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InterviewSolution
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3.47 The criterion of spontaneity in terms of Gibbsenergy is the same as that laid down by secondlaw of thermodynamics. How? |
| Answer» <p>Gibbs free energy and spontaneityWhen a process occurs at constant temperature \text TTT and pressure \text PPP, we can rearrange the second law of thermodynamics and define a new quantity known as Gibbs free energy:\text{Gibbs free energy}=\text G =\text H - \text{TS}Gibbs free energy=G=H−TSG, i, b, b, s, space, f, r, e, e, space, e, n, e, r, g, y, equals, G, equals, H, minus, T, Swhere \text HHH is enthalpy, \text TTT is temperature (in kelvin, \text KKK), and \text SSS is the entropy. Gibbs free energy is represented using the symbol \text GGG and typically has units of \dfrac{\text {kJ}}{\text{mol-rxn}} mol-rxnkJ start fraction, k, J, divided by, m, o, l, negative, r, x, n, end fraction. [Wait, how did we get this equation?][What is a mol-reaction?]\text{mol-rxn}m, o, l, negative, r, x, n\text{mol-reaction}m, o, l, negative, r, e, a, c, t, i, o, n2 \text{Al}(s)+ 3\text{Cl}_2(g) \rightarrow 2 \text{AlCl}_3(s) 2, A, l, left parenthesis, s, right parenthesis, plus, 3, C, l, start subscript, 2, end subscript, left parenthesis, g, right parenthesis, right arrow, 2, A, l, C, l, start subscript, 3, end subscript, left parenthesis, s, right parenthesis1122\text{Al}A, l33\text{Cl}_2 C, l, start subscript, 2, end subscript22\text{AlCl}_3 A, l, C, l, start subscript, 3, end subscript1\,\text{mol-rxn}=2\,\text{mol Al}=3\,\text{mol Cl}_2=2\,\text{mol AlCl}_3 1, space, m, o, l, negative, r, x, n, equals, 2, space, m, o, l, space, A, l, equals, 3, space, m, o, l, space, C, l, start subscript, 2, end subscript, equals, 2, space, m, o, l, space, A, l, C, l, start subscript, 3, end subscriptWhen using Gibbs free energy to determine the spontaneity of a process, we are only concerned with changes in \text GGG, rather than its absolute value. The change in Gibbs free energy for a process is thus written as \Delta \text GΔGdelta, G, which is the difference between \text G_{\text{final}}G final G, start subscript, f, i, n, a, l, end subscript, the Gibbs free energy of the products, and \text{G}_{\text{initial}}G initial G, start subscript, i, n, i, t, i, a, l, end subscript, the Gibbs free energy of the reactants.\Delta \text G =\text G_{\text{final}} - \text{G}_{\text{initial}}ΔG=G final −G initial delta, G, equals, G, start subscript, f, i, n, a, l, end subscript, minus, G, start subscript, i, n, i, t, i, a, l, end subscriptFor a process at constant \text TTT and constant \text PPP, we can rewrite the equation for Gibbs free energy in terms of changes in the enthalpy (\Delta \text H_{\text{system}}ΔH system delta, H, start subscript, s, y, s, t, e, m, end subscript) and entropy (\Delta \text S_{\text{system}}ΔS system delta, S, start subscript, s, y, s, t, e, m, end subscript) for our system:\Delta \text G_{\text{system}} =\Delta \text H_{\text{system}} - \text{T}\Delta \text S_{\text{system}}ΔG system =ΔH system −TΔS system delta, G, start subscript, s, y, s, t, e, m, end subscript, equals, delta, H, start subscript, s, y, s, t, e, m, end subscript, minus, T, delta, S, start subscript, s, y, s, t, e, m, end subscriptYou might also see this reaction written without the subscripts specifying that the thermodynamic values are for the system (not the surroundings or the universe), but it is still understood that the values for \Delta \text HΔHdelta, H and \Delta \text SΔSdelta, S are for the system of interest. This equation is exciting because it allows us to determine the change in Gibbs free energy using the enthalpy change, \Delta \text HΔHdelta, H, and the entropy change , \Delta \text SΔSdelta, S, of the system. We can use the sign of \Delta \text GΔGdelta, G to figure out whether a reaction is spontaneous in the forward direction, backward direction, or if the reaction is at equilibrium.When \Delta \text G<0ΔG<0delta, G, is less than, 0, the process is exergonic and will proceed spontaneously in the forward direction to form more products.When \Delta \text G>0ΔG>0delta, G, is greater than, 0, the process is endergonic and not spontaneous in the forward direction. Instead, it will proceed spontaneously in the reverse direction to make more starting materials.When \Delta \text G=0ΔG=0delta, G, equals, 0, the system is in equilibrium and the concentrations of the products and reactants will remain constant. [What is equilibrium?]</p> | |