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

a)

`K = 2.64 * 10^(-8)`

b)

`15 (5)/(8)` hours

Step-by-step explanation:

Given

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

`S = 2500000` square centimeter

`V(dC)/(dT) = 0.40` grams/minute

`V(dC)/(dT) = (dM)/(dT) = (0.40*60)/(10) = 0.66` mg per second

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

a)

`(dM)/(dT) = K SC_s`

`0.66 = K* 2500000* 10\\`

`K = 2.64 * 10^(-8)` cm /sec

b) Time taken

Time taken to sink

`(10*60)/(0.4) * 37.5 = 56,250`

Time in hours

`15 (5)/(8)` hours