Problem 92 - A Complete Resource Book in Chemistry for JEE Main

Question

The change in entropy, in the conversion of one mole of water at \(373 \mathrm{~K}\) to vapour at the same temperature is (Latent heat of vaporization of water = \(\left.2.257 \mathrm{~kJ} \mathrm{~g}^{-1}\right)\) (a) \(99 \mathrm{JK}^{-1}\) (b) \(129 \mathrm{JK}^{-1}\) (c) \(89 \mathrm{JK}^{-1}\) (d) \(109 \mathrm{JK}^{-1}\)

Step-by-Step Solution

Answer

The change in entropy is approximately \(109 \mathrm{J/K}\), which matches option (d).

Step 1: Understand the Definition of Entropy Change

The change in entropy (\(\Delta S\)) during a phase change is calculated using the formula \(\Delta S = \frac{q_{rev}}{T}\), where \(q_{rev}\) is the heat absorbed or released reversibly and \(T\) is the temperature in Kelvin at which the process occurs. For a phase change, \(q_{rev}\) is the latent heat times the number of moles.

Step 2: Convert Latent Heat to Per Mole

Given the latent heat of vaporization of water is \(2.257 \mathrm{~kJ} \mathrm{~g}^{-1}\). Convert this to a per mole basis using the molar mass of water (\(18.015 \mathrm{~g/mol}\)).\[ q_{rev} = 2.257 \mathrm{~kJ/g} \times 18.015 \mathrm{~g/mol} = 40.79 \mathrm{~kJ/mol} \]

Step 3: Calculate Entropy Change

Using the formula \(\Delta S = \frac{q_{rev}}{T}\), substitute \(q_{rev} = 40.79 \mathrm{~kJ/mol}\) and \(T = 373 \mathrm{~K}\).Convert \(q_{rev}\) to \(J/mol\), where \(1 \mathrm{~kJ} = 1000 \mathrm{~J}\), so \(q_{rev} = 40790 \mathrm{~J/mol}\).\[ \Delta S = \frac{40790}{373} \approx 109.36 \mathrm{~J/K} \]

Step 4: Select the Closest Answer

The calculated entropy change is approximately \(109.36 \mathrm{~J/K}\). Compare this result with the provided options:* (a) 99 \(\mathrm{J/K}\)* (b) 129 \(\mathrm{J/K}\)* (c) 89 \(\mathrm{J/K}\)* (d) 109 \(\mathrm{J/K}\)The closest answer is (d) \(109 \mathrm{~J/K}\).

Key Concepts

Latent Heat of Vaporization

When water changes from a liquid to a vapor, it requires energy to overcome intermolecular forces. This energy is called the "latent heat of vaporization." It's the heat required for phase change without a change in temperature.
- It's an important concept in thermodynamics as it helps predict how much energy is needed for a substance to change its state.
- Each substance has a distinct latent heat value. For water, it's very high, indicating strong forces holding the molecules together.
Latent heat of vaporization is expressed in kilojoules per gram (kJ/g) or kilojoules per mole (kJ/mol). Understanding this helps in the calculation of energy required in processes such as boiling.

Phase Change Calculations

Phase change calculations involve determining the energy or entropy change when a substance changes its state, like from liquid to gas.
Entropy change for phase transitions is calculated with \(\Delta S = \frac{q_{rev}}{T} \). Here, \( q_{rev} \) represents the reversible heat exchange, and \( T \) is the temperature when the change occurs.
- To find \( q_{rev} \) for vaporization, multiply the latent heat per gram by the molar mass of the substance.
- Convert the heat from kJ to J by multiplying by 1000, as entropy is typically in J/K.
These calculations are crucial in fields like engineering and chemistry, as they indicate the energy exchanges involved in everyday processes like boiling water for steam engines.

Thermodynamics

Thermodynamics is the study of energy transformations, and it plays a crucial role in understanding phase changes like vaporization.
Key principles include:

• The First Law – Energy can't be created or destroyed. This means during a phase change, the energy lost or gained by water must equal the energy lost or gained by its surroundings.
• The Second Law – Entropy, a measure of disorder, always increases in an isolated system, explaining why energy spreads out during vaporization.

By using thermodynamic principles, scientists and engineers can calculate, interpret, and predict the outcomes of heating, cooling, and phase transitions effectively. Understanding these laws helps in the design of efficient heating and cooling systems, fuel use, and even explaining climate dynamics.