Question

A powder sample weighing 250 g and having a surface area of 1 m2/g is dispersed in 1 L of water. After 10 minutes, 0.4 g of the sample is dissolved. The aqueous solubility of the sample is 0.01 g/cm3. a) Calculate k. Assume that sink conditions are prevailing and that the surface area of the sample is constant. b) How long will the sink conditions prevail

Answer 1

Answer:

a)

$K = 2.64 * 10^{-8}$

b)

$15 \frac{5}{8}$ hours

Explanation:

Given

Surface Area (S) of 250 grams of powder sample $= 250$ square meter.

$S = 2500000$ square centimeter

$V\frac{dC}{dT} = 0.40$ grams/minute

$V\frac{dC}{dT} = \frac{dM}{dT} = \frac{0.40*60}{10} = 0.66$ mg per second

$C_s = 0.01$ gram per cubic meter $= 10$ mg/ml

a)

$\frac{dM}{dT} = K SC_s$

$0.66 = K* 2500000* 10$

$K = 2.64 * 10^{-8}$ cm /sec

b) Time taken

Time taken to sink

$\frac{10*60}{0.4} * 37.5 = 56,250$

Time in hours

$15 \frac{5}{8}$ hours