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 \(\Delta H_{\text {vap }}^{\circ}\) for \(\mathrm{Br}_{2}\) using data from Appendix \(C\). Assume that $\Delta H_{\text {vap }}^{\circ}$ remains constant with temperature and that Trouton's rule holds. (b) Look up the normal boiling point of \(\mathrm{Br}_{2}\) 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?

First, we need to find the standard molar enthalpy of vaporization (∆Hₐₚ°) for Br₂. You can find this value in Appendix C of your textbook or other chemistry references. The value for ∆Hₐₚ° for Br₂ is approximately 30 kJ/mol.

According to Trouton's rule, the standard molar entropy of vaporization for many liquids at their normal boiling points is about 88 J/mol·K. Therefore, for Br₂, we can assume: \[\Delta S_{\text{vap}}^{\circ} = 88\, \mathrm{J/mol} \cdot \mathrm{K}\]

To estimate the normal boiling point of Br₂, we can use the following relation between ∆Hₐₚ° and ∆Sₐₚ: \[\Delta H_{\text{vap}}^{\circ} = T_{\text{bp}} \cdot \Delta S_{\text{vap}}^{\circ}\] Now, we can rearrange the equation to solve for the normal boiling point (Tₒ) of Br₂: \[T_{\text{bp}} = \frac{\Delta H_{\text{vap}}^{\circ}}{\Delta S_{\text{vap}}^{\circ}}\] Plug in the values for ∆Hₐₚ° and ∆ Sₐₚ: \[T_{\text{bp}} = \frac{30,000\, \mathrm{J/mol}}{88\, \mathrm{J/mol} \cdot \mathrm{K}}\] \[T_{\text{bp}} \approx 340.9\, \mathrm{K}\] So, using Trouton's rule, the estimated normal boiling point of Br₂ is around 340.9 K.

Now, we need to compare our calculated value with the actual value for the normal boiling point of Br₂, which can be found in a chemistry handbook or on the WebElements website. The actual value is 332 K. There is a difference between our estimated value and the actual value. Possible sources of error and incorrect assumptions include: 1. Trouton's rule is an approximation, and it might not hold true for all substances, including halogens such as bromine. 2. We assumed that ∆Hₐₚ° remains constant with temperature, but it can vary for some substances. 3. Errors could also be introduced by using rounded values for ∆Hₐₚ° and ∆Sₐₚₙ. Despite these possible sources of errors, the estimated boiling point is still reasonably close to the actual value, demonstrating the usefulness of Trouton's rule as an estimation tool.