Problem 74 - Advanced Problems in Physical Chemistry for Competitive Examinations

Question

What is the entropy change when \(3.6 \mathrm{~g}\) of liquid water is completely converted into vapours at \(373 \mathrm{~K} ?\) The molar heat of vaporization is \(40.85 \mathrm{~kJ} / \mathrm{mol}\). (a) \(218.9 \mathrm{~J} / \mathrm{K}\) (b) \(2.189 \mathrm{~J} / \mathrm{K}\) (c) \(21.89 \mathrm{~J} / \mathrm{K}\) (d) \(0.2189 \mathrm{~J} / \mathrm{K}\)

Step-by-Step Solution

Answer

The entropy change is \(218.9 \mathrm{~J} / \mathrm{K}\).

Step 1: Calculate the number of moles of water

Use the formula for the number of moles, which is mass (m) divided by molar mass (M). The molar mass of water (H2O) is approximately 18.015 g/mol. Hence, the number of moles of water (n) is given by: \( n = \frac{m}{M} = \frac{3.6 \mathrm{~g}}{18.015 \mathrm{~g/mol}} \).

Step 3: Select the correct answer

From the calculated entropy change, select the answer that matches the calculated value.

Key Concepts

Thermodynamics

Thermodynamics is a branch of physics concerned with heat and temperature and their relation to energy and work. It defines macroscopic variables, such as internal energy, entropy, and pressure, that partly describe a body of matter or radiation. It is concerned with the principles that govern the conversion of energy from one form to another and the direction in which processes can occur.

One of the key concepts in thermodynamics is the First Law, which states that energy cannot be created or destroyed, only transformed. Another crucial concept is the Second Law of thermodynamics, which introduces the notion of entropy. It states that the total entropy of an isolated system can never decrease over time, and is often interpreted as the degree of disorder or randomness in the system. This law predicts that certain processes, such as the spontaneous conversion of heat into work, are impossible, and it underpins the principle behind calculations of entropy change in physical chemistry.

Entropy in Physical Chemistry

In physical chemistry, entropy is a measure of the randomness or disorder of particles in a thermodynamic system. It is a central concept in determining the feasibility and spontaneity of chemical reactions and physical processes. Entropy can be represented by the symbol 'S' and has units of joules per kelvin (J/K).

When a substance undergoes a phase transition, such as from liquid to vapor, there is a change in entropy. The calculation of this entropy change (\( \triangle S \)) in a process where the temperature (T) is constant, often involves using the molar heat of vaporization (\( \triangle H_{vap} \)) and is given by the formula: \[ \triangle S = \frac{\triangle H_{vap}}{T} \].

The entropy change can be further understood by considering molecular order. As a substance vaporizes, the molecules spread out and move more freely, increasing the system’s disorder and, consequently, its entropy. This underlines why the entropy of vapor is greater than that of the corresponding liquid. Understanding entropy change calculations is essential for predicting whether a process will occur spontaneously and for evaluating the energy requirements of industrial processes.

Molar Heat of Vaporization

The molar heat of vaporization (\( \triangle H_{vap} \)) is the amount of energy required to convert one mole of a liquid into its vapor phase at a constant temperature and pressure. The units for molar heat of vaporization are typically joules per mole (J/mol) or kilojoules per mole (kJ/mol). It is an essential thermodynamic quantity that contributes to the understanding of phase transitions.

Knowing the molar heat of vaporization enables the calculation of entropy changes during the vaporization process. For example, in the original exercise, the provided molar heat of vaporization (40.85 kJ/mol) indicates how much energy is required to vaporize each mole of liquid water at the boiling point.

The molar heat of vaporization not only reflects the strength of intermolecular forces within the liquid but also can indicate the increase in entropy when the liquid turns into vapor. Substances with higher molar heats of vaporization require more energy to vaporize because their particles are typically more strongly attracted to one another in the liquid state. In contrast, when such a liquid vaporizes, the increase in disorder (entropy) is also more significant.