Question 1

Q1. What will be the minimum pressure required to compress 500 dm³ of air at 1 bar to 200 dm³ at 30 °C?

Accepted Answer

To compress 500 dm³ of air at 1 bar to 200 dm³ at a constant temperature of 30 °C, the minimum pressure required will be 2.5 bar.

Question 2

Q2. A vessel of 120 mL capacity contains a certain amount of gas at 35 °C and 1.2 bar pressure. The gas is transferred to another vessel of volume 180 mL at 35 °C. What would be its pr

Accepted Answer

When the gas is transferred to another vessel of 180 mL capacity at the same temperature, its pressure would be 0.8 bar.

Question 3

Q3. Using the equation of state pV = nRT; show that at a given temperature density of a gas is proportional to the gas pressure p.

Accepted Answer

To show that at a given temperature, the density of a gas is proportional to its pressure, we start with the ideal gas equation and substitute the definition of moles and density.

Question 4

Q4. At 0 °C, the density of a certain oxide of a gas is 4.4 g L⁻¹ at 2 bar and 5 bar pressure. Calculate the molar mass of the gas.

Accepted Answer

Assuming the density 4.4 g L⁻¹ is at 2 bar pressure (as the question states 'at 2 bar and 5 bar pressure' but provides only one density value), the molar mass of the gas is 50.17 g/mol.

Question 5

Q5. Pressure of 1 g of an ideal gas A at 27 °C is found to be 2 bar. When 2 g of another ideal gas B is introduced in the same flask at same temperature the pressure becomes 3 bar. Fin

Accepted Answer

The relationship between the molecular masses of gas A (M_A) and gas B (M_B) is M_A = 4 * M_B.

Question 6

Q6. What will be the minimum pressure required to compress 500 dm³ of air at 1 bar to 200 dm³ at 30 °C?

Accepted Answer

To compress 500 dm³ of air at 1 bar to 200 dm³ at a constant temperature of 30 °C, the minimum pressure required will be 2.5 bar.

Question 7

Q7. A vessel of 120 mL capacity contains a certain amount of gas at 35 °C and 1.2 bar pressure. The gas is transferred to another vessel of volume 180 mL at 35 °C. What would be its pr

Accepted Answer

When the gas is transferred to another vessel of 180 mL capacity at the same temperature (35 °C), its pressure would be 0.8 bar.

Question 8

Q8. Using the equation of state pV = nRT; show that at a given temperature density of a gas is proportional to the pressure p.

Accepted Answer

The ideal gas equation of state can be manipulated to show that at a given temperature, the density of a gas is directly proportional to its pressure. This relationship is crucial for understanding how gas density changes with external conditions.

Question 9

Q9. What is the effect of temperature on (a) surface tension and (b) viscosity of liquids?

Accepted Answer

The effect of temperature on the properties of liquids is as follows:

**(a) Effect of temperature on surface tension:**
Surface tension is a property of liquids that arises due to the net inward pull experienced by molecules at the surface, caused by cohesive intermolecular forces. As the temperature of a liquid increases, the average kinetic energy of its molecules also increases. This increased kinetic energy allows the molecules to overcome the intermolecular forces of attraction more easily. Consequently, the cohesive forces between the molecules at the surface weaken, leading to a decrease in the net inward pull. Therefore, the surface tension of a liquid decreases with an increase in temperature. At the critical temperature, the surface tension of a liquid becomes zero.

**(b) Effect of temperature on viscosity:**
Viscosity is a measure of a fluid's resistance to flow, which in liquids is primarily due to the strong intermolecular forces of attraction between molecules that resist their relative motion (internal friction). As the temperature increases, the kinetic energy of the liquid molecules increases. This increased kinetic energy helps the molecules to overcome the intermolecular forces more easily, reducing the internal friction between adjacent layers of the liquid. As a result, the resistance to flow decreases. Therefore, the viscosity of liquids decreases significantly with an increase in temperature.

Question 10

Q10. What is the effect of pressure on the viscosity of gases and liquids?

Accepted Answer

The effect of pressure on the viscosity of gases and liquids is different:

**(a) Effect of pressure on the viscosity of gases:**
For gases, viscosity arises mainly from the transfer of momentum between different layers of gas moving at different velocities. As pressure increases (at a constant temperature), the number of molecules per unit volume increases. This leads to more frequent collisions between molecules and thus an increased rate of momentum transfer between the layers. This enhanced momentum transfer increases the internal friction and resistance to flow. Therefore, the viscosity of gases generally increases with an increase in pressure.

**(b) Effect of pressure on the viscosity of liquids:**
For liquids, viscosity is primarily due to the strong intermolecular forces of attraction. Liquids are largely incompressible, meaning that an increase in pressure has a relatively small effect on the intermolecular distances and thus on the intermolecular forces. While a very significant increase in pressure can slightly bring molecules closer, potentially leading to a minor increase in intermolecular forces and thus a slight increase in viscosity, for most practical purposes and typical pressure ranges, the viscosity of liquids is considered to be largely independent of pressure. The effect of pressure on liquid viscosity is negligible compared to the effect of temperature.

Question 11

Q11. How does the vapour pressure of a liquid vary with temperature?

Accepted Answer

The vapour pressure of a liquid increases significantly and non-linearly with an increase in temperature.

This variation can be explained by considering the molecular behavior:

1.  **Increased Kinetic Energy:** As the temperature of a liquid increases, the average kinetic energy of its molecules also increases. This means a larger fraction of molecules possesses sufficient energy to overcome the intermolecular forces of attraction in the liquid phase.
2.  **Enhanced Evaporation:** More molecules at the surface gain enough kinetic energy to escape from the liquid phase into the gaseous (vapour) phase. This leads to an increased rate of evaporation.
3.  **Higher Vapour Concentration:** Consequently, the concentration of vapour molecules above the liquid surface increases at a higher temperature.
4.  **Increased Collisions and Pressure:** These increased vapour molecules collide more frequently with the container walls and with each other, exerting a higher pressure. At equilibrium, the rate of evaporation equals the rate of condensation, and this equilibrium is established at a higher vapour pressure.

Therefore, a higher temperature leads to a higher equilibrium vapour pressure. This relationship is crucial for understanding phenomena like boiling point (where vapour pressure equals external pressure) and is quantitatively described by the Clausius-Clapeyron equation.

Question 12

Q12. What is the significance of critical temperature and critical pressure?

Accepted Answer

Critical temperature and critical pressure are fundamental properties that define the conditions under which a gas can be liquefied and characterize the phase behavior of substances.

**1. Critical Temperature (T_c):**
*   **Definition:** The critical temperature (T_c) is the maximum temperature at which a gas can be liquefied, no matter how high the pressure applied. Above this temperature, the substance exists only as a gas and cannot be condensed into a liquid by increasing pressure alone.
*   **Significance:**
    *   **Liquefaction Limit:** It sets the upper temperature limit for the liquefaction of a gas. For a gas to be liquefied, it must first be cooled to a temperature below its T_c.
    *   **Distinction between Gas and Vapour:** Below T_c, the gaseous substance is often referred to as a 'vapour' because it can be liquefied by simply applying pressure. Above T_c, it is called a 'gas' and cannot be liquefied by pressure alone.
    *   **Intermolecular Forces:** A higher critical temperature indicates stronger intermolecular forces of attraction within the substance. More kinetic energy (higher temperature) is required to overcome these stronger forces and prevent liquefaction.

**2. Critical Pressure (P_c):**
*   **Definition:** The critical pressure (P_c) is the minimum pressure required to liquefy a gas at its critical temperature.
*   **Significance:**
    *   **Minimum Pressure for Liquefaction:** It represents the minimum pressure needed to bring about liquefaction when the gas is exactly at its critical temperature. Below P_c, even at T_c, the gas will not liquefy.
    *   **Critical Point:** Along with critical temperature, it defines the 'critical point' on a phase diagram, which is the point where the liquid and gas phases become indistinguishable, having the same density and other properties.
    *   **Industrial Applications:** Understanding critical pressure is vital in industrial processes involving the storage, transport, and liquefaction of gases (e.g., in refrigeration, chemical synthesis, and handling of compressed gases).

**Overall Significance:**
Critical temperature and pressure are crucial for understanding the deviations of real gases from ideal behavior and for designing processes involving phase changes. They provide valuable insights into the strength of intermolecular forces and are essential for practical applications in chemistry and engineering.

Question 13

Q13. What will be the minimum pressure required to compress 500 dm³ of air at 1 bar to 200 dm³ at 30 °C?

Accepted Answer

To compress 500 dm³ of air at 1 bar to 200 dm³ at a constant temperature of 30 °C, the minimum pressure required will be 2.5 bar.

Question 14

Q14. A vessel of 120 mL capacity contains a certain amount of gas at 35 °C and 1.2 bar pressure. The gas is transferred to another vessel of volume 180 mL at 35 °C. What would be its pr

Accepted Answer

When the gas is transferred to a vessel of 180 mL capacity at the same temperature, its pressure would be 0.8 bar.

Question 15

Q15. Using the equation of state pV = nRT; show that at a given temperature density of a gas is directly proportional to the pressure p.

Accepted Answer

To show that at a given temperature, the density of a gas is directly proportional to its pressure, we can derive the relationship from the ideal gas equation (pV = nRT).

Question 16

Q16. At 0 °C, the density of a certain oxide of a gas is 4.4 g L⁻¹ at 2 bar and 5.0 g L⁻¹ at 3 bar. Calculate the molar mass of the gas.

Accepted Answer

The molar mass of the gas can be calculated using the ideal gas equation in terms of density. However, the given data (density at 2 bar and density at 3 bar) is inconsistent with the ideal gas law at a constant temperature. If we proceed with the first set of data (4.4 g L⁻¹ at 2 bar), the molar mass is approximately 50.04 g/mol. If we use the second set of data (5.0 g L⁻¹ at 3 bar), the molar mass is approximately 37.79 g/mol. This inconsistency suggests a potential error in the problem statement's data. Assuming the first set of data is to be used, the molar mass is 50.04 g/mol.

Question 17

Q17. What is the effect of temperature on (a) surface tension and (b) viscosity of liquids?

Accepted Answer

(a) **Effect of temperature on surface tension of liquids:**
Surface tension of a liquid generally decreases with an increase in temperature. This is because, as the temperature increases, the kinetic energy of the molecules increases. The molecules move more vigorously and are able to overcome the intermolecular forces of attraction more easily. This weakens the net inward pull on the surface molecules, leading to a decrease in surface tension.

(b) **Effect of temperature on viscosity of liquids:**
Viscosity of a liquid generally decreases with an increase in temperature. This is due to the fact that with an increase in temperature, the kinetic energy of the liquid molecules increases. The molecules can then overcome the intermolecular forces of attraction and the resistance to flow (internal friction) more easily. This allows the layers of the liquid to slide past each other with less resistance, resulting in a decrease in viscosity.

Question 18

Q18. What is the effect of temperature on the viscosity of gases?

Accepted Answer

The viscosity of gases generally increases with an increase in temperature. This is contrary to liquids where viscosity decreases with increasing temperature.

In gases, viscosity arises primarily from the transfer of momentum between different layers of gas molecules moving at different velocities. As the temperature increases, the kinetic energy and thus the average speed of gas molecules increase. This leads to more frequent and energetic collisions between molecules of different layers, resulting in a greater transfer of momentum between them. Consequently, the internal friction and resistance to flow increase, leading to an increase in the viscosity of the gas.

Question 19

Q19. Liquid 'A' has a standard boiling point of 80°C while liquid 'B' has a standard boiling point of 120°C. Which of them has a higher vapour pressure at 80°C? Explain.

Accepted Answer

Liquid 'A' will have a higher vapour pressure at 80°C.

**Explanation:**
Standard boiling point is the temperature at which the vapour pressure of a liquid becomes equal to the standard atmospheric pressure (1 bar or 1 atm). A lower boiling point indicates that the liquid requires less energy to overcome its intermolecular forces and vaporize. This implies that the intermolecular forces of attraction in liquid 'A' are weaker than those in liquid 'B'.

At a given temperature (in this case, 80°C), a liquid with weaker intermolecular forces will have a greater tendency to escape into the gaseous phase, resulting in a higher concentration of vapour molecules above its surface. Therefore, liquid 'A', having a lower boiling point (80°C) and thus weaker intermolecular forces, will have a higher vapour pressure at 80°C compared to liquid 'B' (which has stronger intermolecular forces and a boiling point of 120°C). In fact, at 80°C, liquid 'A' is at its boiling point, meaning its vapour pressure is equal to the external atmospheric pressure, while liquid 'B' is still below its boiling point, so its vapour pressure will be significantly lower than the atmospheric pressure.

Question 20

Q20. Why are liquids generally incompressible?

Accepted Answer

Liquids are generally incompressible because their constituent molecules are already very closely packed together, leaving very little empty space between them. Unlike gases, where molecules are far apart and can be pushed closer, in liquids, the molecules are in close contact due to strong intermolecular forces of attraction. When external pressure is applied, there is hardly any free volume for the molecules to move into and occupy. Therefore, a significant amount of pressure is required to reduce their volume even slightly, making them practically incompressible.

Question 21

Q21. What is the effect of temperature on (a) surface tension and (b) viscosity of liquids?

Accepted Answer

The effect of temperature on the properties of liquids is significant due to its influence on the kinetic energy of molecules and intermolecular forces.

**(a) Effect of temperature on Surface Tension:**
Surface tension of a liquid generally **decreases** with an increase in temperature. This is because as the temperature increases, the kinetic energy of the liquid molecules also increases. The increased kinetic energy allows the molecules to overcome the intermolecular attractive forces more easily. Consequently, the cohesive forces between the molecules at the surface weaken, leading to a reduction in the inward pull on the surface molecules and thus a decrease in surface tension. At the critical temperature, the surface tension becomes zero.

**(b) Effect of temperature on Viscosity:**
Viscosity of a liquid generally **decreases** with an increase in temperature. This is because as the temperature rises, the kinetic energy of the liquid molecules increases. The molecules gain enough energy to overcome the intermolecular forces of attraction more readily and move past each other with less resistance. This enhanced molecular mobility reduces the internal friction (resistance to flow) within the liquid, resulting in lower viscosity.

Question 22

Q22. What is the effect of pressure on the viscosity of liquids?

Accepted Answer

The effect of pressure on the viscosity of liquids is generally less pronounced compared to the effect of temperature. However, for most liquids, viscosity **increases** with an increase in pressure.

When pressure is applied to a liquid, the molecules are forced closer together. This leads to an increase in the density of the liquid and strengthens the intermolecular forces of attraction between the molecules. The increased proximity and stronger intermolecular forces make it more difficult for the molecules to move past one another, thereby increasing the internal friction and resistance to flow, which manifests as an increase in viscosity.

It's important to note that this effect is typically small for common liquids under moderate pressure changes, but it becomes more significant at very high pressures.

Question 23

Q23. How does the vapour pressure of a liquid vary with temperature?

Accepted Answer

The vapour pressure of a liquid **increases significantly** with an increase in temperature.

Here's why:
1.  **Increased Kinetic Energy:** As the temperature of a liquid increases, the average kinetic energy of its molecules also increases. A larger fraction of molecules at the surface gain enough kinetic energy to overcome the intermolecular forces of attraction holding them in the liquid phase.
2.  **Enhanced Evaporation:** These higher-energy molecules escape from the liquid surface into the gaseous (vapour) phase at a faster rate. This process is called evaporation.
3.  **Higher Vapour Concentration:** Consequently, the concentration of vapour molecules above the liquid surface increases. In a closed container, this leads to a higher number of vapour molecules colliding with the container walls and exerting pressure.
4.  **Dynamic Equilibrium:** At any given temperature, a dynamic equilibrium is established where the rate of evaporation equals the rate of condensation. At higher temperatures, this equilibrium is achieved with a greater concentration of vapour molecules, resulting in a higher equilibrium vapour pressure.

This relationship is exponential, meaning a small increase in temperature can lead to a substantial increase in vapour pressure. The temperature at which the vapour pressure of a liquid becomes equal to the external atmospheric pressure is defined as its boiling point.

Chapter 5: States of Matter