Calculating The Boiling Point Of Ethanol Using Thermodynamics In ALEKS

Jul 7, 2025 by Admin 71 views

Calculating the Boiling Point of Ethanol Using Thermodynamic Data in ALEKS

Introduction

In the realm of chemistry, thermodynamics plays a crucial role in understanding the behavior of substances and their reactions. One of the key aspects of thermodynamics is the ability to predict phase transitions, such as boiling. Boiling point, the temperature at which a liquid changes into a gas, is a fundamental property of a substance. In this article, we delve into the process of calculating the boiling point of ethanol (C2H5OH) using thermodynamic information accessible within the ALEKS (Assessment and Learning in Knowledge Spaces) Data tab. This comprehensive guide will walk you through the necessary steps, calculations, and concepts to accurately determine the boiling point of ethanol.

Understanding Thermodynamic Principles

Before we embark on the calculation, it's essential to grasp the underlying thermodynamic principles. The boiling point of a liquid is the temperature at which its vapor pressure equals the surrounding atmospheric pressure. At this point, the liquid's molecules have enough kinetic energy to overcome the intermolecular forces holding them together in the liquid phase, transitioning into the gaseous phase. Thermodynamically, boiling occurs when the Gibbs free energy change ( ${\Delta G}$ ) for the liquid-to-gas phase transition is zero. The Gibbs free energy change is defined by the following equation:

${ \Delta G = \Delta H - T\Delta S }$

Where:

${\Delta G}$ is the Gibbs free energy change.
${\Delta H}$ is the enthalpy change (heat absorbed or released during the phase transition).
T is the temperature in Kelvin.
${\Delta S}$ is the entropy change (change in disorder during the phase transition).

At the boiling point, ${\Delta G = 0}$ , so we can rearrange the equation to solve for the boiling temperature (T_b):

${ T_b = \frac{\Delta H}{\Delta S} }$

To calculate the boiling point of ethanol, we need to determine the enthalpy change ( ${\Delta H}$ ) and entropy change ( ${\Delta S}$ ) for the vaporization process. These values can be obtained from thermodynamic data tables, often available in textbooks or online resources like the ALEKS Data tab.

Accessing Thermodynamic Data in ALEKS

ALEKS is a widely used online learning platform that provides students with access to a wealth of chemical information, including thermodynamic data. To find the necessary data for ethanol, follow these steps:

Log in to your ALEKS account and navigate to the relevant chemistry course.
Look for the "Data" tab or a similar section that provides access to reference materials.
Within the data resources, you should find tables containing thermodynamic properties of various substances, including ethanol.
Search for ethanol (C2H5OH) in the table. You will typically find values for:
- Standard enthalpy of formation ( ${\Delta H_f^\circ}$ ) for liquid and gas phases.
- Standard entropy ( ${S^\circ}$ ) for liquid and gas phases.

These standard values are usually given at a reference temperature of 298 K (25 °C) and 1 atm pressure. Make sure to note the units of these values, as they are crucial for accurate calculations. Enthalpy values are typically in kJ/mol, and entropy values are in J/(mol·K).

Calculating Enthalpy Change (ΔH) for Vaporization

The enthalpy change for vaporization ( ${\Delta H_{vap}}$ ) is the amount of energy required to convert one mole of liquid ethanol into gaseous ethanol at its boiling point. We can calculate this using the standard enthalpies of formation ( ${\Delta H_f^\circ}$ ) for the liquid and gas phases:

${ \Delta H_{vap} = \Delta H_f^\circ (gas) - \Delta H_f^\circ (liquid) }$

From the ALEKS Data tab (or a similar source), we can find the following approximate values for ethanol:

${\Delta H_f^\circ (C_2H_5OH(g)) \approx -235.1 \text{ kJ/mol}}$
${\Delta H_f^\circ (C_2H_5OH(l)) \approx -277.7 \text{ kJ/mol}}$

Plugging these values into the equation, we get:

${ \Delta H_{vap} = -235.1 \text{ kJ/mol} - (-277.7 \text{ kJ/mol}) = 42.6 \text{ kJ/mol} }$

So, the enthalpy change for vaporization of ethanol is approximately 42.6 kJ/mol. This positive value indicates that the vaporization process is endothermic, meaning it requires energy input.

Calculating Entropy Change (ΔS) for Vaporization

The entropy change for vaporization ( ${\Delta S_{vap}}$ ) represents the increase in disorder when liquid ethanol transitions into the gaseous phase. We can calculate this using the standard entropies ( ${S^\circ}$ ) for the liquid and gas phases:

${ \Delta S_{vap} = S^\circ (gas) - S^\circ (liquid) }$

From the ALEKS Data tab, we can find the following approximate values for ethanol:

${S^\circ (C_2H_5OH(g)) \approx 240.0 \text{ J/(mol·K)}}$
${S^\circ (C_2H_5OH(l)) \approx 160.7 \text{ J/(mol·K)}}$

Plugging these values into the equation, we get:

${ \Delta S_{vap} = 240.0 \text{ J/(mol·K)} - 160.7 \text{ J/(mol·K)} = 79.3 \text{ J/(mol·K)} }$

Thus, the entropy change for vaporization of ethanol is approximately 79.3 J/(mol·K). This positive value indicates that the vaporization process leads to an increase in disorder, as expected when a liquid transforms into a gas.

Calculating the Boiling Point

Now that we have the enthalpy change ( ${\Delta H_{vap}}$ ) and entropy change ( ${\Delta S_{vap}}$ ) for vaporization, we can calculate the boiling point (T_b) using the equation we derived earlier:

${ T_b = \frac{\Delta H_{vap}}{\Delta S_{vap}} }$

Before we plug in the values, it's crucial to ensure the units are consistent. We have ${\Delta H_{vap}}$ in kJ/mol and ${\Delta S_{vap}}$ in J/(mol·K). To use them in the same equation, we need to convert ${\Delta H_{vap}}$ to J/mol:

${ \Delta H_{vap} = 42.6 \text{ kJ/mol} \times 1000 \text{ J/kJ} = 42600 \text{ J/mol} }$

Now, we can plug the values into the equation:

${ T_b = \frac{42600 \text{ J/mol}}{79.3 \text{ J/(mol·K)}} \approx 537.2 \text{ K} }$

The boiling point we calculated is in Kelvin. To convert it to Celsius, we subtract 273.15:

${ T_b (\text{°C}) = 537.2 \text{ K} - 273.15 \approx 264.05 \text{ °C} }$

The problem asks us to round the answer to the nearest degree. Therefore, the boiling point of ethanol, calculated using the thermodynamic data from ALEKS, is approximately 264 °C.

Factors Affecting Boiling Point

While we have calculated the boiling point of ethanol using thermodynamic principles, it is essential to recognize that several factors can influence the actual boiling point in real-world scenarios. These factors include:

Pressure: The boiling point of a liquid is highly dependent on the surrounding pressure. The standard boiling point is defined at 1 atm pressure. At higher pressures, the boiling point increases, while at lower pressures, it decreases. This is why water boils at a lower temperature at high altitudes.
Intermolecular Forces: The strength of intermolecular forces (such as hydrogen bonding, dipole-dipole interactions, and London dispersion forces) significantly affects the boiling point. Substances with stronger intermolecular forces require more energy to overcome these forces and transition into the gaseous phase, resulting in higher boiling points. Ethanol, with its ability to form hydrogen bonds due to the hydroxyl (-OH) group, has a relatively high boiling point compared to compounds with similar molecular weights but weaker intermolecular forces.
Molecular Weight and Shape: Generally, larger molecules with greater surface areas tend to have higher boiling points due to increased London dispersion forces. The shape of the molecule also plays a role; more elongated molecules have greater surface contact and stronger intermolecular interactions than more spherical molecules.
Impurities: The presence of impurities in a liquid can affect its boiling point. Dissolved non-volatile impurities typically elevate the boiling point, while volatile impurities can lower it.

Common Errors and How to Avoid Them

Calculating the boiling point using thermodynamic data involves several steps, and errors can occur if not approached carefully. Here are some common mistakes and tips on how to avoid them:

Unit Conversions: Failing to convert units correctly is a frequent mistake. Ensure that all values are in consistent units (e.g., converting kJ to J) before performing calculations. Double-check the units of ${\Delta H}$ and ${\Delta S}$ and make necessary conversions.
Sign Conventions: Pay close attention to the sign conventions for enthalpy and entropy changes. Endothermic processes (heat absorbed) have positive ${\Delta H}$ values, while exothermic processes (heat released) have negative ${\Delta H}$ values. An increase in disorder (e.g., vaporization) corresponds to a positive ${\Delta S}$ , and a decrease in disorder corresponds to a negative ${\Delta S}$ .
Data Accuracy: Use reliable sources for thermodynamic data, such as the ALEKS Data tab or reputable chemistry textbooks. Be cautious of using data from unverified sources, as they may contain errors.
Conceptual Understanding: Ensure you have a solid understanding of the underlying thermodynamic principles. Memorizing formulas without understanding the concepts can lead to mistakes. Review the definitions of Gibbs free energy, enthalpy, and entropy, and how they relate to phase transitions.
Rounding Errors: Avoid rounding intermediate results, as this can lead to significant errors in the final answer. Keep as many significant figures as possible throughout the calculation and round only the final answer to the specified number of decimal places.

Conclusion

Calculating the boiling point of ethanol using thermodynamic data from the ALEKS Data tab is a valuable exercise that reinforces your understanding of thermodynamic principles and their application to real-world phenomena. By carefully following the steps outlined in this article, you can accurately determine the boiling point of ethanol and other substances. Remember to pay attention to unit conversions, sign conventions, and the underlying concepts to avoid common errors. Furthermore, understanding the factors that affect boiling point provides a broader perspective on the behavior of liquids and their phase transitions. This knowledge is crucial not only for academic success in chemistry but also for various applications in chemical engineering, materials science, and other related fields. By mastering these calculations, you gain a deeper appreciation for the power of thermodynamics in predicting and explaining the properties of matter.

Further Practice

To solidify your understanding, try calculating the boiling points of other substances using thermodynamic data. Compare your results with literature values and explore how different factors, such as intermolecular forces and molecular structure, influence the boiling points of various compounds. Additionally, consider investigating the applications of boiling point calculations in industrial processes, such as distillation and purification techniques. This hands-on practice will enhance your skills and confidence in applying thermodynamic principles to solve real-world problems.

By engaging in these activities, you will not only improve your understanding of thermodynamics but also develop critical thinking and problem-solving skills that are essential for success in chemistry and related disciplines.