Q: An oxygen cylinder of volume 30 litre has 18.20 moles of oxygen. After some oxygen is withdrawn from the cylinder, its gauge pressure drops to 11 atmospheric pressure at temperature 27^ C . The mass o

aligned & n _ f = P _ f V RT [ P _ abs =12 ~atm ] \\ & = 12 1.01 10^5 30 10^ -3 ( 100 12 ) 300 \\ & =14.544 \\ & moles removed =18.2-14.544=3.656 \\ & mass removed =3.656 32 1000 ~kg =0.116 ~kg aligned

Question 1

The mean free path of molecules in an ideal gas A is half that of another ideal gas B. The diameter of the spherical molecules of gas A is twice the diameter of the molecules of B. If number densities

Accepted Answer

The mean free path of a gas molecule is given by = 1 2 d^2 n Given _A = 1 2 _B and d_A = 2d_B Substituting the formula for mean free path: 1 2 d_A^2 n_A = 1 2 ( 1 2 d_B^2 n_B ) 1 d_A^2 n_A = 1 2 d_B^2 n_B Substituting d_A = 2d_B: 1 (2d_B)^2 n_A = 1 2 d_B^2 n_B 1 4 d_B^2 n_A = 1 2 d_B^2 n_B 4 n_A = 2 n_B n_A = 1 2 n_B Answer: n_A= 1 2 n_B

Question 2

An ideal gas is made of polyatomic molecules. Each of the molecules has three translational, three rotational and f number of vibrational modes. If the ratio of heat capacities C_P/C_V of the gas is 8

Accepted Answer

The internal energy of one mole of the polyatomic gas is given by the equipartition theorem. Each translational and rotational degree of freedom contributes 1 2 RT to the internal energy, while each vibrational mode contributes RT (since it has both kinetic and potential energy components). U = 3 ( 1 2 RT ) + 3 ( 1 2 RT ) + f(RT) = (3+f)RT The molar heat capacity at constant volume is: C_V = dU dT = (3+f)R The molar heat capacity at constant pressure is: C_P = C_V + R = (4+f)R The ratio of heat

Question 3

A flask contains argon and chlorine in the ratio of 2:1 by mass. The temperature of the mixture is 27^ . The ratio of root mean square speed of the molecules of the two gases ( v_ rms ^ Ar v_ rms ^ Cl

Accepted Answer

The root mean square speed of a gas molecule is given by v_ rms = 3RT M , where T is the absolute temperature and M is the molar mass. For argon and chlorine in the same flask, the temperature T is the same. Therefore, the ratio of their rms speeds is inversely proportional to the square root of their molar masses: v_ rms ^ Ar v_ rms ^ Cl = M_ Cl M_ Ar Given the molecular mass of chlorine M_ Cl = 70.0 u and atomic mass of argon M_ Ar = 40.0 u: v_ rms ^ Ar v_ rms ^ Cl = 70.0 40.0 = 7 4 = 7 2 The

Question 4

An oxygen cylinder of volume 30 litre has 18.20 moles of oxygen. After some oxygen is withdrawn from the cylinder, its gauge pressure drops to 11 atmospheric pressure at temperature 27^ C . The mass o

Accepted Answer

aligned & n _ f = P _ f V RT [ P _ abs =12 ~atm ] \ & = 12 1.01 10^5 30 10^ -3 ( 100 12 ) 300 \ & =14.544 \ & moles removed =18.2-14.544=3.656 \ & mass removed =3.656 32 1000 ~kg =0.116 ~kg aligned

Question 5

The following graph represents the T - V curves of an ideal gas (where T is the temperature and V the volume) at three pressures P_1, P_2 and P_3 compared with those of Charles's law represented as do

Accepted Answer

At same temperature, curve with higher volume corresponds to lower pressure. aligned & V_3 _2 _1 \ & P_1 _2 _3 aligned (We draw a straight line parallel to volume axis to get this)

Question 6

According to the law of equipartition of energy, the number of vibrational modes of a polyatomic gas of constant = C_p C_v is ( C_P where C_v are the specific heat capacities of the gas at constant pr

Accepted Answer

A polygamic gas has 3 translational, 3 rotational and f vibration modes U= 3 2 k_B T+ 3 2 k_B T+f k_B T U=(3+f) k_B T C_V=(3+f) R C_p=(4+f) R C_p C_v = 4+f 3+f = 4+f=3 +f 4-3 =f( -1) f= 4-3 -1

Kinetic Theory of Gases — Previous Year Questions & Solutions