Diffusion of a gas is described by Graham's Law, which states that the rate of diffusion (or effusion) of a gas is inversely proportional to the square root of its molecular mass. This law is mathematically represented as:

$$ \text{Rate of diffusion} \propto \frac{1}{\sqrt{\text{Molecular Mass}}} $$

Given this information, let's analyze the options:

• Option A: Directly proportional to its density - This is incorrect because density and molecular mass are related, but the rate of diffusion is inversely related to the square root of molecular mass, not directly proportional to density.
• Option B: Directly proportional to the square root of its molecular weight - This is incorrect. The relationship is inverse; the rate decreases as the molecular weight increases.
• Option C: Inversely proportional to the square root of its molecular weight - This is the correct option. As molecular mass increases, the rate of diffusion decreases in proportion to the inverse of the square root of the molecular mass.
• Option D: Directly proportional to its molecular weight - This is incorrect as it contradicts the principle of Graham's Law.

Thus, the correct answer is Option C: inversely proportional to the square root of its molecular weight.