+$ ions. $\mathrm{K}^+$ ions tend to move out of the cell, down their concentration gradient, leaving behind a negative charge inside.

2. At rest there is an excess of $\mathrm{K}^+$ outside of the cell, and the membrane is permeable chiefly to $\mathrm{K}^+$.

   • Incorrect. There is actually a higher concentration of $\mathrm{K}^+$ inside the cell at rest.

3. At rest there is an excess of $\mathrm{K}^+$ inside the cell, and the membrane is not permeable to $\mathrm{K}^+$.

   • Incorrect. The membrane is permeable to $\mathrm{K}^+$, which is crucial for establishing the resting potential.

4. There is an excess of $\mathrm{K}^+$ outside of the cell at rest and the cell is not permeable to $\mathrm{K}^+$.

   • Incorrect. The excess of $\mathrm{K}^+$ is inside the cell, and the membrane is permeable to $\mathrm{K}^+$.

In summary, the resting potential is negative because of the concentration gradient of $\mathrm{K}^+$ and the membrane's permeability to $\mathrm{K}^+$.