States of matter practice · Medium

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 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 C ($0.985 \mathrm{~atm}$) is correct because it is calculated using the ideal gas law with the total number of moles of gas.

Option A is correct because a pressure cooker increases the boiling point of water, allowing food to cook at a higher temperature and thus reducing cooking time.

Option A (0.8) is correct because the compressibility factor is calculated using the van der Waals equation, considering the given parameters.

Option B is correct because, according to the kinetic molecular theory, lighter gas molecules have a higher average speed at the same temperature.

Option C is correct because NO and O2 react to form NO2, thus Dalton's law is not applicable to the mixture.

Option A (1.4) is correct because the average velocity is proportional to the square root of the temperature, so doubling the temperature increases the average velocity by a factor of $\sqrt{2} \approx 1.4$.

Option B ($2.7 \times 10^{10}$) is correct because it is the number of oxygen molecules calculated using the ideal gas law and Avogadro's number.

Option C (Inversion temperature) is correct because the Joule-Thomson coefficient is zero at the inversion temperature, indicating no temperature change upon expansion.

Option B ($C{H_3} - O - C{H_3} < {C_2}{H_5}OH < {H_2}O$) is correct because the strength of intermolecular forces increases with hydrogen bonding, which is strongest in water due to having two H atoms.

Option C ($100 \text{{ m/s}}$) is correct because the root mean square speed is calculated using the formula $v_{rms} = \sqrt{\frac{{3P}}{{d}}}$, where P is pressure and d is density.

Option C (Remain unchanged in size) is correct because N2O and CO2 have nearly the same molar mass, resulting in similar diffusion rates under the same conditions.

Option A ($1.128$) is correct because the ratio of average velocity to most probable velocity is approximately 1.128.

Option A ($18 \mathrm{~K}$) is correct because it is calculated using the formula $T_b = \frac{a}{Rb}$ with the given van der Waals constants.

Option C ($2u$) is correct because when the temperature is doubled and the diatomic molecule dissociates, the new RMS speed becomes twice the original RMS speed.

The correct answer is C because the compressibility factor (Z) can be greater than 1 for non-ideal gases, but non-ideal gases do not always exert higher pressure than expected.

Option A (6.5) is correct because it is the value of the van der Waals constant 'a' calculated using the given parameters in the van der Waals equation.

Option D ($\mathrm{C}{\mathrm{O}_2} > S{\mathrm{O}_2} > S{\mathrm{O}_3} > PC{\mathrm{l}_3}$) is correct because the rate of diffusion is inversely proportional to the square root of the molecular weight.

Option D (If both the Assertion and Reason are incorrect) is correct because ice melts slower at high altitude due to lower atmospheric pressure, which decreases the melting point.

Option B ($0.5 \mathrm{~atm}$) is correct because the partial pressure of nitrogen is half of the total pressure when equal moles of CO and N2 are present.

The correct answer is B because both statements are correct, but the inertness of helium doesn't explain its positive deviation from ideal behavior, which is due to its small size and weak intermolecular forces.

The correct answer is A (250 K) because the initial temperature is calculated using the relationship between pressure and temperature for a gas at constant volume.

Option C (Increase four fold) is correct because using the ideal gas law, when temperature doubles and pressure is halved, the volume increases by a factor of four.

Option B ($0.007\, \mathrm{~kg}\, \mathrm{~m}^{-3}$) is correct because it represents the difference in density between dry air and moist air calculated considering the partial pressure of water vapor.

Option A (If both assertion and reason are true and the reason is the correct explanation of the assertion) is correct because gases combine in simple ratios when they behave ideally, and deviations from ideal behavior explain why this isn't always the case.

Option D ($Z=\frac{p V_m}{R T}=1-\frac{a}{R T V_m}$) is correct because it represents the van der Waals equation at low pressure, where the volume is large and the 'b' term can be neglected.

Option D (Dipole-dipole interaction) is correct because the dipole-dipole interaction energy is inversely proportional to the cube of the distance between the molecules.