Question

Two methanol-water mixtures are contained in separate tanks. The first mixture contains 40.0 wt% methanol and the second contains 70.0 wt% methanol. If 200 kg of the first mixture is combined with 150 kg of the second, what are the mass and composition of the product (Total balance, Methanol balance, Physical constraint)?

(a) 350 kg, 0.529, 0.471

(b) 320 kg, 0.529, 0.521

(c) 360 kg, 0.620, 0.471

(d) 350 kg, 0.690, 0.760

The question was posed to me in unit test.

My question comes from Law of Conservation of Mass topic in section Material Balance of Bioprocess Engineering

Answer 1

Right answer is (a) 350 kg, 0.529, 0.471

To elaborate: Material Balances (Steady-State, Non-Reactive Process) :

Total Balance: m1 + m2 = m3

Methanol-Balance: m1xM1 + m2xM2 = m3xM3

Water-Balance: m1xw1 + m2xw2 = m3xw3

(choose only 2 equations since one of them is no longer independent)

Physical Constraint (applied to mixture 3):

xM3 + xW3 = 1.00

Always start with the equation with the least number of unknowns if possible and minimize solving equations simultaneously.

Total Balance (m3)

   ↓

Methanol Balance (xM3)

   ↓

Physical Constraint (xW3)

Total balance:

m3 = (200 kg) + (150 kg)

m3 = 350 kg

CH3OH balance:

(200 kg)(0.40) + (150 kg)(0.70) = (350 g)xM3

xM3  = 0.529

Physical constraint:

xW3 = 1.00 – xM3 = 1 – 0.529

xW3 = 0.471.