Mass Conservation Law - Bioprocess Engineering Questions and Answers

This set of Bioprocess Engineering Multiple Choice Questions & Answers (MCQs) focuses on “Law of Conservation of Mass”.

1. Which is the correct order for the equation of mass balance of the system?

  {A} – {B} + {C} – {D} = {Mass accumulated within system}

a) A. Mass consumed within system, B. Mass in through system boundaries, C. Mass out through system boundaries, D. Mass generated within system
b) A. Mass generated within system, B. Mass in through system boundaries, C. Mass out through system boundaries, D. Mass consumed within system
c) A. Mass in through system boundaries, B. Mass out through system boundaries, C. Mass generated within system, D. Mass consumed within system
d) A. Mass consumed within system, B. Mass generated within system, C. Mass out through system boundaries, D. Mass in through system boundaries
View Answer

Answer: c
Explanation: A mass balance for the system can be written in a general way to account for these possibilities:
{Mass in through system boundaries} – {Mass out through system boundaries} + {Mass generated within system} – {Mass consumed within system} = {Mass accumulated within system}.

2. If the Reactant iron is combined with Reactant Sulfur to form the product Iron sulfide, then what will be the atomic mass of the product?
a) 88
b) 44
c) 22
d) 80
View Answer

Answer: a
Explanation: Fe (iron) + S (Sulfur) = FeS (Iron sulfide),
Atomic masses: Fe = 56, S = 32
One atom of each element on each side of the equations
Law of conservation of mass balance: 56 + 32 = 88.

3. If the reactant Magnesium reacts with Reactant Hydrochloric acid to form the product Magnesium chloride + Hydrogen, then what will be the atomic mass of both the product?
a) 90
b) 97
c) 80
d) 87
View Answer

Answer: b
Explanation: Mg (Magnesium) + 2 HCl (Hydrochloric acid) = MgCl₂ (Magnesium chloride) + H₂ (Hydrogen),
Atomic masses: Mg = 24, H = 1, Cl = 35.5
one atom of Mg, 2 atoms of H and 2 atoms of Cl on both sides of the equation,
Law of conservation of mass balance: 24 + 2 × (1+ 35.5) = 24+ (2 × 35.5) + (2×1) = 97 (Both equal 97)
Note the subscript 2 after the Cl in magnesium chloride or the 2 after the H in the hydrogen molecule, means two atoms of that element.
The 2 before the HCl doubles the number of hydrochloric acid molecules.

4. A continuous process is set up for treatment of wastewater. Each day, 10³ kg cellulose and 10⁵ kg bacteria enter in the feed stream, while 10² kg cellulose and 1.5 x 10² kg bacteria leave in the effluent. The rate of cellulose digestion by the bacteria is 8 x 10² kg d^-1. The rate of bacterial growth is 4x 10² kg d^-l; the rate of cell death by lysis is 6 x 10² kg d^-1. Write balances for cellulose and bacteria in the system.
a) 1× 10³ kg, 9 × 10³ kg
b) 1× 10² kg, 9.965 × 10⁴ kg
c) 1× 10³ kg, 9.964 × 10⁴ kg
d) 1× 10² kg, 9 × 10³ kg
View Answer

Answer: b
Explanation: Cellulose is not generated by the process, only consumed. Using a basis of 1 day, the cellulose balance in kg is :
(10³ – 10² + 0 – 8 x 10²) = accumulation
Therefore, 1× 10² kg cellulose accumulates in the system each day.
Performing the same balance for bacteria:
(10⁵ – 1.5 x 10² + 4 x 10² – 6 x 10²) = accumulation
Therefore, 9.965 × 10⁴ kg bacterial cells accumulate in the system each day.

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5. Which of the following system follows the differential equation?
a) Semi- Batch process
b) Batch process
c) Fed- Batch process
d) Continuous process
View Answer

Answer: d
Explanation: Amounts of mass entering and leaving the system are specified using flow rates, a mass balance based on rates is called a differential balance. Whereas, each term of the mass-balance equation in this case is a quantity of mass, not a rate. This type of balance is called an integral balance. Differential balances for continuous systems operating at steady state and integral balances for batch and semi-batch systems between initial and final states are used.

6. 2SO₂+O₂ → 2SO₃. What is the stoichiometric ratio of SO₂ to SO₃?
a) 3
b) 1
c) 2
d) 0
View Answer

Answer: b
Explanation: stoichiometric ratio of SO₂ to SO₃ = (2 mole of SO₂ reacted)/(2 mole of SO₃ produced) = 1.

7. 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
View Answer

Answer: a
Explanation: Material Balances (Steady-State, Non-Reactive Process) :
Total Balance: m₁ + m₂ = m₃
Methanol-Balance: m₁x_M1 + m₂x_M2 = m₃x_M3
Water-Balance: m₁x_w1 + m₂x_w2 = m₃x_w3

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

Physical Constraint (applied to mixture 3):
x_M3 + x_W3 = 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 (x_M3)
↓
Physical Constraint (x_W3)
Total balance:
m₃ = (200 kg) + (150 kg)
m₃ = 350 kg

CH₃OH balance:
(200 kg)(0.40) + (150 kg)(0.70) = (350 g)x_M3
x_M3 = 0.529

Physical constraint:
x_W3 = 1.00 – x_M3 = 1 – 0.529
x_W3 = 0.471.

8. A solution of common salt in water is prepared by adding 20 kg of salt to 100 kg of water, to make a liquid of density 1323 kg/m³. Calculate the concentration of salt in this solution as a (a) weight fraction, (b) weight/volume fraction, (c) mole fraction, (d) molal concentration.
a) 15.7%, 23.1%, 0.058, 3.88 moles in m³
b) 14.5%, 22.4%, 0.059, 2.88 moles in m³
c) 16.7%, 22.1%, 0.058, 3.77 moles in m³
d) 14.7%, 23.1%, 0.059, 2.77 moles in m³
View Answer

Answer: c
Explanation: (i) Weight fraction:
20/(100+20) = 0.167; %weight/weight = 16.7%

(ii) Weight/volume:
A density of 1323kg/m³ means that lm³ of solution weighs 1323kg, but 1323kg of salt solution contains
(20×1323kg of salt) / (100+20) = 220.5 kg salt/m³
1 m³ solution contains 220.5 kg salt.
Weight/volume fraction = 220.5 / 1000 = 0.2205
And so weight / volume = 22.1%

(iii) Moles of water = 100 / 18 = 5.56
Moles of salt = 20 / 58.5 = 0.34
Mole fraction of salt = 0.34 / (5.56 + 0.34) = 0.058

(iv) The molar concentration (M) is 220.5/58.5 = 3.77 moles in m³.

9. Calculate the degree of reduction for ethanol, where the degree of reduction of C=4, H=1, O=-2.
a) γ = 9
b) γ = 6
c) γ = 3
d) γ = 2
View Answer

Answer: b
Explanation: Ethanol (C₂H₅OH) = 2(4) + 6(1) + 1(-2) = 12,
γ = 12/2 = 6
As, the number of equivalents of available electrons per gram atom C is the measure of degree of reduction.

10. Propane (C₃H₈) burns in this reaction:
C₃H₈ + 5O₂ = 4H₂O + 3CO₂
If 200 g of propane is burned, how many g of H₂O is produced?
a) 327.27 g
b) 345.5 g
c) 323.2 g
d) 232.3 g
View Answer

Answer: a
Explanation: Steps to getting this answer:

Since you cannot calculate from grams of reactant to grams of products you must convert from grams of C₃H₈ to moles of C₃H₈ then from moles of C₃H₈ to moles of H₂O. Then convert from moles of H₂O to grams of H₂O.

Step 1: 200 g C₃H₈ is equal to 4.54 mol C₃H₈.
Step 2: Since there is a ratio of 4:1 H₂O to C₃H₈, for every 4.54 mol C₃H₈ there are 18.18 mol H₂O.
Step 3: Convert 18.18 mol H₂O to g H₂O. 18.18 mol H₂O is equal to 327.27 g H₂O.

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