Solved Numericals: Ideal Gas Laws and their graphs | Physical Chemistry PDF Download

Q.1. What is the shape of a P-T curve for ideal gas?
(a) Straight line
(b) Parabolic
(c) Hyperbolic
(d) Ellipse

Correct Answer is Option (a)
P-T curve is a straight line for ideal gas. 

Q.2. What is the shape of a P-V curve for an ideal gas?
(a) Straight line
(b) Parabolic
(c) Hyperbolic
(d) Ellipse

Correct Answer is Option (c)
P-V curve is hyperbolic for an ideal gas. 

Q.3. What is the pressure of a 5 liter/mole ideal gas at temperature 27^oC?
(a) 2.5 atm
(b) 3.8 atm
(c) 4.4 atm
(d) 5.3 atm

Correct Answer is Option (d)
PV = nRT, => P*5 = 0.0821*300, => P = 5.3 atm. 

Q.4. First of the two ideal gases has twice molar volume as much as the second at same temperature, what is the ratio of their pressures?
(a) 4 : 1
(b) 1 : 4
(c) 2 : 1
(d) 1 : 2

Correct Answer is Option (d)
P₁V₁ = n₁RT₁, P₂V₂ = n₂RT₂ dividing both the equations, => P₁ : P₂ = 1 : 2.

Q.5. What is the density of O₂ at 27^oC with pressure 1 atm?
(a) 1.1 g/L
(b) 1.3 g/L
(c) 1.5 g/L
(d) 1.7 g/L

Correct Answer is Option (b)
Molecular wt. of O₂= 44 g, PV = nRT, => PV = (m/M)RT, => d = PM/RT = (1*32)/(0.0821*300) = 1.3 g/L. 

Q.6. What is the specific gravity of CO₂ at 27^oC and pressure 1 atm with respect to air of with density 1 g/L?
(a) 1.23
(b) 1.55
(c) 1.78
(d) 1.96

Correct Answer is Option (c)
Density of CO₂ = PM/RT = 1*44/(0.0821*300) = 1.78 g/L, => Specific gravity = 1.78/1 = 1.78. 

Q.7. What is the compressibility factor for an ideal gas?
(a) 1
(b) 2
(c) 3
(d) Depends on the gas

Correct Answer is Option (a)
Compressibility of an ideal gas is always 1. 

Q.8. Which of the following term does not involve in ideal gas law?
(a) Pressure
(b) Volume
(c) Temperature
d) Time

Correct Answer is Option (d)
Ideal gas law is PV = nRT, which does not involve time. 

Q.9. What is the shape of a V-T curve for ideal gas?
(a) Straight line
(b) Parabolic
(c) Hyperbolic
(d) Ellipse

Correct Answer is Option (a)
V-T curve is straight line for ideal gas. 

Q.10. Which of the following is not true about ideal gas molecules?
(a) They have negligible size
(b) They do not have attractive forces
(c) They do not apply pressure
(d) They move in random motion

Correct Answer is Option (c)
Ideal gas molecules apply pressure to the walls of a container. 

Q.11. What is the Temperature of a 2 liter/mole ideal gas with pressure 10 atm?
(a) 243.6 K
(b) 268.4 K
(c) 289.1 K
(d) 313.5 K

Correct Answer is Option (a)
PV = nRT, => 10*2 = 0.0821*T, => T = 243.6 K. 

Q.12. 88 grams of CO₂ at 27^oC is applying 5 atm pressure, what is the volume occupied by it?
(a) 5.6 liter
(b) 7.9 liter
(c) 9.8 liter
(d) 12.2 liter

Correct Answer is Option (c)
n = 88/44 = 2, PV = nRT, => 5*V = 2*0.0821*300, => V = 9.8 liter. 

Q.13. What is the molecular mass of an ideal gas with pressure 1 atm, and density 10 g/L at temperature 27^oC?
(a) 84.5 g
(b) 135.1 g
(c) 186.8 g
(d) 246.3 g

Correct Answer is Option (d)
M = dRT/P = 10*0.0821*300/1 = 246.3 g. 

Q.14. What is the specific gravity of CO at 27^oC and pressure 5 atm with respect to air (molecular wt. = 29 g) at 27^oC and pressure 10 atm?
(a) 0.48
(b) 0.56
(c) 0.64
(d) 0.72

Correct Answer is Option (a)
Density of CO = 5*28/(0.0821*300) = 5.68 g/L, density of air = 10*29/(0.0821*300) = 11.77 g/L, => specific gravity = 5.68/11.77 = 0.48. 

Q.15. Which of the following is not the unit of R?
(a) Atm.liter/K.mole
(b) Pa.m³/K
(c) N.Kg.m³/K.mole
(d) None of the mentioned

Correct Answer is Option (c)
N.Kg.m/K.mole is the unit of R.