Q1: 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

ANS:C - 1.24

To find the ratio of the rate of dissolution in water at 𝑡=0t=0 for the cubic tablet to the spherical tablet, we need to consider the surface area to volume ratio for each shape. For a sphere, the surface area 𝐴sphereAsphere​ is given by: 𝐴sphere=4𝜋𝑟2Asphere​=4πr2 For a cube, the surface area 𝐴cubeAcube​ is given by: 𝐴cube=6𝑠2Acube​=6s2 Where 𝑟r is the radius of the sphere and 𝑠s is the side length of the cube. Given that the amount of drug is the same in both tablets and assuming shape and size do not influence mass transfer, we can assume that the rate of dissolution is directly proportional to the surface area exposed to the solvent (water). Let's denote 𝑘sphereksphere​ and 𝑘cubekcube​ as the dissolution rate constants for the spherical and cubic tablets, respectively. Therefore, the ratio of the rate of dissolution for the cubic tablet to the spherical tablet at 𝑡=0t=0 is: 𝑘cube𝑘sphere=𝐴cube𝐴sphereksphere​kcube​​=Asphere​Acube​​ 𝑘cube𝑘sphere=6𝑠24𝜋𝑟2ksphere​kcube​​=4πr26s2​ Given that the amount of drug is the same, we can equate the volumes of the cube and sphere: 𝑠3=43𝜋𝑟3s3=34​πr3 From this, we can find the relationship between 𝑠s and 𝑟r: 𝑠=(43𝜋𝑟3)1/3s=(34​πr3)1/3 Now, substitute 𝑠s in terms of 𝑟r into the ratio equation: 𝑘cube𝑘sphere=6(43𝜋𝑟3)2/34𝜋𝑟2ksphere​kcube​​=4πr26(34​πr3)2/3​ 𝑘cube𝑘sphere=6×42/3𝜋2/3𝑟24𝜋𝑟2ksphere​kcube​​=4πr26×42/3π2/3r2​ 𝑘cube𝑘sphere=6×42/3𝜋2/3ksphere​kcube​​=6×42/3π2/3 𝑘cube𝑘sphere≈6×1.587ksphere​kcube​​≈6×1.587 𝑘cube𝑘sphere≈9.522ksphere​kcube​​≈9.522 So, the ratio of the rate of dissolution for the cubic tablet to the spherical tablet at 𝑡=0t=0 is approximately 9.522. However, you should note that the options provided in the question don't match this result. There may be a mistake in the calculation or in the options provided. Let me know if you'd like me to review it again.