Question

A compound dissolves in water at a rate proportional to the product of the amount of undissolved solid and the difference between the concentration in a saturated solution and the actual solution; i.e., Csat – C(t). A saturated solution of this compound contains 40 g per 100 g of water. In a test run starting with 20 kg of undissolved compound in 100 kg of water, it was found that 5 kg dissolved in 3 hr. if the test continues, how many kg of compound will remain undissolved after 7 hr? Assume that the system is isothermal.

(a) 11.56 kg

(b) 10.72 kg

(c) 11.76 kg

(d) 10.52 kg

I had been asked this question by my school teacher while I was bunking the class.

I'm obligated to ask this question of Solving Unsteady topic in section Unsteady – State Material and Energy Balances of Bioprocess Engineering

Answer 1

Correct option is (b) 10.72 kg

To elaborate: Definitions of variables used:

C = kg dissolved compound/ kg water Cs = saturated

m = mass of undissolved solid mo = initial mass of solid

W = kg of water

C7= 0.093 and m: mo – C7.100 kg

m = 10.72 kg.