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

Verified step by step guidance

Step 1: Recall the Gibbs free energy equation: \( \Delta G = \Delta H - T \Delta S \). This equation helps determine the spontaneity of a reaction.

Step 2: Convert \( \Delta S \) from J/K to kJ/K by dividing by 1000, since \( \Delta H \) is given in kJ.

Step 3: For each scenario, substitute the given values of \( \Delta H \), \( \Delta S \), and \( T \) into the Gibbs free energy equation to calculate \( \Delta G \).

Step 4: Determine spontaneity: If \( \Delta G < 0 \), the reaction is spontaneous; if \( \Delta G > 0 \), the reaction is nonspontaneous.

Step 5: Determine if the reaction is exothermic or endothermic: If \( \Delta H < 0 \), the reaction is exothermic; if \( \Delta H > 0 \), the reaction is endothermic.

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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 spontaneity of a reaction at constant temperature and pressure. The change in Gibbs Free Energy (ΔG) is calculated using the equation ΔG = ΔH - TΔS, where ΔH is the change in enthalpy, T is the temperature in Kelvin, and ΔS is the change in entropy. A negative ΔG indicates a spontaneous reaction, while a positive ΔG indicates nonspontaneity.

Enthalpy (ΔH)

Enthalpy (ΔH) is a measure of the total heat content of a system. It can be classified as exothermic (ΔH < 0) when heat is released during a reaction, or endothermic (ΔH > 0) when heat is absorbed. The sign of ΔH is crucial for determining the energy changes associated with a reaction and influences the overall spontaneity when combined with entropy changes.

Entropy (ΔS)

Entropy (ΔS) is a measure of the disorder or randomness in a system. A positive ΔS indicates an increase in disorder, which generally favors spontaneity, while a negative ΔS suggests a decrease in disorder, which can hinder spontaneity. The interplay between ΔS and ΔH at a given temperature is essential for determining whether a reaction will occur spontaneously.

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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: ∆H_vap/T_bp ≈ 88 J/(K*mol) (a) Check the reliability of Trouton's rule for the liquids listed in the following table.

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Textbook Question

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: ∆H_vap/T_bp ≈ 88 J/(K*mol) (b) Explain why liquids tend to have the same value of ∆Hvap/Tbp.

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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?

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The following reaction, sometimes used in the laboratory to generate small quantities of oxygen gas, has ∆G° = -224.4 kJ/mol at 25°C:

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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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A mixture of 14.0 g of N2 and 3.024 g of H2 in a 5.00 L container is heated to 400 °C. Use the data in Appendix B to calculate the molar concentrations of N2, H2, and NH3 at equilibrium. Assume that ∆H° and ∆S° are independent of temperature, and remember that the standard state of a gas is defined in terms of pressure.