Domanda del libro di testo
Is it possible for a reaction to be nonspontaneous yet exo-thermic? Explain.
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Ch.18 - Thermodynamics: Entropy, Free Energy & Equilibrium
McMurry8th EditionChemistryISBN: 9781292336145
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TOC.tableOfContents
- Ch.1 - Chemical Tools: Experimentation & Measurement170
- Ch.2 - Atoms, Molecules & Ions160
- Ch.3 - Mass Relationships in Chemical Reactions169
- Ch.4 - Reactions in Aqueous Solution199
- Ch.5 - Periodicity & Electronic Structure of Atoms102
- Ch.6 - Ionic Compounds: Periodic Trends and Bonding Theory92
- Ch.7 - Covalent Bonding and Electron-Dot Structures61
- Ch.8 - Covalent Compounds: Bonding Theories and Molecular Structure59
- Ch.9 - Thermochemistry: Chemical Energy122
- Ch.10 - Gases: Their Properties & Behavior155
- Ch.11 - Liquids & Phase Changes54
- Ch.12 - Solids and Solid-State Materials73
- Ch.13 - Solutions & Their Properties120
- Ch.14 - Chemical Kinetics98
- Ch.15 - Chemical Equilibrium125
- Ch.16 - Aqueous Equilibria: Acids & Bases110
- Ch.17 - Applications of Aqueous Equilibria147
- Ch.18 - Thermodynamics: Entropy, Free Energy & Equilibrium86
- Ch.19 - Electrochemistry154
- Ch.20 - Nuclear Chemistry96
- Ch.21 - Transition Elements and Coordination Chemistry156
- Ch.22 - The Main Group Elements187
- Ch.23 - Organic and Biological Chemistry51
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McMurry 8th EditionCh.18 - Thermodynamics: Entropy, Free Energy & EquilibriumProblema 128
McMurry 8th EditionCh.18 - Thermodynamics: Entropy, Free Energy & EquilibriumProblema 128Capitolo 18, Problema 128
The normal boiling point of bromine is 58.8 °C, and the standard entropies of the liquid and vapor are S°[Br2(l) = 152.2 J/(K*mol); S°[Br2(g) = 245.4 J/(K*mol). At what temperature does bromine have a vapor pressure of 227 mmHg?
Guida verificata passo dopo passo1
Convert the given vapor pressure from mmHg to atm using the conversion factor (1 atm = 760 mmHg).
Use the Clausius-Clapeyron equation to relate the change in vapor pressure with temperature. The equation is: \(\ln\left(\frac{P_2}{P_1}\right) = \frac{\Delta H_{vap}}{R}\left(\frac{1}{T_1} - \frac{1}{T_2}\right)\), where \(P_1\) and \(P_2\) are the initial and final pressures, \(T_1\) and \(T_2\) are the initial and final temperatures, \(\Delta H_{vap}\) is the enthalpy of vaporization, and R is the gas constant.
Calculate the enthalpy of vaporization (\(\Delta H_{vap}\)) using the entropy values at the boiling point. The relationship is \(\Delta H_{vap} = T_{boil} \times (S°[Br2(g)] - S°[Br2(l)])\), where \(T_{boil}\) is the boiling temperature in Kelvin.
Substitute the known values into the Clausius-Clapeyron equation. Use the boiling point of bromine as \(T_1\) and convert it to Kelvin by adding 273.15 to the Celsius value. Solve for \(T_2\) in Kelvin.
Convert the final temperature \(T_2\) from Kelvin back to Celsius by subtracting 273.15.
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Boiling Point and Vapor Pressure
The boiling point of a substance is the temperature at which its vapor pressure equals the external pressure surrounding the liquid. For bromine, the normal boiling point is 58.8 °C at 1 atm pressure. When the vapor pressure of a liquid reaches a specific value, such as 227 mmHg, it indicates the temperature at which the liquid will boil under that pressure.
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Percorso guidato
03:05
Boiling Point Elevation
Entropy and Phase Changes
Entropy is a measure of the disorder or randomness in a system. In phase changes, such as from liquid to gas, the entropy of the gas is typically higher than that of the liquid due to increased molecular motion. The standard entropies provided for liquid and vapor bromine (152.2 J/(K*mol) and 245.4 J/(K*mol), respectively) are essential for calculating the temperature at which the vapor pressure reaches 227 mmHg.
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01:46Entropy in Phase Changes
Clausius-Clapeyron Equation
The Clausius-Clapeyron equation relates the change in vapor pressure with temperature to the enthalpy of vaporization. It can be used to determine the temperature at which a specific vapor pressure occurs by incorporating the entropies of the liquid and vapor phases. This equation is crucial for solving the problem of finding the temperature at which bromine has a vapor pressure of 227 mmHg.
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00:59Clausius-Clapeyron Equation
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Domanda del libro di testo
Trouton's rule says that the ratio of the molar heat of vaporization of a liquid to its normal boiling point (in kelvin) is approximately the same for all liquids: ∆Hvap/Tbp ≈ 88 J/(K*mol) (b) Explain why liquids tend to have the same value of ∆Hvap/Tbp.
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Domanda del libro di testo
Tell whether reactions with the following values of ΔH and ΔS are spontaneous or nonspontaneous and whether they are exothermic or endothermic. (a) ΔH = - 48 kJ; ΔS = + 135 J>K at 400 K
(b) ΔH = - 48 kJ; ΔS = - 135 J>K at 400 K
(c) ΔH = + 48 kJ; ΔS = + 135 J>K at 400 K
(d) ΔH = + 48 kJ; ΔS = - 135 J>K at 400 K
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Domanda del libro di testo
Suppose that a reaction has ΔH = - 33 kJ and ΔS = - 58 J>K. At what temperature will it change from spontaneous to nonspontaneous?
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Domanda del libro di testo
The following reaction, sometimes used in the laboratory to generate small quantities of oxygen gas, has ∆G° = -224.4 kJ/mol at 25°C: Use the following additional data at 25 °C to calculate the standard molar entropy S° of O2 at 25°C: ∆H°f(KClO3) = -397.7 kJ/mol, ∆H°f(KCl) = -436.5 kJ/mol, S°(KClO3) = 143.1 J/(K*mol), and S°(KCl) = 82.6 J/(K*mol).
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Domanda del libro di testo
Trouton's rule says that the ratio of the molar heat of vaporization of a liquid to its normal boiling point (in kelvin) is approximately the same for all liquids: ∆Hvap/Tbp ≈ 88 J/(K*mol) (a) Check the reliability of Trouton's rule for the liquids listed in the following table.
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