You place an excitable cell in a solution of 10 mEq/L potassium. The cell would...

This is known as hyperkalemia, I think.

Increased extracellular potassium levels result in depolarization of the membrane potentials of cells due to the increase in the equilibrium potential of potassium. This depolarization opens some voltage-gated sodium channels, but also increases the inactivation at the same time. Since depolarization due to concentration change is slow, it never generates an action potential by itself instead, it results in accommodation. Above a certain level of potassium the depolarization inactivates sodium channels, opens potassium channels, thus the cells become refractory. This leads to the impairment of neuromuscular, cardiac, and gastrointestinal organ systems. Of most concern is the impairment of cardiac conduction which can result in ventricular fibrillation or asystole.