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Chapter 19: Problem 94

(a) Write the chemical equations that correspond to \(\Delta G_{i}^{9}\) for \(\mathrm{CH}_{4}(g)\) and for \(\mathrm{NaCl}(s) .\) (b) For these formation reactions, compare \(\Delta G_{f}^{\circ}\) and \(\Delta H_{f}\). (c) In general, under which condition is \(\Delta G\), more negative (less positive) than \(\Delta H_{f}\) ? (i) When the temperature is high, (ii) when \(\Delta S_{f}^{\circ}\) is positive, (iii) when the reaction is reversible.

Short Answer

Expert verified
(a) The chemical equations for the Gibbs free energy of formation for CH₄(g) and NaCl(s) are: C(s) + 2H₂(g) → CH₄(g) Na(s) + 1/2Cl₂(g) → NaCl(s) (b) In both cases, ΔGf° is less negative (more positive) than ΔHf: For CH₄(g): ΔGf° = -50.8 kJ/mol, ΔHf = -74.8 kJ/mol For NaCl(s): ΔGf° = -384.1 kJ/mol, ΔHf = -411.0 kJ/mol (c) ΔG becomes more negative (less positive) than ΔH when the condition (ii) ΔSf° is positive.

Step by step solution

01

(a) Chemical Equations for Gibbs Free Energy of Formation

For CH₄(g) C(s) + 2H₂(g) → CH₄(g) For NaCl(s) Na(s) + 1/2Cl₂(g) → NaCl(s)
02

(b) Comparison of ΔGf° and ΔHf for CH₄(g) and NaCl(s)

For the formation reactions, the values of Gibbs free energy of formation (ΔGf°) and enthalpy of formation (ΔHf) can be found in standard thermodynamic tables. Let's compare the values for CH₄(g) and NaCl(s). For CH₄(g): ΔGf° = -50.8 kJ/mol ΔHf = -74.8 kJ/mol For NaCl(s): ΔGf° = -384.1 kJ/mol ΔHf = -411.0 kJ/mol In both cases, ΔGf° is less negative (more positive) than ΔHf.
03

(c) Condition for ΔG to be more negative (less positive) than ΔH

To analyze this situation, we need to consider the relationship between Gibbs free energy (ΔG), enthalpy (ΔH), and entropy (ΔS) at a constant temperature. The equation is given by: ΔG = ΔH - TΔS For ΔG to be more negative (less positive) than ΔH, the following condition must be true: ΔG < ΔH Substituting the equation above, we get: ΔH - TΔS < ΔH Which simplifies to: -TΔS < 0 Or: ΔS > 0 So, the condition under which ΔG becomes more negative (less positive) than ΔH is: (ii) When ΔSf° is positive.

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