States of Matter MCQ Quiz - Objective Question with Answer for States of Matter - Download Free PDF

CONCEPT:

Kinetic Energy in Kinetic Theory of Gases

• The kinetic energy of a gas molecule is derived from the kinetic theory of gases, which states that the energy is proportional to the temperature of the gas.
• For a single molecule in a system, the average kinetic energy per degree of freedom is given as:

  ½ kT

• For a diatomic or monatomic gas, the total kinetic energy depends on the degrees of freedom of the system.
• The most probable kinetic energy is distinct from the average kinetic energy, and for a single molecule, it is:

  kT / 2

• For one mole of gas, the kinetic energy is scaled up by Avogadro’s number (N_A), where k × N_A = R (the universal gas constant). Hence, the most probable kinetic energy for one mole is:

  RT / 2

EXPLANATION:

• Given the options, we need to identify the most probable kinetic energy per molecule and per mole, respectively.
• From the kinetic theory:
  • The most probable kinetic energy per molecule is kT / 2.
  • The most probable kinetic energy per mole is RT / 2, where R = k × N_A.
• Thus, the correct option is: kT / 2 and RT / 2

Therefore, the correct answer is Option 1: kT / 2 and RT / 2.

CONCEPT:

Surface Tension

• Surface tension is the property of a liquid that allows it to resist an external force due to the cohesive nature of its molecules.
• It arises because the molecules at the surface of the liquid experience an imbalance of forces. Molecules at the surface are pulled inward by cohesive forces from neighboring molecules, causing the liquid to behave as though its surface is in a state of tension.
• This phenomenon leads to the contraction of the surface area of the liquid, minimizing the liquid's surface energy.

EXPLANATION:

• The force responsible for the contraction of the surface of a liquid is surface tension.
• While other forces such as vapor pressure and surface energy are related to the behavior of liquids, they do not directly cause the contraction of the surface.
• Surface tension is the key factor that leads to the minimization of the surface area of a liquid, which is why it is responsible for the contraction of the liquid surface.

Therefore, the correct answer is option 2: Surface tension.

CONCEPT:

Boyle Temperature

• The Boyle temperature (T_B) is the temperature at which a real gas behaves like an ideal gas over a range of pressures. At this temperature, the second virial coefficient (B₂) becomes zero.
• The van der Waals equation is given as:

  (P + a/V²)(V − b) = RT

  where a and b are van der Waals constants.

• The Boyle temperature can be derived using the condition for ideal gas behavior. The equation for T_B is:

  T_B = a / (Rb)

• Where:
  • a = van der Waals constant for intermolecular attraction
  • b = van der Waals constant for volume exclusion
  • R = universal gas constant

EXPLANATION:

• In the given problem, the van der Waals constants for CO₂ gas are:
  • a = 4
  • b = 2
• Using the formula for Boyle temperature:

  T_B = a / (Rb)

• Substitute the given values:

  T_B = 4 / (R × 2) = 2 / R

Therefore, the Boyle temperature of CO₂ gas is 2 / R.

CONCEPT:

Van der Waals Equation and Molar Volume

• The Van der Waals equation for real gases is given by:

  (P + a/V²) * (V - b) = RT

  where:
  • P is the pressure,
  • V is the volume,
  • R is the universal gas constant,
  • T is the temperature,
  • a and b are Van der Waals constants that account for intermolecular forces and the finite volume of gas molecules, respectively.
• The ratio of the coefficients of V² to V can be derived from the cubic form of the equation for molar volume (V) of the gas.
• We are given the values for the Van der Waals constants a = 6.0 dm6 atm mol−2 and b = 0.060 dm3 mol−1

EXPLANATION:

• The Van der Waals equation can be rewritten as:

  P + (a/V²) = (RT / (V - b))

• For calculating the ratio of the coefficients of V^2 and V in the cubic equation, we rearrange the equation as:

  P(V - b) + a/V² = RT

• The molar volume of the gas is related to this equation, and the coefficients of V² and V can be derived by comparing terms after expansion of the equation into a cubic form.
• After substituting the given values for the constants:

  a = 6.0, b = 0.060, R = 0.0821 dm³·atm/mol·K, and T = 300 K

• Ratio of coefficient of Vn to Vn:
  (Pb + RT) / a = (300 x 0.06 + 0.082 x 300) / 6
  = -7.1

Calculation:

\({V_{rms}}^{2}=\dfrac{3RT}{M}\)

\(V_{a}:V_{b}:V_{c}=1:\dfrac{1}{\sqrt{2}}:\dfrac{1}{\sqrt{3}}\)

\({V_{A}}^{2}:{V_{B}}^{2}:{V_{C}}^{2}=1:\dfrac{1}{2}:\dfrac{1}{3}\)

\(\dfrac{1}{M_{A}}:\dfrac{1}{M_{B}}:\dfrac{1}{M_{C}}=1:\dfrac{1}{2}:\dfrac{1}{3}\)

\(M_{A}:M_{B}:M_{C}=1:2:3\)

Hence, the correct answer is option 5.

Concept :

• Food is cooked faster in a pressure cooker because due to high pressure the boiling point of water is raised.
• A pressure cooker works on the principle that with rising pressure the boiling point of water increases.
• Due to the high-pressure boiling point of water rises from 100o C to around 120o C.
• So, the steam also becomes hotter and is also trapped inside the cooker resulting in faster cooking of food.
• When cooked in open vessels the hot air escapes.
• But in the pressure cooker moisture surrounding the food itself reaches higher temperatures than it would without the pressure which speeds the cooking.
• So, the cooking speed is increased nearly four times. 

Hence we can conclude that the beans are cooked faster in pressure cooker because boiling point increase with increasing pressure.

The correct answer is Colloidal.

Key Points

• Features of Liquids:
  • Liquids do not have a definite shape.
  • Liquids have fixed volumes.
  • They can change their shape.
  • Their intermolecular force of attraction is less than solids.
  • The kinetic energy of its particles is more than solids.
• Features of Gaseous: 
  • They can take any shape.
  • Gases neither have a definite shape nor have a fixed volume.
  • Their intermolecular force of attraction is least.
  • The kinetic energy of its particles is maximum.
• Features of Solids:
  •  Solids have fixed volumes.
  • Solids have a definite shape and distinct boundaries.
  • Negligible compressibility.
  • Their intermolecular force of attraction is maximum.
  • The kinetic energy of its particles is minimum.

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 It depends on the room temperature.

Key Points

• The boiling point of a liquid depends on: 
  • the temperature, not the room temperature.
  • the atmospheric pressure,
  • It depends on the nature and purity of the liquid.
  • the vapor pressure of the liquid. 
• The normal boiling point is the temperature at which the vapor pressure is equal to the standard sea-level atmospheric pressure, at sea level, water boils at 100° C (212° F).

CONCEPT:

Surface tension: 

• Surface tension is the tension of the surface film of a liquid caused due to the attraction of the particles in the surface layer by the bulk of the liquid, which tends to minimize surface area.
• It is defined as the ratio of the surface force F to the length L along which the force acts.

​\(\Rightarrow T=\frac{F}{l}\)

Where T = surface tension

• When impurities are added to the water the intermolecular distance increases due to which van der wall forces decrease, so the surface tension decreases on adding impurities to the water.

EXPLANATION:

• Surface tension is given as,

\(\Rightarrow T=\frac{F}{l}\)     -----(1)

• By equation 1 it is clear that the surface tension does not depend on the area.
• Surface tension decreases with the increase in temperature.
• The decrease of surface tension with an increase in temperature results because of the kinetic energy (or speeds) of the molecules increases. Thus, the strength of intermolecular forces decreases resulting in the decrease of the surface tension.
• Hence, option 4 is correct.

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 rate of evaporation depends on temperature, the presence of wind, the humidity of the surrounding, and the surface area of the liquid exposed to the atmosphere. It doesn't depend on the mass of the liquid.

• The larger the surface area, the more would be the rate of evaporation.
• The higher the humidity, the slower would be the rate of evaporation.
• The higher the presence of wind, the faster would be the rate of evaporation.
• The higher the temperature, the faster would be the rate of evaporation.

CONCEPT:

Vander-Waals equation

• The equation is basically a modified version of the Ideal Gas Law which states that gases consist of point masses that undergo perfectly elastic collisions.
  • However, this law fails to explain the behavior of real gases. Therefore, the Van der Waals equation was devised and it helps us define the physical state of a real gas.
  • Van der Waals equation is an equation relating the relationship between the pressure, volume, temperature, and amount of real gases. For a real gas containing ‘n’ moles, the equation is written as,

​\(\Rightarrow \left ( P+\frac{an^{2}}{V^{2}} \right )\left ( V-nb \right )=nRT\)     -----(1)

Where P, V, T, n are the pressure, volume, temperature, and moles of the gas and  ‘a’ and ‘b’ constants specific to each gas

Rearranging the above equation, we get 

\(P = \dfrac{nRT}{V-nb} - \dfrac{n^2 a}{V^2}\)

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

Explanation:

States of Matter and Phase Change: Substances change their states/phases with the change in temperature.

Several processes of phase change:

• Melting: It occurs when a substance changes from a solid to a liquid.
• ​Vaporization: It occurs when a substance changes from a liquid to a gas. 
• Condensation: It occurs when a substance changes from a vapor to a liquid.
• Sublimation: It occurs when a substance changes from a solid into a gas.
• Deposition: It occurs when a substance converts directly from its gaseous state to a solid state.
• Fusion: It implies the conversion from solid-state to liquid (melting) as well as from liquid-state to solid-state (freezing).

Additional Information

• Evaporation vs Vaporization: Evaporation is a specific type of vaporization, where phase change (liquid-> gas) occurs only at the surface of the liquid. 
• Common examples of Sublimation
  • Dry ice (a frozen form of carbon dioxide)
  • Naphthalene (organic compound).