Question

The normal boiling point of ${\mathrm{Br}}_2(l)$ is ${58.8}^{\circ }\mathrm{C},$ and its molar enthalpy of vaporization is $\mathrm{\Delta }{H}_{\mathrm{vap}}=29.6\mathrm{kJ}/\mathrm{mol}$ (a) When ${\mathrm{Br}}_2(l)$ boils at its normal boiling point, does its entropy increase or decrease? (b) Calculate the value of $\mathrm{\Delta }S$ when 1.00 mol of ${\mathrm{Br}}_2(l)$ is vaporized at ${58.8}^{\circ }\mathrm{C}$ .

Short answer

During the boiling of Br2(l) at its normal boiling point, the entropy increases. The entropy change (∆S) when 1.00 mol of Br2(l) is vaporized at 58.8°C is 89.1 J/(mol·K).

Step-by-step solution

Part (a): Determining if Entropy Increases or Decreases

When a substance undergoes a phase change, such as boiling, the particles become more disordered and more dispersed. In the case of liquid bromine boiling and becoming gaseous bromine, the increased freedom of movement and spacing between the particles contribute to a higher entropy, which is a measure of disorder in a system. Thus, during the boiling of Br2(l) at its normal boiling point, the entropy increases.

Part (b): Calculate the Entropy Change (∆S)

Next, we calculate the entropy change (∆S) when 1.00 mol of Br2(l) is vaporized at its boiling point. We use the equation: $\mathrm{\Delta }S=\frac{\mathrm{\Delta }{H}_{vap}}{T}$ We are given the molar enthalpy of vaporization $\mathrm{\Delta }{H}_{vap}=29.6kJ/mol$ and the boiling point temperature $T={58.8}^{\circ }C$. First, we need to convert the temperature from Celsius to Kelvin: $T_{(K)}=T_{(C)}+273.15$ $T_{(K)}=58.8+273.15=331.95K$ Now, we apply the equation: $\mathrm{\Delta }S=\frac{29.6kJ/mol}{331.95K}$ Note that we need to convert kJ to J by multiplying with 1000: $\mathrm{\Delta }S=\frac{29.6\times 1,000J/mol}{331.95K}=89.1\frac{J}{mol\cdot K}$ Therefore, the entropy change, ∆S, when 1.00 mol of Br2(l) is vaporized at its normal boiling point is 89.1 J/(mol·K).

Key concepts

Entropy

Entropy is a crucial concept in thermodynamics referring to the degree of disorder or randomness in a system. When a substance experiences a phase change, such as boiling, its entropy tends to increase. This is because the molecules in the gaseous state have more freedom to move compared to their arrangement in the liquid state.
For example, as bromine transitions from liquid to vapor, its molecules spread out becoming more disordered, thus leading to a rise in entropy. It's this tendency toward greater disorder that fundamentally drives many natural processes.

• Bromine in liquid form is more structured than in vapor form.
• When it boils, the increased molecular freedom results in higher entropy.

Molar Enthalpy

Molar enthalpy, specifically the molar enthalpy of vaporization, is the amount of energy required to vaporize one mole of a substance at its boiling point. It's an important measure of the energy change involved in phase changes.
For bromine (${\mathrm{Br}}_2(l)$), the molar enthalpy of vaporization is given as 29.6 kJ/mol. Understanding this helps in calculating the change in entropy, as it directly relates to the energy absorbed during the boiling process.

• It indicates the energy input needed for the phase change from liquid to gas.
• The knowledge of this value aids in further thermodynamic calculations, such as entropy change.

Phase Change

Phase change, or phase transition, refers to the transformation from one state of matter to another. In the context of the exercise, bromine undergoes a phase change from liquid (${\mathrm{Br}}_2(l)$) to gas (${\mathrm{Br}}_2(g)$).
This process involves breaking intermolecular forces and requires specific energy inputs, as represented by the molar enthalpy of vaporization. The transition also involves changes in entropy, as the system gains disorder in the gaseous state.

• Phase changes are significant in studying energy transfer and entropy changes.
• Each type of phase change, such as melting or vaporization, has unique energy and volume implications.

Boiling Point

The boiling point of a substance is the temperature at which its vapor pressure equals the external pressure surrounding the liquid. For bromine (${\mathrm{Br}}_2(l)$), this occurs at 58.8°C, where it transitions to vapor.
Understanding the boiling point is critical to evaluating how temperature influences the energy and entropy during phase changes. It allows us to pinpoint the conditions under which a substance changes its state from liquid to gas and enables precise thermodynamic calculations.

• Indicates the temperature for the liquid-to-gas transition.
• Influences both the enthalpy and entropy calculations of a substance.