Question 1

A sample of gas has a volume of 300 cc at 27°C under a pressure of 620 mm. What will its volume be at 47°C and 640 mm pressure?

Accepted Answer

310 cc. The correct option is derived from applying the combined gas law, which states that the volume of a gas is directly proportional to its temperature and inversely proportional to its pressure. By substituting the initial and final conditions into the equation, the calculations yield a final volume of 310 cc.

Question 2

When the temperature of neon is increased from 20°C to 40°C, by what factor does the mean kinetic energy of its atoms change?

Accepted Answer

313/293. Mean kinetic energy = (3/2)kT scales linearly with absolute T, so the factor is 313/293 (40C=313K, 20C=293K), not the square root of it.

Question 3

Which gas is expected to show the greatest departure from ideal-gas behavior?

Accepted Answer

NH₃(g). Ammonia (NH₃) exhibits strong hydrogen bonding and has a relatively high molecular weight compared to the other gases listed, leading to significant intermolecular forces that cause it to deviate more from ideal gas behavior.

Question 4

Equal amounts (in moles) of hydrogen gas and oxygen gas are kept in a vessel that has a tiny pinhole, allowing both gases to effuse out. By the time one-half of the hydrogen has escaped, what fraction of the oxygen has escaped?

Accepted Answer

1/8. Rate ratio = sqrt(32/2) = 4, so when half (0.5) of H2 has escaped, the fraction of O2 escaped is 0.5/4 = 1/8, not 1/4.

Question 5

Which of the following statements is incorrect regarding how raising the temperature affects the distribution of molecular speeds in a gas?

Accepted Answer

The proportion of molecules having the most probable speed increases. As temperature increases, the distribution of molecular speeds broadens, leading to a decrease in the proportion of molecules at the most probable speed, rather than an increase. This is because higher temperatures result in a greater variety of speeds among the molecules.

Question 6

As stated by the kinetic theory of gases, how does an ideal gas molecule move during the interval between two consecutive collisions?

Accepted Answer

Along a straight-line trajectory. According to the kinetic theory of gases, ideal gas molecules move in straight lines between collisions, as they are assumed to have no interactions except during these brief collisions.

Question 7

For 1 mole of an ideal gas maintained at a fixed temperature T, what is the nature of the graph between log(P) and log(V), where P denotes pressure and V denotes volume?

Accepted Answer

A straight line having a negative slope. The relationship between pressure and volume for an ideal gas at constant temperature is described by Boyle's Law, which states that pressure is inversely proportional to volume. When both pressure and volume are expressed in logarithmic form, this inverse relationship results in a straight line with a negative slope on a log-log graph.

Question 8

In the gaseous state, let the most probable speed be represented by C*, the mean speed by C̅, and the root mean square speed by C. For a very large number of molecules, what is the correct ratio among these speeds?

Accepted Answer

C*: C̅: C = 1: 1.128: 1.225. C* : Cbar : Crms = sqrt2 : sqrt(8/pi) : sqrt3 = 1 : 1.128 : 1.225 (most probable smallest, rms largest). The stored ratio is reversed.

Question 9

When concentrated hydrochloric acid is left exposed to the atmosphere, it may give off a white fuming cloud. This happens because

Accepted Answer

HCl gas has a strong attraction for moisture in air, causing tiny droplets of acid solution to form and look like white smoke. Concentrated HCl gives off HCl gas, which is strongly hygroscopic. The gas attracts water vapour from the air to form tiny droplets of hydrochloric acid that appear as white fumes.

Question 10

Which of the following is employed to generate and maintain strong superconducting magnets, which are an essential component of an NMR spectrometer?

Accepted Answer

Helium. Helium is used in superconducting magnets because it remains in a liquid state at very low temperatures, which is necessary to achieve and maintain the superconducting state required for optimal performance in NMR spectrometers.

Question 11

What is the numerical value of the universal gas constant R?

Accepted Answer

8.3 J mol⁻¹ K⁻¹. The universal gas constant R is defined as 8.314 J mol⁻¹ K⁻¹, which is commonly rounded to 8.3 J mol⁻¹ K⁻¹ for simplicity in calculations, making option C the correct choice.

Question 12

The kinetic theory of gases is able to explain which of the following gas laws?

Accepted Answer

All of these laws. The kinetic theory of gases provides a molecular-level understanding of gas behavior, which encompasses the relationships described by Boyle's law, Charles' law, and Avogadro's law, thus explaining all of these laws collectively.

Question 13

As stated by the kinetic theory of gases, how does a molecule of an ideal gas move during the interval between two consecutive collisions?

Accepted Answer

Along a straight-line path. According to the kinetic theory of gases, molecules of an ideal gas move in straight lines between collisions, as they are considered to have no interactions except during these brief collisions.

Question 14

When the temperature is increased from 20°C to 40°C, by what factor does the average kinetic energy of neon atoms change?

Accepted Answer

313/293. The average kinetic energy of gas particles is directly proportional to the absolute temperature in Kelvin. By converting the given temperatures to Kelvin (293 K and 313 K), the ratio of the average kinetic energies is calculated as 313/293.

Question 15

In the van der Waals equation of state for a gas, the constant 'b' represents the measure of

Accepted Answer

the space occupied by the gas molecules. The constant 'b' in the van der Waals equation accounts for the volume occupied by the gas molecules themselves, reflecting the finite size of the particles and thus adjusting the ideal gas behavior to more accurately represent real gases.

Question 16

Which of the following statements is incorrect regarding how raising the temperature affects the distribution of molecular speeds in a gas?

Accepted Answer

The proportion of molecules having the most probable speed increases. As temperature increases, the distribution of molecular speeds broadens, meaning that while the most probable speed increases, the proportion of molecules at that speed actually decreases. Therefore, option C is incorrect.

Question 17

A volume of 10⁻⁴ dm³ of liquid water is placed in a 1.0 dm³ container and kept at 300 K. At equilibrium, how many moles of water will be present in the vapour phase? (Given: vapour pressure of H2O at 300 K = 3170 Pa; R = 8.314 J K⁻¹ mol⁻¹)

Accepted Answer

1.27 × 10⁻³ mol. The correct option is derived from applying the ideal gas law to the vapor pressure of water at the given temperature, which allows us to calculate the number of moles of water vapor that can exist in the container at equilibrium. By using the vapor pressure and the volume of the container, we find that the moles of water in the vapor phase is 1.27 × 10⁻³ mol.

Question 18

If r, P, and M denote the diffusion rate, pressure, and molecular mass respectively, then the ratio of diffusion rates of two gases A and B, rA/rB, is expressed as:

Accepted Answer

(P_A/P_B)(M_B/M_A)^(1/2). The correct option is derived from Graham's law of effusion, which states that the rate of diffusion of a gas is inversely proportional to the square root of its molecular mass and directly proportional to its pressure. Therefore, the ratio of diffusion rates incorporates both the pressure ratio and the inverse square root of the molecular mass ratio.

Question 19

For a gas, its molecular speed varies with temperature as:

Accepted Answer

directly proportional to the square root of temperature.. Molecular speeds (rms, average, most probable) all scale as v ~ sqrt(3RT/M), i.e. directly proportional to the square root of absolute temperature.

Question 20

The compressibility factor for a real gas at high pressure is:

Accepted Answer

1 + Pb/RT. At high pressure the molecular-volume term of the van der Waals equation dominates, giving Z = PV/RT = 1 + Pb/RT, i.e. Z > 1.

Question 21

For gaseous state, if most probable speed is denoted by C*, average speed by C̄ and mean square speed by C, then for a large number of molecules the ratios of these speeds are:

Accepted Answer

C*: C̄: C = 1: 1.128: 1.225. The correct option reflects the established relationships between the most probable speed, average speed, and mean square speed of gas molecules, where the most probable speed is the lowest, followed by the average speed, and the mean square speed is the highest, consistent with kinetic theory.

Question 22

If Z is a compressibility factor, van der Waals equation at low pressure can be written as:

Accepted Answer

Z = 1 - a/VRT. At low pressure the volume is large so b is negligible and the a/V^2 term dominates the deviation, giving Z = 1 - a/(VRT).

Question 23

The intermolecular interaction that is dependent on the inverse cube of distance between the molecules is:

Accepted Answer

hydrogen bond. Ion-ion energy varies as 1/r, ion-dipole as 1/r^2, London dispersion as 1/r^6, while dipole-dipole (and hydrogen bonding, which is a strong dipole-dipole interaction) varies as 1/r^3. So the interaction with inverse-cube distance dependence is the hydrogen bond.

Question 24

Two closed bulbs of equal volume (V) containing an ideal gas initially at pressure p1 and temperature T1 are connected through a narrow tube of negligible volume. The temperature of one of the bulbs is then raised to T2. The final pressure p_f is:

Accepted Answer

2p1 (T2/(T1 + T2)). Total moles are conserved: 2 p1 V/(R T1) = pf V/(R T1) + pf V/(R T2). Solving gives pf = 2 p1 T2/(T1 + T2).

Question 25

0.5 moles of gas A and x moles of gas B exert a pressure of 200 Pa in a container of volume 10 m³ at 1000 K. Given R is the gas constant in JK⁻¹ mol⁻¹, x is:

Accepted Answer

(4 - R)/(2R). PV=nRT gives total moles = (200*10)/(R*1000) = 2/R. With 0.5 + x = 2/R, x = 2/R - 0.5 = (4 - R)/(2R).

Question 26

Consider the van der Waals constants, a and b, for the following gases.
Gas: Ar, Ne, Kr, Xe
 a/(atm dm⁶ mol⁻²): 1.3, 0.2, 5.1, 4.1
 b/(10⁻² dm³ mol⁻¹): 3.2, 1.7, 1.5, 0.9
Which gas is expected to have the highest critical temperature?

Accepted Answer

Xe. Critical temperature Tc = 8a/(27Rb), so it scales with a/b. Computing a/b: Ar=0.41, Ne=0.12, Kr=3.4, Xe=4.56. Xe has the largest a/b and thus the highest critical temperature.

Question 27

A pressure cooker shortens the time needed to cook food because

Accepted Answer

the boiling point of water used in cooking gets raised. Inside a sealed cooker the increased pressure raises the boiling point of water above 100 C, so cooking proceeds at a higher temperature and finishes faster.

Question 28

Concentrated hydrochloric acid when kept in open air, sometimes produces a cloud of white fumes. The explanation for it is that

Accepted Answer

strong affinity of HCl gas for moisture in air results in forming of droplets of liquid solution which appears like a cloudy smoke.. Concentrated HCl is volatile; the escaping HCl gas has a strong affinity for water vapour in the air and condenses it into tiny droplets of hydrochloric acid solution, which appear as white fumes. No oxidation to chlorine occurs.

Question 29

For gaseous state, if most probable speed is denoted by C*, average speed by C̄ and mean square speed by C, then for a large number of molecules the ratios of these speeds are -

Accepted Answer

C*: C̄: C = 1: 1.128: 1.225. The correct option reflects the established relationships between the most probable speed, average speed, and mean square speed of gas molecules, where the most probable speed is the lowest, followed by the average speed, and the mean square speed is the highest, consistent with kinetic theory.

Question 30

If Z is a compressibility factor, Vander Waals equation at low pressure can be written as:

Accepted Answer

Z = 1 − a / VRT. The correct option reflects how the compressibility factor Z deviates from ideal gas behavior due to intermolecular forces, specifically accounting for the attractive forces represented by the parameter 'a' in the Van der Waals equation, which becomes significant at low pressures.

Question 31

The intermolecular interaction that is dependent on the inverse cube of distance between the molecules is:

Accepted Answer

Ion - dipole interaction. Ion-dipole interactions arise from the electrostatic attraction between an ion and a polar molecule, and their strength decreases with the cube of the distance between them, making this relationship distinct from other types of intermolecular forces.

Question 32

A mixture of one mole each of H2, He and O2 each are enclosed in a cylinder of volume V at temperature T. If the partial pressure of H2 is 2 atm, the total pressure of the gases in the cylinder is -

Accepted Answer

6 atm. With one mole each, all partial pressures are equal; since p(H2) = 2 atm, total = 3 x 2 = 6 atm.

Question 33

An empty LPG cylinder weighs 14.8 kg. When full, it weighs 29.0 kg and shows a pressure of 3.47 atm. In the course of use at ambient temperature, the mass of the cylinder is reduced to 23.0 kg. The final pressure inside of the cylinder is ____ atm. (Nearest integer) (Assume LPG to be an id

Accepted Answer

2. The pressure of an ideal gas is directly proportional to its mass when temperature and volume are constant. Since the mass of the LPG in the cylinder decreases from 14.2 kg (29.0 kg - 14.8 kg) to 8.2 kg (23.0 kg - 14.8 kg), the pressure also decreases proportionally, leading to a final pressure of approximately 2 atm.

Question 34

Two small drops of mercury each of radius R coalesce to form a single large drop. The ratio of total surface energy before and after the change is:

Accepted Answer

2^(1/3): 1. Volume conservation gives R' = 2^(1/3) R. Surface energy is proportional to area (r^2). Before/after = (2*4piR^2)/(4pi*2^(2/3)R^2) = 2/2^(2/3) = 2^(1/3). So the ratio is 2^(1/3):1.

Question 35

The water having more dissolved O2 is:

Accepted Answer

water at 4°C. Dissolved oxygen increases as water temperature decreases, so water at 4 degC holds more dissolved O2 than warm, boiling, or polluted water.

Question 36

The interaction energy of London forces between two particles is proportional to r−x, where r is the distance between the particles. The value of x is:
(1) 3 (2) −3 (3) −6 (4) 6

Accepted Answer

6. The instantaneous-dipole induced-dipole (London) interaction energy is proportional to 1/r^6 = r^-6, so the exponent x in r^-x is 6.

Question 37

The unit of the van der Waals gas equation parameter 'a' in (P + a n²/V²)(V - nb) = nRT is:

Accepted Answer

atm dm⁶ mol⁻². The parameter 'a' in the van der Waals equation accounts for the attractive forces between gas molecules, and its units must reflect pressure multiplied by volume squared per mole squared. Therefore, the correct unit is atm dm⁶ mol⁻², which aligns with the dimensional analysis of the equation.

Question 38

A rigid nitrogen tank stored inside a laboratory has a pressure of 30 atm at 06:00 am when the temperature is 27°C. At 03:00 pm, when the temperature is 45°C, the pressure in the tank will be ______ atm. [nearest integer]

Accepted Answer

32.00. The pressure of a gas is directly proportional to its temperature when the volume is constant, according to Gay-Lussac's law. As the temperature increases from 27°C to 45°C, the pressure also increases, resulting in a calculated pressure of approximately 32 atm.

Question 39

Decreasing order of the hydrogen bonding in following forms of water is correctly represented by
A. Liquid water
B. Ice
C. Impure water
Choose the correct answer from the options given below:

Accepted Answer

B > A > C. Ice has a structured lattice that maximizes hydrogen bonding, making it the strongest in terms of hydrogen bonds. Liquid water has a high degree of hydrogen bonding but is less structured than ice, while impure water has fewer hydrogen bonds due to the presence of solutes, resulting in the weakest hydrogen bonding.

Question 40

Arrange the following gases in increasing order of van der Waals constant ‘a’:
(A) Ar
(B) CH4
(C) H2O
(D) C6H6
Choose the correct option from the following.

Accepted Answer

A, B, C and D. The van der Waals constant 'a' reflects the strength of intermolecular forces; noble gases like Ar have weak interactions, while polar molecules like H2O have stronger forces, leading to a higher 'a' value. Thus, the order from lowest to highest 'a' is Ar, CH4, H2O, and C6H6.

Question 41

A big drop is formed by coalescing 1000 small identical drops of water. If E1 be the total surface energy of 1000 small drops of water and E2 be the surface energy of single big drop of water, then E1: E2 is x: 1 where x = _____.

Accepted Answer

10. The surface energy of a drop is proportional to its surface area, which scales with the square of the radius. When 1000 small drops coalesce into one larger drop, the total surface area decreases, leading to a reduction in surface energy. Specifically, the ratio of the surface energy of the small drops to that of the big drop is 10:1, as the surface area of the big drop is 10 times that of each small drop.

Question 42

If the collision frequency of hydrogen molecules in a closed chamber at 27°C is Z, then the collision frequency of the same system at 127° C is:

Accepted Answer

2/√3 Z. The collision frequency of gas molecules is proportional to the square root of the temperature in Kelvin. By converting the temperatures from Celsius to Kelvin and applying the formula, we find that the collision frequency at 127°C is 2/√3 times that at 27°C.

Question 43

Ice and water are placed in a closed container at a pressure of 1 atm and temperature 273.15 K. If pressure of the system is increased 2 times, keeping temperature constant, then identify correct observation from following:
(1) Volume of system increases.
(2) Liquid phase disappears comple

Accepted Answer

(4). Increasing the pressure while keeping the temperature constant will favor the liquid phase over the solid phase in a system containing ice and water. At 273.15 K, the solid phase (ice) will disappear completely as the pressure increases, leading to a complete transition to the liquid phase.

Question 44

Given below are two statements:
Statement I: When a system containing ice in equilibrium with water (liquid) is heated, heat is absorbed by the system and there is no change in the temperature of the system until whole ice gets melted.
Statement II: At melting point of ice, there is absorp

Accepted Answer

Both Statement I and Statement II are true. Both statements accurately describe the process of melting ice; heat is absorbed without a temperature change until all ice melts, and during melting, energy is used to overcome intermolecular forces, not to increase kinetic energy.

Question 45

Given below are two statements:
Statement-I: Sublimation is used for the separation and purification of compounds with low melting point.
Statement-II: The boiling point of a liquid increases as the external pressure is reduced.
In the light of the above statements, choose the correct answ

Accepted Answer

Both Statement-I and Statement-II are false.. Sublimation is typically used for substances that can transition directly from solid to gas without passing through a liquid phase, often applicable to compounds with low melting points, making Statement-I misleading. Additionally, the boiling point of a liquid actually decreases when external pressure is reduced, contradicting Statement-II.

Question 46

A pressure cooker reduces cooking time for food because

Accepted Answer

boiling point of water involved in cooking is increased. Inside a pressure cooker the increased pressure raises the boiling point of water above 100 C, so food cooks at a higher temperature and therefore faster. The crushing/even-distribution options are not the mechanism.

Question 47

Concentrated hydrochloric acid when kept in open air sometimes produces a cloud of white fumes. The explanation for it is that

Accepted Answer

it reacts with moisture in air to form HCl fumes. Concentrated hydrochloric acid releases hydrogen chloride gas, which readily reacts with moisture in the air to form hydrochloric acid mist, resulting in the visible white fumes.

Question 48

Which one of the following statements is NOT true about the effect of an increase in temperature on the distribution of molecular speeds in a gas?

Accepted Answer

The peak of the distribution curve shifts to lower speeds. Raising temperature increases the most probable speed and broadens/flattens the curve while the area (total fraction) stays 1. The peak shifts to HIGHER speeds, so the statement that it shifts to lower speeds is the false (not true) one.

Question 49

Equal masses of methane and oxygen are mixed in an empty container at 25°C. The fraction of the total pressure exerted by oxygen is

Accepted Answer

1/3. For equal mass m, moles of CH4 = m/16 and O2 = m/32. Mole fraction of O2 = (1/32)/(1/16+1/32) = (1/32)/(3/32) = 1/3, so oxygen exerts 1/3 of the total pressure.

Question 50

'a' and 'b' are van der Waals' constants for gases. Chlorine is more easily liquefied than ethane because

Accepted Answer

a for Cl2 > a for C2H6 but b for Cl2 < b for C2H6. Chlorine has a higher 'a' constant, indicating stronger intermolecular attractions compared to ethane, which facilitates its liquefaction. Meanwhile, a lower 'b' constant for chlorine suggests it occupies less volume per mole, further aiding in its ability to be liquefied.

JEE Main Chemistry: States of Matter questions with solutions

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