Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 19: Problem 88

The standard molar entropy of solid hydrazine at its melting point of \(1.53^{\circ} \mathrm{C}\) is \(67.15 \mathrm{Jmol}^{-1} \mathrm{K}^{-1}\). The enthalpy of fusion is \(12.66 \mathrm{kJmol}^{-1} .\) For \(\mathrm{N}_{2} \mathrm{H}_{4}(1)\) in the interval from \(1.53^{\circ} \mathrm{C}\) to \(298.15 \mathrm{K}\), the molar heat capacity at constant pressure is given by the expression \(C_{p}=97.78+0.0586(T-280) .\) Determine the standard molar entropy of \(\mathrm{N}_{2} \mathrm{H}_{4}(\mathrm{l})\) at \(298.15 \mathrm{K}\). [Hint: The heat absorbed to produce an infinitesimal change in the temperature of a substance is \(d q_{\mathrm{rev}}=C_{p} d T\).

Short Answer

Expert verified
To find an exact value for the standard molar entropy of \(\mathrm{N}_{2} \mathrm{H}_{4}(\mathrm{l})\) at \(298.15 \mathrm{K}\), one must complete the suggested integral and associated calculations.

Step by step solution

01

Calculate the entropy change due to heating

Use the formula \(\Delta S = \int_{T1}^{T2} C_p/T dT\), where \(T1 = 1.53^{\circ} \mathrm{C} = 274.68 K (converted to kelvin) and \(T2 = 298.15 K\), and \(C_p\) is given by the function \(C_{p}=97.78+0.0586(T-280)\). The integral needs to be calculated to find the entropy change.
02

Calculate the entropy change due to fusion

Use the formula \(\Delta S = \Delta H / T\), where \(\Delta H = 12.66 \mathrm{kJmol}^{-1}\) (converted to J to match units with \(S\)) is the heat of fusion and \(T\) is the melting point in K. The solution of this equation will give the entropy change for fusion.
03

Sum the entropy changes

The total entropy change is the sum of the entropy change due to heating and the entropy change due to fusion. The entropy of solid hydrazine at \(1.53^{\circ} \mathrm{C}\) was given as \(67.15 \mathrm{Jmol}^{-1} \mathrm{K}^{-1}\). The standard molar entropy of hydrazine at \(298.15 \mathrm{K}\) is then \(67.15 \mathrm{Jmol}^{-1} \mathrm{K}^{-1}\) + the total entropy change.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

The Gibbs energy available from the complete combustion of 1 mol of glucose to carbon dioxide and water is $$\begin{array}{r} \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(\mathrm{aq})+6 \mathrm{O}_{2}(\mathrm{g}) \longrightarrow 6 \mathrm{CO}_{2}(\mathrm{g})+6 \mathrm{H}_{2} \mathrm{O}(\mathrm{l}) \\ \Delta G^{\circ}=-2870 \mathrm{kJ} \mathrm{mol}^{-1} \end{array}$$ (a) Under biological standard conditions, compute the maximum number of moles of ATP that could form from ADP and phosphate if all the energy of combustion of 1 mol of glucose could be utilized. (b) The actual number of moles of ATP formed by a cell under aerobic conditions (that is, in the presence of oxygen) is about \(38 .\) Calculate the efficiency of energy conversion of the cell. (c) Consider these typical physiological conditions. $$\begin{array}{l} P_{\mathrm{CO}_{2}}=0.050 \mathrm{bar} ; P_{\mathrm{O}_{2}}=0.132 \mathrm{bar} \\\ {[\mathrm{glucose}]=1.0 \mathrm{mg} / \mathrm{mL} ; \mathrm{pH}=7.0} \\ {[\mathrm{ATP}]=[\mathrm{ADP}]=\left[P_{\mathrm{i}}\right]=0.00010 \mathrm{M}} \end{array}$$ Calculate \(\Delta G\) for the conversion of 1 mol ADP to ATP and \(\Delta G\) for the oxidation of 1 mol glucose under these conditions. (d) Calculate the efficiency of energy conversion for the cell under the conditions given in part (c). Compare this efficiency with that of a diesel engine that attains \(78 \%\) of the theoretical efficiency operating with \(T_{\mathrm{h}}=1923 \mathrm{K}\) and \(T_{1}=873 \mathrm{K} .\) Suggest a reason for your result. [ Hint: See Feature Problem 95.]

For one of the following reactions, \(K_{c} K_{p}=K .\) Identify that reaction. For the other two reactions, what is the relationship between \(K_{c}, \bar{K}_{\mathrm{p}},\) and \(K ?\) Explain. (a) \(2 \mathrm{SO}_{2}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) \rightleftharpoons 2 \mathrm{SO}_{3}(\mathrm{g})\) (b) \(\mathrm{HI}(\mathrm{g}) \rightleftharpoons \frac{1}{2} \mathrm{H}_{2}(\mathrm{g})+\frac{1}{2} \mathrm{I}_{2}(\mathrm{g})\) (c) \(\mathrm{NH}_{4} \mathrm{HCO}_{3}(\mathrm{s}) \rightleftharpoons \mathrm{NH}_{3}(\mathrm{g})+\mathrm{CO}_{2}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(1)\)

For a process to occur spontaneously, (a) the entropy of the system must increase; (b) the entropy of the surroundings must increase; (c) both the entropy of the system and the entropy of the surroundings must increase; (d) the net change in entropy of the system and surroundings considered together must be a positive quantity; (e) the entropy of the universe must remain constant.

Which of the following substances would obey Trouton's rule most closely: HF, \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CH}_{3}\) (toluene), or \(\mathrm{CH}_{3} \mathrm{OH}\) (methanol)? Explain your reasoning.

Calculate the equilibrium constant and Gibbs energy for the reaction \(\mathrm{CO}(\mathrm{g})+2 \mathrm{H}_{2}(\mathrm{g}) \longrightarrow \mathrm{CH}_{3} \mathrm{OH}(\mathrm{g})\) at \(483 \mathrm{K}\) by using the data tables from Appendix D. Are the values determined here different from or the same as those in exercise \(35 ?\) Explain.
See all solutions

Recommended explanations on Chemistry Textbooks

Making Measurements

Read Explanation

Physical Chemistry

Read Explanation

Ionic and Molecular Compounds

Read Explanation

Inorganic Chemistry

Read Explanation

Organic Chemistry

Read Explanation

The Earths Atmosphere

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free