Question

Calculate the rate of dissolution (dM/dt) of relatively hydrophobic drug particles with a surface area of 2.5×103 cm2 and saturation solubility of 0.35 mg/mL at 25°C in water. The diffusion coefficient is 1.75×10-7 cm2/s, and the thickness of the diffusion layer is 1.25m. The concentration of the drug in the bulk solution is 2.1×10-4 mg/mL.

Answer 1

Answer:

$\large \boxed{\text{1.22 mg/s}}$

Explanation:

We can use the Noyes-Whitney equation to calculate the rate of dissolution.

$\dfrac{\text{d}M}{\text{d}t} = \dfrac{DA(C_{s} - C)}{d}$

Data:

D = 1.75 × 10⁻⁷ cm²s⁻¹

A = 2.5 × 10³ cm²

Cₛ = 0.35 mg/mL

C = 2.1 × 10⁻⁴ mg/mL

d = 1.25 µm

Calculations:

Cₛ - C = (0.35 - 2.1 × 10⁻⁴) mg·cm⁻³ = 0.350 mg·cm⁻³

d = 1.25 µm = 1.25 × 10⁻⁶ m = 1.25 × 10⁻⁴ cm

$\dfrac{\text{d}M}{\text{d}t} = \dfrac{(1.75 \times 10^{-7} \text{cm}^{2}\text{s}^{-1})(2.5 \times 10^{3} \text{ cm}^{2})(0.350\text{ mg \cdot cm ^{-3} })}{1.25 \times 10^{-4} \text{ cm}} = \textbf{1.22 mg/s}\\\\\text{The rate of dissolution is \large \boxed{\textbf{1.22 mg/s}} }$