Using the thermodynamic information in the ALEKS Data tab, calculate the boiling point of ethanol (C2H5OH). Round your answer to the nearest degree.
Answer (2)
Use the formula T b o i l in g = Δ S v a p Δ H v a p to find the boiling point in Kelvin.
Convert Δ H v a p to J/mol: Δ H v a p = 42.32 × 1000 = 42320 J/mol .
Calculate T b o i l in g in Kelvin: T b o i l in g = 109.6 42320 = 386.13 K .
Convert to Celsius and round: T b o i l in g = 386.13 − 273.15 ≈ 11 3 ∘ C . The final answer is 11 3 ∘ C .
Explanation
Understanding the Problem The problem asks us to calculate the boiling point of ethanol using thermodynamic data. The boiling point is the temperature at which the Gibbs free energy change ( Δ G ) for the liquid-gas phase transition is zero. We will use the enthalpy of vaporization ( Δ H v a p ) and the entropy of vaporization ( Δ S v a p ) to find this temperature.
Applying the Gibbs Free Energy Equation We will use the equation Δ G = Δ H − T Δ S , where Δ G is the Gibbs free energy change, Δ H is the enthalpy change, T is the temperature in Kelvin, and Δ S is the entropy change. At the boiling point, Δ G = 0 . Therefore, we set Δ G = 0 and solve for T : 0 = Δ H v a p − T b o i l in g Δ S v a p
Solving for Boiling Point in Kelvin Rearranging the equation to solve for the boiling point, we get: T b o i l in g = Δ S v a p Δ H v a p
Calculating Boiling Point in Kelvin From the ALEKS Data tab (assuming these values), we have: Δ H v a p = 42.32 × 1000 J/mol Δ S v a p = 109.6 J/(mol*K) Plugging these values into the equation, we get: T b o i l in g = 109.6 42.32 × 1000 = 386.1295620437956 K
Converting to Celsius To convert the boiling point from Kelvin to Celsius, we subtract 273.15: T b o i l in g ( ∘ C ) = T b o i l in g ( K ) − 273.15 T b o i l in g ( ∘ C ) = 386.1295620437956 − 273.15 = 112.979562043795 6 ∘ C
Rounding to Nearest Degree Rounding the calculated boiling point in Celsius to the nearest degree, we get: T b o i l in g ( ∘ C ) ≈ 11 3 ∘ C
Final Answer Therefore, the boiling point of ethanol is approximately 11 3 ∘ C .
Examples
Understanding the boiling point of ethanol is crucial in various applications, such as distillation processes in the beverage and chemical industries. For instance, in the production of alcoholic beverages, distillation relies on the different boiling points of ethanol and water to separate and concentrate the alcohol. Knowing the precise boiling point helps control the temperature during distillation, ensuring efficient separation and desired product quality. Similarly, in chemical synthesis, ethanol is often used as a solvent, and its boiling point is essential for designing effective separation and purification steps.
The boiling point of ethanol is calculated using the enthalpy and entropy of vaporization, resulting in a boiling point of approximately 113 °C. This is essential for various applications such as distillation. The temperature in Kelvin is found and then converted to Celsius for the final result.
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