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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

Respuesta :

Answer:

a)

[tex]K = 2.64 * 10^{-8}[/tex]

b)

[tex]15 \frac{5}{8}[/tex] hours

Explanation:

Given

Surface Area (S) of 250 grams of powder sample [tex]= 250[/tex] square meter.

[tex]S = 2500000[/tex] square centimeter

[tex]V\frac{dC}{dT} = 0.40[/tex] grams/minute

[tex]V\frac{dC}{dT} = \frac{dM}{dT} = \frac{0.40*60}{10} = 0.66[/tex] mg per second

[tex]C_s = 0.01[/tex] gram per cubic meter [tex]= 10[/tex] mg/ml

a)

[tex]\frac{dM}{dT} = K SC_s[/tex]

[tex]0.66 = K* 2500000* 10\\[/tex]

[tex]K = 2.64 * 10^{-8}[/tex] cm /sec

b) Time taken

Time taken to sink

[tex]\frac{10*60}{0.4} * 37.5 = 56,250[/tex]

Time in hours

[tex]15 \frac{5}{8}[/tex] hours

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