Gaseous State And Gas Laws MCQ Quiz - Objective Question with Answer for Gaseous State And Gas Laws - Download Free PDF

CONCEPT:

Avogadro's Law

• Avogadro's law states that equal volumes of all gases, at the same temperature and pressure, have the same number of molecules.
• The law is often stated mathematically as:

  V ∝ n

  where V is the volume of the gas, and n is the number of moles of the gas.

EXPLANATION:

• Avogadro's law is valid for ideal gases.
• In the context of real gases, Avogadro's law is an approximation that holds true under conditions of low pressure and high temperature where the gas behaves more ideally.
• Van der Waals gases are real gases that have been corrected for intermolecular forces and molecular volumes, and while Avogadro's law can be applied, the deviations from ideal behavior must be taken into account.

Therefore, the correct option is: 2) ideal gas

CONCEPT:

Root Mean Square Speed (Crms) and Most Probable Speed (Cmp)

• The root mean square (r.m.s) speed (Crms) of a gas is given by the formula:

  Crms = √(3kT/m)

• The most probable speed (Cmp) of a gas is given by the formula:

  Cmp = √(2kT/m)

• Here, k is the Boltzmann constant, T is the temperature, and m is the mass of the gas molecule.

EXPLANATION:

• Given:
  • (Crms)H2 at 150 K
  • We need to find the temperature at which (Cmp)He = 1/2 (Crms)H2
• Using the formulas for r.m.s speed and most probable speed:
  • (Crms)H2 = √(3k * 150 / m_H2)
  • (Cmp)He = √(2kT / m_He)
• Given (Cmp)He = 1/2 (Crms)H2, we have:
  • √(2kT / m_He) = 1/2 * √(3k * 150 / m_H2)
  • Squaring both sides:

    2kT / m_He = 1/4 * 3k * 150 / m_H2

  • Solving for T:

    T = (3/8) * (150 * m_He / m_H2)

• Since the molar mass of H2 is 2 g/mol and that of He is 4 g/mol:
  • T = (3/8) * 150 * (4 / 2)
  • T = (3/8) * 150 * 2
  • T = 112.5 K

Therefore, the temperature at which the most probable speed of helium will be half of the r.m.s speed of H2 at 150 K is 112.5 K.

CONCEPT:

Thermodynamic Properties of Gases and Liquids

• The critical point is a state in the phase diagram of substances beyond which the gas and liquid phases are indistinguishable.
• In thermodynamics, the compressibility factor (z) is used to determine how much a real gas deviates from ideal gas behavior. Below the critical point, gases can be liquefied by applying pressure.
• The equation P(V - b) = RT describes the behavior of gases, where P is the pressure, V is the volume, b is the volume occupied by the gas molecules, R is the gas constant, and T is the temperature.

EXPLANATION:

• Statement (A): For solid and liquid, the heat capacity at constant pressure (C_P) is almost equal to that at constant volume (C_V). This is because for solid and liquid states, the volume changes are negligible and do not significantly affect the heat capacity.
• Statement (B): The gas following the equation P(V - b) = RT is described by the Van der Waals equation for real gases. Below the critical temperature, gases can indeed be liquefied by increasing pressure, contrary to the statement's claim. Thus, this statement is incorrect.
• Statement (C): The total energy of an ideal gas molecule consists of its kinetic energy, as ideal gas theory assumes that potential energy and interactions between molecules are neglected.
• Statement (D): Below the critical temperature, the compressibility factor z is less than 1. This is because gases behave non-ideally as they approach the liquid state, and intermolecular forces become more significant. Thus, z < 1 below the critical point. Therefore, this statement is incorrect.

Therefore, the incorrect statements are (B) and (D).

Concept:

• Matter is anything that has mass and volume.
• There are 3 types of matter-
  • Solid- The matter in which the particles are closely paced together.
  • Liquid - The matter in which the particles are less closely packed than solid and more than gas.
  • Gases - In this state of matter, the constituent particles are free for random movement in all directions.

Explanation:

• The intermolecular forces of attraction are strong in solid because the constituent particles are closely packed. So, the shape and size of the solids do not easily change.
• In liquid, the intermolecular forces of attraction in between the molecules are weaker than in solid because the constituent particles are less closely packed. So, the shape and size of the liquids are easily changed.
• The shape of the liquid can be changed easily but the volume of a given mass of liquid is not easy to change and it takes a lot of effort to change the density of the liquid.

Thus, the correct statements are 1, 2, and 4.

Important Points

CONCEPT:

Ideal Gas Law and Density

• The ideal gas law relates the pressure, volume, temperature, and number of moles of a gas. It is given by the equation:

  PV = nRT

• Density (ρ) of a gas can be related to the ideal gas law by:

  ρ = (PM) / (RT)

  where P is the pressure, M is the molar mass, R is the gas constant, and T is the temperature in Kelvin.

EXPLANATION:

• Given that the density of O₂ is 16 at NTP (Normal Temperature and Pressure), we need to find the temperature at which its density will be 14, assuming pressure remains constant.
• At NTP, T₁ = 273.15 K (0°C), and ρ₁ = 16.
• We need to find T₂ when ρ₂ = 14.
• Using the density relation ρ = (PM) / (RT), we can write:

  ρ₁ / ρ₂ = T₂ / T₁

• Substituting the values:

  16 / 14 = T₂ / 273.15

• Simplifying for T₂:

  T₂ = (16 / 14) * 273.15

  T₂ ≈ 312.6 K

• Converting T₂ to Celsius:

  T₂ - 273.15 ≈ 39.45°C

Therefore, the temperature at which the density of O₂ will be 14, assuming constant pressure, is approximately 39°C. 

The correct answer is Ammonia.

Key Points

• Vapour density for ammonia is 8.5 while for chlorine is 35.5, HCl is 18.25 and oxygen is 16. Hence option c is correct

Important Points

• The molecular weight of carbon dioxide is 44. The molecular weight of carbon dioxide is more than the molecular weight of nitrogen. Hence option A is Incorrect.
• The molecular weight of the chlorine molecule is 71. The molecular weight of the chlorine is more than the molecular weight of the nitrogen. Hence option D is incorrect.
• The molecular weight of the oxygen molecule is 32. The molecular weight of oxygen is more than the molecular weight of nitrogen. Hence option B is Incorrect.
• Additional Information
• The molecular weight of the Hydrogen molecule is 2. The molecular weight of hydrogen is less than the molecular weight of nitrogen.
•  hydrogen gas is a lighter gas than air. We should calculate the molecular weight of the compounds to know whether they are lighter than the air or heavier than the air. The molecular weight of some elements is as follows. The Atomic weight of the hydrogen is 1.

The correct answer is Low compressibility 

Key Points

• Gases exert pressure equally in all directions. 
• The gas particles have a very weak attractive force between them and move randomly ultimately exerting pressure in all directions.
• The gaseous state of matter occurs between the liquid and plasma states. 
• Gases that contain permanently charged ions are known as plasmas.

Additional Information

• In a gas, particles are in continual straight-line motion. 
• The kinetic energy of the molecule is greater than the attractive force between them, thus they are much farther apart and move freely from each other, hence volume is Not fixed.
• Compared to the other states of matter, gases have low density and viscosity.

The correct answer is Random

Explanation:-

• Each molecule or atom in a gaseous sample behaves independently of the others. Therefore, they are equally likely to travel in any direction at any given time, making their motion random.
• Gas particles are in constant motion and share a large number of rapid, elastic collisions. These collisions are perfectly efficient, meaning they don't lose kinetic energy.
• Kinetic theory of gases assumes randomness: According to the kinetic theory of gases, the motion of gas particles is random, with their direction and speed constantly changing due to collisions with other particles and the container walls.
• The intermolecular space in gases is much larger than in solids or liquids. This property gives gas molecules freedom to move randomly without a fixed path.
• The speed at which gas particles move is influenced by temperature and pressure. Higher temperature means more kinetic energy and faster, more random motion. Inversely, higher pressure can hinder their movement, but not the random nature of it.
• No significant intermolecular forces: Unlike in liquids and solids, intermolecular attractive forces in gases are negligible because particles are far apart from each other. Therefore, they are free to move in a random manner.
• 

Conclusion:-

So, The motion between the particles in a gaseous substance is Random

The correct answer is option 2) i.e. At constant volume, the pressure of a fixed amount of gas varies directly with temperature.

• In 1809, Joseph Louis Gay- Lussac gave the Gay-Lussac's law or the pressure law also known as Amontons' Law.
• According to this law, at constant volume, the pressure of a fixed amount of gas varies directly with temperature.
• Mathematically it can be represented as P/T = Constant, where P = Pressure and T = Temperature. 

​Note:

• At constant temperature, the pressure of a fixed amount (i.e., number of moles n) of gas varies inversely with its volume. This is known as Boyle’s law.
• We can write it as PV = k (where k is a constant) or  P = k / V.
• At constant pressure, the volume of a fixed mass of gas is directly proportional to its absolute temperature. This is known as Charles's law.
• We can write it as V/T = k (where k is a constant) or V = kT.

The correct answer is Both 1 and 2.

Explanation:

• The rate of diffusion of liquids is higher than that of solids. This is due to the fact that particles in the liquid state move freely and have greater space between each other than particles in the solid-state. Hence, statement 1 is true.
• Solids have a definite shape, distinct boundaries, and fixed volumes, implying that their compressibility is negligible.  
• Because there is no space between the particles in a solid, no compression is possible.
• Gases are highly compressible as compared to solids and liquids.
• Gases are compressible because their intermolecular space is large, whereas liquids are not compressible because their intermolecular space is small. Hence, statement 2 is true.

So both statements are correct.

Statement I :

• When air is heated, the molecules will start to vibrate and bump into each other Because each molecule uses more space for motion, the air expands and becomes less dense.
• Therefore, the air expands when heated.
• Statement I is true

Statement II :

• When air is heated air becomes warm. This warm air rises and when it rises it becomes cooler and settle down.
• Warm air rises because it became lighter while cool air became heavier and settle down.
• Therefore the warm air is lighter than the cold air.
• Statement II is wrong.

Hence, we conclude that Only I statement is true.

CONCEPT:

EXPLANATION:

• The statement of the question implies the Gay-Lussac law.
• According to the Gay-Lussac law, pressure is directly proportional to the temperature.
• As the temperature increase, the average kinetic energy of molecules increases, and pressure also increase.

CONCLUSION:

Therefore, the pressure increases as we increase the temperature.

The correct answer is diffusion.

Concept:

• Non-reacting gases are the ones that do not undergo molecular rearrangement or alteration easily.
• Non-reacting gases are also known as inert gases.
• Some examples of non-reacting gases are N₂ gas, He gas, Argon gas, etc.
• Group 18 elements due to their nin reacting tendency, are also known as noble gases or inert gases.

Explanation:

• .The non-reacting gases can be made to react by adopting a method called diffusion.

• In this method, the gases are passaged through an atmosphere of high concentration to a low concentration, under high pressure.

• Mixing of non-reacting gases is associated with an increase in randomness and entropy.

Additional Information

The answer is None of these.

Explanation:-

• Thermal energy refers to the energy contained within a system that is responsible for its temperature.
• Heat is the flow of thermal energy.
• A whole branch of physics, thermodynamics, deals with how heat is transferred between different systems and how work is done in the process 
• So, Thermal energy is not equal to the temperature of 1 Kelvin of water. Temperature is not the same thing as energy. Temperature is a measure of the average kinetic energy of the particles in a substance or system, whereas thermal energy indicates the total kinetic and potential energy of the particles in that system. While they are related, a temperature of 1 Kelvin does not give you information about the total thermal energy present, as energy calculations also consider factors like volume and type of substance.
• Thermal energy is not equal to 100 °C.
  This option is incorrect for reasons similar to the first one. 100 °C refers to a temperature, not an energy value. An object at 100 °C will have more thermal energy than the same object at a lower temperature, but the thermal energy of a substance is not dependent solely on its temperature. It also relies on the mass of the substance and its specific heat capacity.
• Thermal energy is not equal to the latent heat of vaporization absorbed by the body.
  The latent heat of vaporization refers to the amount of heat absorbed or released by a substance during the change of state from a liquid to a gas or vice versa at a constant temperature. While this process involves thermal energy, it is not synonymous with thermal energy, which includes all kinetic and potential energy of all the particles in a system.

Conclusion:-

So, the answer is None of These

NOTE:-  According to official answer key the answer is option 3 but according to question statement the answer will be option 4

Concept:

• Boiling point: It is the temperature at which vapour pressure of liquid is equal to the external atmospheric pressure. 
• As we move higher in the altitude, pressure of the air decreases. 
   

Explanation: 

• At the sea level, there are more number of particles of the air in the atmosphere.
• As we move higher, this numbers of air particles decrease, and air become less denser.
• As density of air decreases, pressure exerted by air is also decreases.
• So, when we boil water at higher altitude, it starts to boil at lower temperature than 100^oC.
• At lower altitudes water boils at 100^oC, and as pressure decreases, boiling point of the water also decreases.
• Since water is boiling at lower temperature, it gets converted into vapour easily at higher altitudes than lower altitudes. Therefore, less water will be available for the cooking of the food. Therefore, food will take longer time to cook.
   

Conclusion:

• Therefore, food takes longer time to cook in higher altitude regions like Shimla.