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Ch.19 - Chemical Thermodynamics
All textbooksBrown 15th EditionCh.19 - Chemical ThermodynamicsProblem 23b
Chapter 19, Problem 23b

The normal boiling point of Br2(𝑙) is 58.8 °C, and its molar enthalpy of vaporization is Δ𝐻vap=29.6kJ/mol. (b) Calculate the value of Δ𝑆 when 1.00 mol of Br2(𝑙) is vaporized at 58.8 °C.

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1
Identify the formula to calculate the change in entropy (\( \Delta S \)) for a phase change: \( \Delta S = \frac{\Delta H_{\text{vap}}}{T} \).
Convert the temperature from degrees Celsius to Kelvin by adding 273.15 to the given temperature: \( T = 58.8 + 273.15 \).
Substitute the given values into the formula: \( \Delta S = \frac{29.6 \text{ kJ/mol}}{T} \), where \( T \) is the temperature in Kelvin.
Ensure the units are consistent. Since \( \Delta H_{\text{vap}} \) is given in kJ/mol, the result for \( \Delta S \) will be in kJ/(mol·K).
Calculate the value of \( \Delta S \) using the substituted values.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Enthalpy of Vaporization

The enthalpy of vaporization (ΔH_vap) is the amount of energy required to convert one mole of a liquid into its vapor at constant temperature and pressure. For Br₂, this value is given as 29.6 kJ/mol, indicating the energy needed to vaporize the liquid at its boiling point. Understanding this concept is crucial for calculating changes in entropy during phase transitions.
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Entropy (ΔS)

Entropy (ΔS) is a measure of the disorder or randomness in a system. When a substance transitions from a liquid to a gas, such as Br₂ vaporizing, the entropy increases due to the greater freedom of movement of gas molecules compared to liquid molecules. The change in entropy can be calculated using the formula ΔS = ΔH/T, where ΔH is the enthalpy change and T is the temperature in Kelvin.
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Temperature Conversion

In thermodynamic calculations, it is essential to convert temperatures from Celsius to Kelvin. The Kelvin scale is used because it is an absolute temperature scale, where 0 K represents absolute zero. To convert Celsius to Kelvin, simply add 273.15 to the Celsius temperature. For the boiling point of Br₂ at 58.8 °C, the corresponding temperature in Kelvin is 331.95 K.
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Related Practice
Textbook Question

Indicate whether each statement is true or false. (a) ΔS is a state function. (b) If a system undergoes a reversible change, the entropy of the universe increases. (c) If a system undergoes a reversible process, the change in entropy of the system is exactly matched by an equal and opposite change in the entropy of the surroundings. (d) If a system undergoes a reversible process, the entropy change of the system must be zero.

Textbook Question

The normal boiling point of Br2(l) is 58.8 °C, and its molar enthalpy of vaporization is ΔHvap = 29.6 kJ/mol. (a) When Br2(l) boils at its normal boiling point, does its entropy increase or decrease?

Textbook Question

The element gallium (Ga) freezes at 29.8 °C, and its molar enthalpy of fusion is ΔHfus = 5.59 kJ/mol. (a) When molten gallium solidifies to Ga(s) at its normal melting point, is ΔS positive or negative?

Textbook Question

The element gallium (Ga) freezes at 29.8 °C, and its molar enthalpy of fusion is ΔHfus = 5.59 kJ/mol. (b) Calculate the value of ΔS when 60.0 g of Ga(l) solidifies at 29.8 °C.

Textbook Question

Indicate whether each statement is true or false. (c) In a certain spontaneous process the system undergoes an entropy change of 4.2 J/K; therefore, the entropy change of the surroundings must be -4.2 J/K.