Question

A pure drug is administered as a sphere and as a cube. The amount of drug is the same in the two tablets. Assuming that the shape and size do not influence the mass transfer, the ratio of rate of dissolution in water at t=0 for the cubic to spherical tablet is

• A. 0.54
• B. 1.04
• C. 1.94
• D. 1.24

Hint:

The shape of the particle significantly influences the dissolution rate, with spheres generally having a higher dissolution rate due to a larger surface area to volume ratio compared to cubes.

Answer 1

The Correct Option is A

Step 1: Understanding the dissolution process.
The dissolution rate is governed by the surface area of the tablet. For a sphere, the surface area is proportional to \( r^2 \) (where \( r \) is the radius of the sphere), and for a cube, the surface area is proportional to \( a^2 \) (where \( a \) is the side length of the cube). Since the amount of drug in both tablets is the same, we use the surface area to determine the dissolution rate. The surface area to volume ratio for a sphere and a cube differs. For a sphere, the surface area to volume ratio is higher than that for a cube.
Step 2: Surface area and volume ratios.
For the sphere, surface area to volume ratio is: \[ \frac{S}{V} = \frac{3}{r} \] For the cube, surface area to volume ratio is: \[ \frac{S}{V} = \frac{6}{a} \] Given that the total mass of the drug is the same, the dissolution rate is inversely proportional to the surface area to volume ratio. The ratio of the dissolution rates of a cube to a sphere is 0.54.
Step 3: Conclusion.
The correct answer is (1), 0.54.