Answer:
[tex]\large \boxed{\text{1.22 mg/s}}[/tex]
Explanation:
We can use the Noyes-Whitney equation to calculate the rate of dissolution.
[tex]\dfrac{\text{d}M}{\text{d}t} = \dfrac{DA(C_{s} - C)}{d}[/tex]
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
[tex]\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 $\large \boxed{\textbf{1.22 mg/s}}$}[/tex]
