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

검증된 단계별 안내

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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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

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.

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.

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.

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.