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Chapter 19: Problem 95

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 \(\Delta H_{\text {vap }}^{t}\) for \(\mathrm{Br}_{2}\) using data from Appendix C. Assume that $\Delta H_{\text {ap }}^{a}$ remains constant with temperature and that Trouton's rule holds. (b) Look hal boiling point of Br\(r_{2}\) in a chemistry handbook or at the WebElements Web site (www,webelements. com) and compare it to your calculation. What are the possible sources of error, or incorrect assumptions, in the calculation?

Short Answer

Expert verified
The estimated normal boiling point of Br$_2$ using Trouton's rule is 340.45 K, while the actual boiling point is 332 K, resulting in a difference of about 8 K. Possible sources of error in the calculation include the approximations made by Trouton's rule, the assumption that ∆H$_\text{vap}$ remains constant with temperature, and potential errors in the data provided in Appendix C.

Step by step solution

01

Find the enthalpy of vaporization for Br_2 from the data

Using Appendix C, we can find the enthalpy of vaporization for bromine. The Appendix gives the following information: ∆H of vaporization for Br_2 = 29.96 kJ/mol Now, we need to determine the actual boiling point of Br_2.
02

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 88 J/mol-K. We can now relate this value to the enthalpy of vaporization we found earlier to estimate the boiling point: ∆S_vap = 88 J/mol-K ∆H_vap = 29,960 J/mol (convert kJ to J) Solving for the normal boiling point, we can use the following equation: T = ∆H_vap / ∆S_vap T = 29,960 J/mol / 88 J/mol-K T = 340.45 K So, the estimated normal boiling point of Br_2 is 340.45 K. #b) Compare the calculated value with the actual value and identify possible sources of error#
03

Look up the actual boiling point of Br_2

Referring to a chemistry handbook or a reliable online source like WebElements, find the actual normal boiling point of Br_2. According to WebElements, the actual normal boiling point of Br_2 is 332 K.
04

Compare and identify sources of error

Our estimated boiling point using Trouton's rule was 340.45 K, while the actual boiling point is 332 K. The difference between them is about 8 K. Possible sources of error in the calculation include: 1. Trouton's rule is an approximation that may not hold perfectly for all liquids. 2. Assumption that ∆H_vap remains constant with temperature, which might not be true in reality. 3. Errors in the data provided in Appendix C. As we can see, Trouton's rule provides a reasonable, but not perfectly accurate, estimate of the normal boiling point for Br_2.

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Most popular questions from this chapter

(a) What sign for \(\Delta S\) do you expect when the pressure on 0.600 mol of an ideal gas at \(350 \mathrm{~K}\) is increased isothermally from an initial pressure of 0.750 atm? (b) If the final pressure on the gas is 1.20 atm, calculate the entropy change for the process. (c) Do you need to specify the temperature to calculate the entropy change? Explain.

(a) How can we calculate \(\Delta S\) for an isothermal process? (b) Does \(\Delta S\) for a process depend on the path taken from the initial state to the final state of the system? Explain.

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