**Core Concept**
The balance and distribution of ions across cell membranes are crucial for maintaining proper cellular function, including nerve impulse transmission, muscle contraction, and cellular signaling. The concentration of ions such as sodium (Na+), potassium (K+), calcium (Ca2+), and chloride (Cl-) varies between the intra- and extracellular compartments.

**Why the Correct Answer is Right**
The correct answer is related to the concept that the intracellular compartment has a higher concentration of potassium (K+) ions compared to the extracellular compartment. This is due to the active transport of potassium ions into the cell through the Na+/K+-ATPase pump, which maintains the resting membrane potential. The high concentration of potassium ions inside the cell is essential for the proper functioning of the nervous system and muscle contraction.

**Why Each Wrong Option is Incorrect**
**Option A:** This statement is true as the extracellular compartment has a higher concentration of sodium (Na+) ions compared to the intracellular compartment. The Na+/K+-ATPase pump actively transports sodium ions out of the cell and potassium ions into the cell.
**Option B:** This statement is true as the intracellular compartment has a higher concentration of magnesium (Mg2+) ions compared to the extracellular compartment. Magnesium ions play a crucial role in many cellular processes, including muscle contraction and nerve impulse transmission.
**Option C:** This statement is false as the intracellular compartment has a higher concentration of potassium (K+) ions compared to the extracellular compartment, not a lower concentration. The high concentration of potassium ions inside the cell is essential for the proper functioning of the nervous system and muscle contraction.

**Clinical Pearl / High-Yield Fact**
When considering the balance of ions across cell membranes, it is essential to remember the "Sodium-Potassium Pump" concept, which actively transports sodium ions out of the cell and potassium ions into the cell, maintaining the resting membrane potential.

**Correct Answer: C. This statement is false as the intracellular compartment has a higher concentration of potassium (K+) ions compared to the extracellular compartment.**