States of matter practice · Mixed difficulty

Option A ($1:1.128:1.224$) is correct because the ratio of most probable speed, average speed, and RMS speed is derived from their respective formulas.

The correct answer is C (921.58 m / s) because the average velocity is calculated from the root mean square velocity using the appropriate formula.

Option A (46.6) is correct because it is calculated by using Graham's law of diffusion to find the molecular weight of the mixture and then solving for the molecular weight of gas X.

Option D (All of these) is correct because the ratio a/b in van der Waals' equation can be expressed in multiple equivalent units, including atm litre mol$^{-1}$, atm dm$^3$ mol$^{-1}$, and dyne cm mol$^{-1}$.

Option D (Increases both the average kinetic energy and rms velocity, but not significantly) is correct because the temperature change is small relative to the absolute temperature, leading to only a slight increase in both average kinetic energy and rms velocity.

Option B ($z = \frac{{P{V_{obs}}}}{{nRT}}$) is correct because the compressibility factor (z) is defined as the ratio of the observed volume to the ideal volume, which is represented by the formula.

Option B (1.73) is correct because the root mean square speed is proportional to the square root of the temperature, so tripling the temperature increases the speed by a factor of $\sqrt{3}$ ≈ 1.73.

Option C ($u_{ {r.m.s. }}=\sqrt{\frac{2 E}{M}}$) is correct because the root mean square velocity is related to the average kinetic energy by the formula E = (1/2) * M * u_rms².

Option B (5.26%) is correct because it is the percentage increase in pressure required to decrease the volume by 5% according to Boyle's Law.

Option C ($LiOH > NaOH > KOH > RbOH > CSOH$ (Solubility)) is incorrect because the solubility of group 1 hydroxides increases down the group due to decreasing lattice energy.

Option D (All of these) is correct because Boyle's law, Charles's law, and Avogadro's law can all be derived from the kinetic theory of gases.

Option D (None of these) is correct because the value of the universal gas constant (R) depends only on the units of measurement used for pressure, volume, and temperature, not on the properties of the gas itself.

Option A (960) is correct because the total kinetic energy is calculated by summing the kinetic energies of each gas and dividing by the total number of moles.

Option A (Benzo) is correct because the benzo group ($\mathrm{C_6H_5C<}$) has three valencies available for bonding, making it trivalent.

Option A (4.32 litres) is correct because it is the original volume calculated using Charles's Law, which relates volume and temperature at constant pressure.

Option B (${CCl}_4$ and ${CH}_4$) is correct because instantaneous dipole-induced dipole interactions (London dispersion forces) exist between non-polar molecules.

Option C (1) is correct because the compressibility factor (Z) for an ideal gas is always 1, as the ideal gas law (PV=nRT) is perfectly obeyed.

Option D ($81.8 \%$) is correct because it is calculated by finding the fraction of nitrogen remaining and subtracting it from 1 to find the fraction escaped.

Option C is correct. A gas can be easily liquefied by applying pressure when it is cooled to below its critical temperature. Above the critical temperature, no amount of pressure can liquefy the gas.

Option C (Inter molecular hydrogen bonding) is correct because it leads to higher boiling points due to increased intermolecular forces.

Option D (As temperature increases, pressure increases at constant volume) is correct because Gay-Lussac's law states that pressure is directly proportional to temperature at constant volume.

Option B (40) is correct because the percentage of air escaped is calculated using Charles's Law, and the result is 40%.

Option A ($\mathrm{N}_1$) is correct because the number of gas molecules remains the same when the kinetic energy doubles and the temperature doubles.

Option C ($8/3$) is correct because the compressibility factor at critical conditions is 3/8, so the inverse is 8/3.

The correct answer is B ($\frac{{a{n^2}}}{{{V^2}}}$) because this term represents the pressure correction in the van der Waals equation for real gases, accounting for intermolecular forces.

Option A ($1.8 \mathrm{~atm}$) is correct because it is calculated by using the ideal gas law to find the number of moles of each gas and then finding the total pressure.

Option D (64 min) is correct because it accurately applies Graham's law of diffusion to calculate the time taken for oxygen to diffuse.

Option C (1) is correct because the ratio of root mean square speeds is calculated using the formula involving temperature and molar mass, and in this case, the ratio simplifies to 1.

Option B is correct. The kinetic theory of gases assumes that gas molecules are in constant, random motion, not at rest.

Option B (Ion-ion forces) is correct because ion-ion forces are electrostatic interactions between charged ions, which are significantly stronger than dipole-dipole, ion-dipole, or ion-induced dipole forces.