Textbook Question
Which of the following reactions has ∆Ssys> 0?(a) N2(g) + 3H2(g) -> 2NH3(g)(b) Ag+(aq) + Cl-(aq) -> AgCl(s)(c) 2H2O2(aq) -> 2H2O(l) + O2(g)(d) 2I(g) -> I2(g)
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Ch.18 - Thermodynamics: Entropy, Free Energy & Equilibrium
Chapter 18, Problem 5
Magnesium m#etal has ΔHfusion = 9.037 kJ>mol and ΔSfusion = 9.79 J>1K mol2. What is the melting point of magnesium in °C? (LO 11.4)(a) 0.923 °C (b) 923 °C(c) 650 °C (d) 1.08 * 103 °C
Verified step by step guidance1
Identify the given values: ΔH_fusion = 9.037 kJ/mol and ΔS_fusion = 9.79 J/(K mol).
Convert ΔH_fusion from kJ/mol to J/mol for consistency in units. Recall that 1 kJ = 1000 J.
Use the formula for the melting point (T_m) based on thermodynamics: T_m = ΔH_fusion / ΔS_fusion.
Plug the converted ΔH_fusion and ΔS_fusion values into the formula to calculate T_m in Kelvin.
Convert the temperature from Kelvin to Celsius using the formula: °C = K - 273.15.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Gibbs Free Energy
Gibbs Free Energy (G) is a thermodynamic potential that helps predict the direction of chemical reactions and phase changes. It combines enthalpy (ΔH) and entropy (ΔS) into a single value, allowing us to determine if a process is spontaneous at constant temperature and pressure. The relationship is given by the equation ΔG = ΔH - TΔS, where T is the temperature in Kelvin.
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Gibbs Free Energy of Reactions
Phase Change and Melting Point
The melting point of a substance is the temperature at which it transitions from solid to liquid. This process involves a change in enthalpy (ΔHfusion) and entropy (ΔSfusion). At the melting point, the Gibbs Free Energy change (ΔG) is zero, indicating that the solid and liquid phases are in equilibrium.
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Calculating Melting Point
To find the melting point of magnesium, we can rearrange the Gibbs Free Energy equation to solve for temperature: T = ΔHfusion / ΔSfusion. By substituting the given values of ΔHfusion and ΔSfusion into this equation, we can calculate the melting point in Kelvin and then convert it to Celsius by subtracting 273.15.
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Related Practice
Textbook Question
What is the change in entropy (∆S) when 1.32 g of propane (C3H8) at 0.100 atm pressure is compressed by a factor of five at a constant temperature at 20°C? Assume that propane behaves as an ideal gas. (a) ∆S = +13 J/K(b) ∆S = -13 J/K (c) ∆S = - 0.40 J/K(d) ∆S = + 0.40 J/K
Textbook Question
Identify the true statement about a spontaneous process. (a) A reaction that is nonspontaneous in the forward direction is spontaneous in the reverse direction.(b) Adding a catalyst will cause a nonspontaneous reaction to become spontaneous.(c) In a spontaneous process, the entropy of the system always decreases.(d) An endothermic reaction is always spontaneous.
Textbook Question
Calculate ∆Stotal, and determine whether the reaction is spon-taneous or nonspontaneous under standard-state conditions. (a) -429 J/K; nonspontaneous (b) -123 J/K; spontaneous (c) +3,530 J/K; nonspontaneous (d) +184 J/K; nonspontaneous
Textbook Question
Consider the following endothermic reaction of gaseous AB3 molecules with A2 molecules. Identify the true statement about the spontaneity of the reaction. (a) The reaction is likely to be spontaneous at high temperatures. (b) The reaction is likely to be spontaneous at high temperatures. (c) The reaction is always spontaneous.(d) The reaction is always spontaneous.