Question

Trouton's rule states that for many liquids at their normal boiling points, the standard molar entropy of vaporization is about $88\mathrm{J}/\mathrm{mol}-\mathrm{K}$ (a) Estimate the normal boiling point of bromine, ${\mathrm{Br}}_2,$ by determining $\mathrm{\Delta }{H}_{\mathrm{vap}}^{\circ }$ for ${\mathrm{Br}}_2$ using data from Appendix C. Assume that $\mathrm{\Delta }{H}_{\text{ vap }}^{\circ }$ remains constant with temperature and that Trouton's rule holds. (b) Look up the normal boiling point of $B{r}_2$ in a chemistry handbook or at the WebElements website (www..webelements.com) and compare it to your calculation. What are the possible sources of error, or incorrect assumptions, in the calculation?

Short answer

The normal boiling point of bromine ($B{r}_2$) can be estimated using Trouton's rule and the given data for enthalpies of formation. First, calculate the enthalpy of vaporization ($\mathrm{\Delta }{H}_{vap}^{\circ }$) for bromine using the data from Appendix C. Next, apply Trouton's rule and the calculated $\mathrm{\Delta }{H}_{vap}^{\circ }$ to estimate the normal boiling point ($T_b$). Compare this estimated value with the actual normal boiling point found in a chemistry handbook or online database. Possible sources of error or incorrect assumptions in the calculation include the assumption that Trouton's rule is valid for bromine, the assumption that $\mathrm{\Delta }{H}_{vap}^{\circ }$ remains constant with temperature, and uncertainties in the given data for enthalpies of formation.

Step-by-step solution

To find the enthalpy of vaporization for bromine, navigate to Appendix C and find the enthalpies of formation of both gaseous and liquid forms of bromine. Then, calculate the difference between the enthalpies: $\mathrm{\Delta }{H}_{vap}^{\circ }=H_g^{\circ }-H_l^{\circ }$ #Step 2: Use Trouton's Rule to Estimate the Normal Boiling Point#

According to Trouton's rule, the standard molar entropy of vaporization for many liquids at their normal boiling points is approximately 88 J/(mol·K). So, assuming that Trouton's rule holds for bromine, we can use the following equation: $\mathrm{\Delta }{S}_{vap}^{\circ }=\frac{\mathrm{\Delta }{H}_{vap}^{\circ }}{T_b}$ Rearrange the equation to find the normal boiling point: $T_b=\frac{\mathrm{\Delta }{H}_{vap}^{\circ }}{\mathrm{\Delta }{S}_{vap}^{\circ }}$ Plug in the values: $T_b=\frac{\mathrm{\Delta }{H}_{vap}^{\circ }}{88J/mol\cdot K}$ Calculate $T_b$, which is the estimated normal boiling point of bromine (in kelvin). #Step 3: Compare the Estimated and Actual Normal Boiling Points#

Navigate to a chemistry handbook or the WebElements website (www.webelements.com) to find the actual normal boiling point of $B{r}_2$. Compare this value to the calculated value obtained in step 2. #Step 4: Discuss Possible Errors and Incorrect Assumptions#

Some of the possible sources of error or incorrect assumptions in this calculation can include: 1. The assumption that Trouton's rule is valid for bromine. Trouton's rule works well for many liquids, but there can be exceptions. 2. The assumption that $\mathrm{\Delta }{H}_{vap}^{\circ }$ remains constant with temperature. Although this assumption simplifies the calculation, it might not hold for all liquids and can lead to errors. 3. Uncertainties in the given data for enthalpies of formation. Errors in measurement or reporting of these values can affect the final calculated normal boiling point. Overall, the calculation gives an estimate of the normal boiling point of bromine, but the actual value might vary due to the factors discussed above.

Key concepts

Enthalpy of Vaporization

The enthalpy of vaporization, denoted as $\mathrm{\Delta }{H}_{vap}^{\circ }$, is the energy required to convert a substance from its liquid phase to its gaseous phase. This thermodynamic quantity is measured when the substance is at a constant pressure and is pivotal in understanding the phase transition of materials.
In practical applications, knowing the enthalpy of vaporization helps us understand how much energy is involved in boiling a liquid. The concept applies not just to water, but also to other substances such as bromine. In educational exercises, it's often calculated using the difference between the enthalpies of formation of the gaseous and liquid states of a substance, normally found in chemistry data tables or appendices.
For students grappling with this concept, it's important to remember that precisely calculated values of $\mathrm{\Delta }{H}_{vap}^{\circ }$ are key in accurately estimating boiling points and are also used as inputs for applying Trouton's rule.

Standard Molar Entropy of Vaporization

The standard molar entropy of vaporization, $\mathrm{\Delta }{S}_{vap}^{\circ }$, represents the amount by which the entropy of a substance increases when it vaporizes at a constant temperature and pressure. Entropy characterizes the disorder or randomness in a system, and a phase transition from liquid to gas considerably increases this randomness as molecules move from a more ordered state to a less ordered one.
Trouton's rule, which states that for many liquids the $\mathrm{\Delta }{S}_{vap}^{\circ }$ is approximately 88 J/(mol·K) at the boiling point, simplifies the process of estimating the normal boiling point. However, this is an approximation and may not hold true for all substances, a limitation students should acknowledge when applying this rule to exercises.

Normal Boiling Point Estimation

Estimating the normal boiling point of a substance is a fundamental skill in chemistry. The normal boiling point is the temperature at which the vapor pressure of a liquid equals the externa atmospheric pressure, normally 1 atm. Using Trouton's rule and the enthalpy of vaporization, one can rearrange the formula $\mathrm{\Delta }{S}_{vap}^{\circ }=\frac{\mathrm{\Delta }{H}_{vap}^{\circ }}{T_b}$ to solve for $T_b$, the boiling point.
While estimating $T_b$, students should be aware that the approach relies on standard conditions and assumptions. Discrepancies between the estimated and actual normal boiling points can serve as a practical lesson on the limitations of theoretical models and the complexities of real-world substances.

Bromine Properties

Bromine $B{r}_2$ is a halogen element with distinctive properties that are often examined in chemistry. As a diatomic molecule, bromine exists as a reddish-brown liquid at room temperature. It's unique among the non-metals for being a liquid under standard conditions and has a high atomic number and atomic weight among the elements.
Understanding the properties of bromine, including its enthalpy of vaporization and boiling point, is important in a variety of chemical processes and industrial applications. When students approach exercises involving bromine, it highlights the applicability of theoretical chemistry concepts to actual substances with distinct physical and chemical properties.

Thermodynamics in Chemistry

Thermodynamics is a branch of physical science concerned with heat and energy and their conversion into work. In chemistry, thermodynamics helps us understand the energy changes that accompany chemical reactions and phase changes. Key concepts include the first and second laws of thermodynamics, entropy, and enthalpy.
In the context of educational exercises, students are exposed to thermodynamic principles such as the enthalpy of vaporization and entropy through practical examples like the estimation of boiling points. These principles form the foundation for more advanced studies in physical chemistry and are critical for understanding the behavior of chemical systems under various conditions.