States of matter practice · Mixed difficulty

Option D (A, B, C and D) is correct because the van der Waals constant 'a' increases with the size and complexity of the molecule, reflecting stronger intermolecular forces.

Option C ($\mathrm{S}{\mathrm{O}_2}$) is correct because it has the highest value of van der Waals' forces of attraction among the given options, making it the most readily liquefied.

Option D (Amount of the substance in $mol\,{L^{ - 1}}$) is correct because the SI unit for the amount of substance is 'mol', and $mol\,{L^{ - 1}}$ represents concentration (molarity), not the amount of substance.

Option B is correct because 1 poise is defined as 1 dyne second per square centimeter.

Option B (${\left( {\partial P/\partial V} \right)_T} = - K/{V^2}$) is correct because it represents the derivative of Boyle's Law (PV = constant) with respect to volume at constant temperature.

Option D (${V_t} = {V_0}\left( {1 + \frac{t}{{273}}} \right)$) is correct because it accurately represents Charles's Law, which describes the relationship between volume and temperature.

Option C ($PV = RT + Pb$) is correct because at high pressure, the volume 'V' is small, so 'b' is not negligible compared to 'V', and the term $\frac{a}{V^2}$ becomes negligible.

Option C ($N{H_3}$) is correct because it has the highest 'a' value, indicating stronger intermolecular forces and easier liquefaction.

Option B (4) is correct because equating the RMS speed of gas X to the most probable speed of gas Y and solving for the molecular weight of Y yields 4.

Option D is correct because at very low pressure, the volume is large, and the compressibility factor Z approaches $1-\frac{a}{\text { VRT }}$ for a real gas.

Option B (Manometer) is correct because a manometer is a device used to measure gaseous pressure, often based on the principles of Boyle's law.

Option A (Both A and R are true and R is correct explanation of A) is correct because if gas molecules move only in one direction, their average speed is zero due to equal and opposite velocities.

Option C (${\left[ {\frac{{8RT}}{{\pi M}}} \right]^{1/2}}$) is correct because it is the formula for the average speed of gas molecules, derived from kinetic theory of gases.

Option A (If both Assertion and Reason are correct and the Reason is a correct explanation of the Assertion) is correct because hydrogen's compressibility factor increases with pressure due to repulsive forces dominating even at low pressures.

Option B (Moist ${O_2}$) is correct because the presence of water vapor increases the effective molecular weight compared to dry air.

Option A ($298 \mathrm{~K}, 1$ bar) is correct because the standard state is defined as 298 K (25°C) and 1 bar pressure.

Option A (1) is correct because the compressibility factor (Z) for an ideal gas is always 1, as the gas follows the ideal gas law (pV = nRT).

Option A ($9:10$) is correct because the ratio of diffusion rates is inversely proportional to the square root of their molecular weights.

Option C (= 20 mL) is correct because toluene and benzene form an ideal solution, meaning there is no volume change upon mixing.

Option B (27/8) is correct because the Boyle temperature is a/Rb and the critical temperature is 8a/27Rb, so their ratio is 27/8.

Option A (0.71) is correct because it is calculated using the compressibility factor formula, Z = PV/nRT.

Option B (The pressure decreases) is correct because intermolecular attractions reduce the force with which gas molecules collide with the container walls.