Question

The normal boiling point of the element mercury (Hg) is \(356.7{ }^{\circ} \mathrm{C},\) and its molar enthalpy of vaporization is \(\Delta H_{\text {vap }}=59.11 \mathrm{~kJ} / \mathrm{mol} .\) (a) When Hg boils at its nor- mal boiling point, does its entropy increase or decrease? (b) Calculate the value of \(\Delta S\) when \(2.00 \mathrm{~mol}\) of \(\mathrm{Hg}\) is vaporized at \(356.7^{\circ} \mathrm{C}\).

Short answer

(a) When Hg boils at its normal boiling point, its entropy increases due to the higher amount of disorder in the vapor state compared to the liquid state. (b) The value of ΔS when 2.00 mol of Hg is vaporized at 356.7°C is 0.18776 kJ/K.

Step-by-step solution

Determine if the entropy increases or decreases when Hg boils at its normal boiling point.

We know that when a substance boils, it changes from liquid to vapor. Since the vapor state has a higher amount of disorder compared to the liquid state, the entropy increases during boiling.

Convert the temperature from Celsius to Kelvin.

Given that the normal boiling point of mercury is 356.7°C, we need to convert it to Kelvin before we can use it in our calculations: T = 356.7 + 273.15 = 629.85 K

Calculate the change in entropy ΔS.

Using the relationship between enthalpy of vaporization, temperature, and entropy changes: ΔH_vap = TΔS We are given ΔH_vap = 59.11 kJ/mol and have calculated T = 629.85 K. Now we can solve for ΔS: ΔS = ΔH_vap / T = 59.11 kJ/mol / 629.85 K = 0.09388 kJ/(mol·K)

Calculate the change in entropy for 2.00 mol of Hg.

Now that we have the change in entropy per mole, we can calculate the total entropy change for 2.00 mol of Hg: ΔS_total = ΔS * n = 0.09388 kJ/(mol·K) * 2.00 mol = 0.18776 kJ/K So, the value of ΔS when 2.00 mol of Hg is vaporized at 356.7°C is 0.18776 kJ/K.

Key concepts

Entropy

Entropy is a measure of the disorder or randomness in a system. When a substance changes state, such as from liquid to vapor, its entropy often changes as well. For most phase transitions from liquid to gas, entropy increases. This is because gases have more disorder than liquids due to the increased movement and spacing of the particles. In the case of mercury (Hg) boiling at 356.7°C, the transformation from the liquid phase to the vapor phase leads to higher entropy as the molecules become more spread out and move freely. It's crucial to remember:

• Entropy is denoted by the symbol ΔS.
• It is expressed in units of kJ/K or J/K.
• An increase in entropy means a system becomes more disordered.

Calculations for entropy change often involve understanding the state change and the energies involved in the process, which fits into the broader field of thermodynamics.

Enthalpy of vaporization

The enthalpy of vaporization, denoted as ΔH_vap, is the amount of energy required to convert a substance from a liquid to a gas at a constant temperature and pressure. This process is endothermic, meaning it absorbs heat from the surroundings. For mercury, the provided enthalpy of vaporization is 59.11 kJ/mol. This value is specific to mercury's normal boiling point. Key points:

• ΔH_vap is the heat absorbed during the phase transition.
• Measured in kJ/mol, it is essential for predicting how substances interact with thermal energy when boiling.
• This energy input breaks intermolecular forces, allowing molecules to move apart into a gaseous state.

Understanding enthalpy helps in calculating how much energy is needed to convert specific amounts of liquid into gas, providing insights into the energy changes associated with phase transitions.

Phase transition

Phase transitions involve changing a substance from one state (solid, liquid, gas) to another. This change involves energy exchange and leads to variations in entropy and enthalpy depending on the direction and nature of the transition. The transition of mercury from liquid to gas demonstrates a phase change where both the entropy and enthalpy are affected:

• The liquid-to-vapor transition requires input of energy (enthalpy), leading to increased disorder (entropy).
• Occurs at a characteristic temperature that defines the boiling point.
• During the phase transition, temperature remains constant, even though heat is constantly added.

In thermodynamics, understanding these transitions is crucial for analyzing how energy and matter interact under varying conditions. They form the basis of many industrial and natural processes crucial for fields ranging from chemistry to meteorology.