States of matter practice · Mixed difficulty

Option D (Van der Waals’ forces) is correct because non-polar molecules interact through weak, temporary dipoles induced by electron fluctuations.

Option A (400) is correct because the critical temperature can be calculated using the critical compressibility factor and the ideal gas law.

Option C (Mole fraction) is correct because, according to Dalton's law of partial pressures, the ratio of the partial pressure of a gas to the total pressure is equal to its mole fraction.

Option B ($N{H_3}$) is correct because it has the lowest molecular weight among the given gases, leading to the highest rate of diffusion according to Graham's law.

Option A (6) is correct because using the ideal gas law in terms of density, the ratio of pressures can be found to be 6.

The correct answer is B ($KE$ of the molecules becomes zero and the molecular motion also becomes zero) because at absolute zero (0 Kelvin), all molecular motion ceases, and the kinetic energy becomes zero.

Option B (72) is correct because the molecular weight is calculated using Graham's law of diffusion, relating the rates of diffusion to the square root of their molecular weights.

Option C (0.9213) is correct because the average speed of gas molecules is approximately 0.9213 times their root-mean-square (RMS) speed, based on the kinetic theory of gases.

Option B is correct because both statements are correct, but the second statement (pressure difference) does not explain the first statement (boiling point difference); the boiling point difference is a direct consequence of the pressure difference.

Option D (26.94 cc) is correct because it involves converting the given conditions to STP, then using stoichiometry to find the volume of oxygen required for complete combustion of methane.

Option B ($6.17 \times {10^{ - 21}}\mathrm{J}$) is correct because it is the average kinetic energy calculated using the formula $\frac{3}{2}kT$ with the correct Boltzmann constant and temperature.

Option C ($\frac{{2{P_{\mathrm{total}}}}}{3}$) is correct because the partial pressure of a gas is the product of the total pressure and its mole fraction.

Option C ($9: 4$) is correct because the ratio of densities is the inverse square of the ratio of diffusion rates.

Option A (Assertion is correct, reason is correct; reason is a correct explanation for assertion) is correct because gases have high kinetic energy, which prevents them from settling at the bottom of a container.

Option A ($2\mathrm{ }\,atm$) is correct because the pressure is calculated using the ideal gas law, $pV = nRT$.

Option C ($\mathrm{N}{\mathrm{m}^{ - \mathrm{1}}}$) is correct because surface tension is defined as force per unit length, hence the unit is Newton per meter.

Option C (N2O, CO2) is correct because gases with equal molecular masses have equal rates of diffusion, and N2O and CO2 both have a molecular mass of 44.

The correct answer is B ($\sqrt{6} \mathrm{~V}_0$) because the new RMS velocity can be found by relating it to the initial most probable velocity, considering the dissociation of hydrogen molecules into atoms.

Option A ($2.5$) is correct because the relative density is calculated using the ideal gas law and the definition of relative density, resulting in approximately 2.5.

Option C ($T_i=2T_b$) is correct because the inversion temperature ($T_i$) is twice the Boyle's temperature ($T_b$).

Option C is correct because hydrogen gas effuses faster than sulfur dioxide due to its lower molar mass, leading to a lower partial pressure of hydrogen in the remaining mixture over time.

Option B (2) is correct because the ratio of diffusion rates is inversely proportional to the square root of the molar masses, resulting in a ratio of 2.

Option B ($40\mathrm{ }L$) is correct because the change in volume is calculated using Charles's Law, resulting in a 40 L increase.

Option B ($p\mathrm{S}{\mathrm{O}_2} > p\mathrm{C}{\mathrm{H}_4} > p{\mathrm{H}_2}$) is correct because the rate of diffusion is inversely proportional to the square root of the molecular mass. Therefore, the gas with the highest molecular mass will have the lowest diffusion rate and hence the highest partial pressure after 3 hours.

Option B (40) is correct because using Charles's Law, the volume increases proportionally with temperature, and the percentage of air escaped is calculated based on the change in volume.

The correct answer is A (Due to the presence of ${\mathrm{H}^ + }$ and ${\mathrm{OH}^ - }$ions in water) because the high boiling point of water is primarily due to hydrogen bonding between water molecules.

Option B (5 atm) is correct because the partial pressure of a gas in a mixture is equal to its mole fraction multiplied by the total pressure. Since the mole fraction of Helium is 0.5, its partial pressure is 5 atm.

Option B (40) is correct because using Charles's Law, the volume increases proportionally with temperature, and the percentage of air escaped is calculated based on the change in volume.

Option A (3.5 cm/s) is correct because the average speed is calculated by summing the speeds and dividing by the number of particles.

Option A (4f / (e * sqrt(pi))) is correct because it represents the fraction of molecules within the specified speed range, derived from the Maxwell-Boltzmann distribution.