physical chemistry ch5 & some of ch6

chemical equilibrium in terms of a minimum of Gibbs energy with respect to extent of a reaction

Extent of Reaction

($n_i$ - $n_{i,0}$)/$\nu$_i

• $n_i$ is the current moles.

• $n_{i,0}$ is the initial moles.

• $\nu$_i is the stoichiometric coefficient (negative for reactants, positive for products)

The extent of reaction quantifies the progress of a chemical reaction in terms of the change in the number of moles of reactants and products, allowing for analysis of reaction completeness.

Gibbs energy under nonstandard conditions

The Gibbs energy under nonstandard conditions refers to the change in Gibbs free energy for a reaction at specified conditions that differ from standard state conditions. It is calculated using the equation: ${\Delta G}=\Delta{G}^{}{°}+RT{ln}Q$ , where $Q$ is the reaction quotient.

Gibbs Fundamental Equation

dG=−SdT+Vdp+∑μidni

Non-pV work

Delta G represents the maximum non-expansion work

Standard entropy Delta S (knot of reaction)

Sigma S products - Sigma S reactants

Maximum Extent

Maximum extent is determined by the limiting reactant. The point where one reactant is completely consumed. (ni=0)

Euler’s criterion

(dM/dy)x=(dN/dx)y

Delta G knot =-RTlnK

K>1 producted favored

K<1 reactants favored

Q in Delta G =Delta G knot + RTlnQ

Q<K reaction goes forward

Q>K, reaction goes backward

Gibbs and spontaneity vs equilibrium

dG<0: Spontaneous (Reaction proceeds forward).

dG=0: Equilibrium.

dG>0: Non-spontaneous (Reaction proceeds backward).

Matter flow

Matter moves spontaneously from a phase with higher chemical potential to a phase with lower chemical potential.

A chemical reaction is at equilibrium when

A chemical reaction is at equilibrium when the sum of the chemical potentials of the reactants and products (weighted by stoichiometry) equals zero:

∑νi μi =0

Slope of Delta G

The "Slope" Interpretation: If the slope (∂G/∂ξ ) is negative, the reaction must move forward (ξ increases) to reach the minimum energy.

Ideal Gas Chemical Potential:

μ=μ∘+RTln(P/P^o)

Gibbs and P vs V

1. The Standard Version (No negative sign)

ΔG=nRTln(Vf Vi )

• Logic: Since P∝1/V, the ratio Pf /Pi  is replaced by Vi /Vf .

2. The Version with a Negative Sign

If you want to keep the "final over initial" (Vf /Vi ) format inside the natural log, you must pull a negative sign out front using the log property ln(a/b)=−ln(b/a):

ΔG=−nRTln(Vi Vf )