Question

For entropy, enthalpy, or gibbs energy the change produced on mixing can be calculated from ∆fmix = fmix – nafa(pure) – nbfb(pure) where f = s, h, or g and n refers to the numbers of moles mixed. derive a general expression for ∆gmix and ∆smix in terms of xa and xb.

Answer 1

The general expression for changes in Gibbs free energy (ΔG_mix) and entropy (ΔS_mix) upon mixing is based on mole fractions of the substances being mixed and the individual pure substances' properties. Mole fractions and the provided equation are utilized to derive expressions for ΔG_mix and ΔSmix, and enthalpy and entropy values are essential to predict the spontaneity of chemical reactions.

Step-by-step explanation:

To calculate the change in Gibbs free energy (ΔG_mix) and the change in entropy (ΔS_mix) upon mixing two substances A and B, we use mole fractions and the provided equation Δf_mix = f_mix – n_af_a(pure) – n_bf_b(pure), where f represents the molar Gibbs energy or molar entropy of the substances. Let xa be the mole fraction of substance A and xb be the mole fraction of substance B, with x_a + x_b = 1. The general expression for ΔG_mix in terms of mole fractions is ΔG_mix = G_mix – n_aG_a(pure) – n_bG_b(pure) and similarly for ΔS_mix. When combining the standard enthalpy of formation and standard entropy, we can calculate the standard Gibbs free energy of formation to predict the spontaneity of reactions using Gibbs free energy (ΔG). If ΔG is negative, the reaction is spontaneous. To calculate ΔG, we subtract energy lost to entropy (ΔS) from the total energy change in the system (ΔH_enthalpy). The formula for ΔG is ΔG = ΔH - TΔS, where T is the absolute temperature.