250+ TOP MCQs on Equations of State and Answers

Basic Chemical Engineering Multiple Choice Questions on “Equations of State”.

1. Which of the following is not the equation of state?
a) Van der Waals Equation
b) Charles Equation
c) Holborn Equation
d) Peng Robinson Equation

Answer: b
Clarification: Charles equation is simply P α 1/V which is not the equation of state.

2. Virial Equation is a ______
a) Arithmetic Progression
b) Geometric Progression
c) Harmonic Progression
d) None of the mentioned

Answer: b
Clarification: Virial equation is PV = RT (1 + 1/V + 1/V² + 1/V³ + – – – – -), which is a geometric progression.

3. If the vander waal equation has only one root, what is the relation between a and b?
a) 729a = pb²
b) 243a = pb²
c) 81a = pb²
d) 9a = pb²

Answer: a
Clarification: Vander waal equation, V³ – (nb + nRT/p)V² + (n²a/p)V – n³ab/p = 0, comparing with (V – V_c)³ = 0, => 3n(a/p)^1/2 = n(ab/p)^1/3, => 729a = pb².

4. A container has O₂ at 5 atm and molar volume 2 liter/mole, if a = 9.24 atm(liter/mole), b = 0.0907 liter/mole, what is the temperature of O₂? (Use vander waal equation)
a) 140 K
b) 150 K
c) 170 K
d) 190 K

Answer: c
Clarification: (p + a/V²)(V – b) = RT, => T = (5 + 9.24/2²)(2 – 0.0907)/0.0821 = 170 K.

5. A container has H₂ at 27^oC and molar volume 1 liter/mole, if a = 9.24 atm(liter/mole), b = 0.0907 liter/mole, what is the temperature of H₂? (Use vander waal equation)
a) 7.5 atm
b) 12.4 atm
c) 15.6 atm
d) 17.8 atm

Answer: d
Clarification: (p + a/V²)(V – b) = RT, => p = 0.0821*300/(1 – 0.0907) – 9.24/1² = 17.8 atm.

6. What is the pressure of CO₂ at 0^oC, molar volume = 4 liter/mole, if B = – 0.053 liter/mole, C = 0.0026 liter²/mole²? (Use virial equation, neglect higher terms)
a) 2.4 atm
b) 4.1 atm
c) 5.5 atm
d) 6.9 atm

Answer: c
Clarification: pV = RT(1 + B/V + C/V²), => p = (0.0821*273/4)(1 – 0.053/4 + 0.0026/16) = 5.5 atm.

7. A container is filled with a gas at 10 atm with molar volume 1 liter/mole, if B = – 0.053 liter/mole, C = 0.0026 liter²/mole², what is the temperature of gas? (Use virial equation, neglect higher terms)
a) 128.2 K
b) 156.9 K
c) 198.5 K
d) 243.6 K

Answer: a
Clarification: PV = RT(1 + B/V + C/V²), => T = 10*1/[0.0821*(1 – 0.053/1 + 0.0026/1²)] = 128.2 K.

8. What is the unit of ‘b’ in Peng Robinson equation?
a) Liter/mole
b) Liter²/mole²
c) Mole/Liter
d) Mole²/Liter²

Answer: a
Clarification: Peng Robinson equation is p = RT/(V – b) – aα/[V(V + b) + b(V – b)], => unit of b = unit of molar volume = liter/mole.

9. What is the unit of λ in the SRK equation?
a) Liter/mole
b) Mole/Liter
c) Atm(liter/mole)
d) It is dimensionless

Answer: d
Clarification: In the SRK equation, λ is a dimensionless function of reduced temperature.

10. What is the unit of ‘a’ in RK equation?
a) Liter/mole
b) Atm(liter/mole)
c) Atm(liter/mole)K^0.5
d) Atm(liter/mole)K

Answer: c
Clarification: RK equation is p = RT/(V – b) – a/[T^0.5V(V + b)], => unit of a = atm(liter/mole)K^0.5.