Q: Molar volume (V_m ) of a van der Waals gas can be calculated by expressing the van der Waals equation as a cubic equation with V_m as the variable. The ratio (in mol dm ^ -3 ) of the coefficient of V_

aligned & (P+ a V_m^2 ) (V_m-b )=R T \\ & P V_m-b P+ a V_m - a b V_m^2 -R T=0 \\ & P V_m^2-(b P+R T) V_m^2+a V_m-a b=0 aligned Coefficient of V _ m ^2=-( bP + RT ) Coefficient of V _ m = a Ratio =- ( bP + RT ) a =- [ 0.06 300+24.6 6 ]=-7.1 .

Q: A gas has a compressibility factor of 0 . 5 and a molar volume of 0 . 4 dm 3 mol - 1 at a temperature of 800 K and pressure x atm . If it shows ideal gas behaviour at the s

Compressibility factor ( Z )= V real V ideal = 0 . 5 V real = 0 . 4 dm 3 mol - 1 = 0 . 4 L / mol ∴ V ideal = 0 . 4 0 . 5 = 0 . 8 L / mol ∴ y = 0 . 8 L / mol Using ideal gas equation : PV = nRT P = 1 × 8 × 10 - 2 × 800 0 . 8 x = 80 atm ∴ x y = 80 0 . 8 = 100

Question 1

Two cylinders, both fitted with frictionless pistons, are filled with mixtures of He and Ar gases. In the first cylinder, the masses of He and Ar are m_1 and m_2, respectively. In the second cylinder,

Accepted Answer

Let the molar mass of He be M. Then the molar mass of Ar is 10M. In the first cylinder, the total number of moles is given by: n_1 = m_1 M + m_2 10M = 10m_1 + m_2 10M In the second cylinder, the total number of moles is given by: n_2 = m_2 M + m_1 10M = 10m_2 + m_1 10M Using the ideal gas equation PV = nRT, since the volume and temperature are the same for both cylinders, the pressure is directly proportional to the number of moles. Thus, P_1 P_2 = n_1 n_2 . Given that P_1 = 5P_2, we have: n_1 n

Question 2

Molar volume (V_m ) of a van der Waals gas can be calculated by expressing the van der Waals equation as a cubic equation with V_m as the variable. The ratio (in mol dm ^ -3 ) of the coefficient of V_

Accepted Answer

aligned & (P+ a V_m^2 ) (V_m-b )=R T \ & P V_m-b P+ a V_m - a b V_m^2 -R T=0 \ & P V_m^2-(b P+R T) V_m^2+a V_m-a b=0 aligned Coefficient of V _ m ^2=-( bP + RT ) Coefficient of V _ m = a Ratio =- ( bP + RT ) a =- [ 0.06 300+24.6 6 ]=-7.1 .

Question 3

A closed vessel contains 10 ~g of an ideal gas X at 300 ~K , which exerts 2 atm pressure. At the same temperature, 80 ~g of another ideal gas Y is added to it and the pressure becomes 6 ~atm . The rat

Accepted Answer

For Ideal Gas PV = nRT n P at constant T \& ~V . mole = Mass Molar mass For gas X : 10 M _ X 2 ~atm (1) For gas X \& Y : 10 M _ X + 80 M _ Y 6 ~atm (2) From (2)-(1) 80 M _ y 4 (3) On dividing (1) by (3) M _ Y 8 M _ X = 1 2 M _ Y M _ X =4 (4) V _ rms = 3 RT M v _ rms 1 M ( V _ ms )_ X ( V _ ms )_ Y = M _ Y M _ x = 4 1 = 2 1

Question 4

A gas has a compressibility factor of 0 . 5 and a molar volume of 0 . 4 &#160; dm 3 &#160; mol - 1 at a temperature of 800 &#160; K and pressure x &#160; atm . If it shows ideal gas behaviour at the s

Accepted Answer

Compressibility factor  ( Z )= V real &#160; V ideal = 0 . 5 V real &#160; = 0 . 4 dm 3 &#160; mol - 1 = 0 . 4 &#160; L / mol &#8756; &#160;&#160; V ideal &#160; = 0 . 4 0 . 5 = 0 . 8 &#160; L / mol &#8756; &#160; &#160; y = 0 . 8 &#160; L / mol Using ideal gas equation : PV = nRT P = 1 &#215; 8 &#215; 10 - 2 &#215; 800 0 . 8 x = 80 &#160; atm &#8756; &#160;&#160; x y = 80 0 . 8 = 100

Question 5

If the distribution of molecular speeds of a gas is as per the figure shown below, then the ratio of the most probable, the average, and the root mean square speeds, respectively, is

Accepted Answer

Due to symmetrical graph given, the average value of velocities will be at the middle, symmetrical velocity which is also most probable velocity. While calculating rms speed, we have to take average of square of speeds and its root. In square of speeds, higher speeds will give more contribution so the value will be more than the average value.

Question 6

Which of the following statement(s) (are) correct regarding the root mean square speed U r m s and average translational kinetic energy &#949; a v of a molecule in a gas at equilibrium?

Accepted Answer

U rms = 3RT M , E av = 3 2 RT If temperature is made 4 times, U rms between twice. Avg. kinetic energy ( F av ) is independent of molecular man at a given temperature, U rms inversely proportional to the square not of molecular mass.

States of Matter — Previous Year Questions & Solutions