The Gibbs free energy equation

Cells metabolize in an aqueous environment and, except for those of the cells, the thermodynamic properties of the reactants and products of growth-processes are those of these substances in aqueous solution. Values for the free energy, enthalpy, and entropy of formation of all substances from the elements at 298.15 K and 1 atm are referred to as thermodynamic properties. These can be found in several compendia [32-34] listed for quantities of one mol in a given standard state. In aqueous solution, all substances are taken to be at a concentration of one mol at unit activity for values of A , and of a hypothetical one mol at infinite dilution for Af//°. Values for Af5 can be calculated using the following form of the Gibbs free energy equation, where the superscript refers to the aqueous standard state. 

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Now, let s return to the Gibbs free energy equation to determine if hydrogen will react spontaneously with oxygen to form water. The equation for the reaction may be written as... 

Which of the following is NOT a variable in the Gibbs free energy equation, which determines reaction spontaneity ... 

Coupling-in-series Reactions are said to be coupled-inseries when the product of one reaction is the substrate for the next reaction the principle underlying this coupling is explained by reference to the Gibbs free energy equation. In the reaction A B, in the hypothetical pathway S —> P, reaction A to B is catalysed by enzyme E2 as follows ... 

The Gibbs free energy equation explains why glucose 6-phosphate cannot be formed, in vivo, from glucose and phosphate, as follows ... 

Define the change in entropy in the Gibbs free energy equation. 

Increasing temperature widens the solubility window (i.e., the largest distance between the solubility parameter values of two solvents for a given polymer). This can be perceived from the Gibbs free energy equation. The same holds true for the narrowing effect of increasing molar mass that diminishes the entropy term. 

FIGURE 8.14 The melting of ice is disfavored by enthalpy (+ AH) but favored by entropy (+ AS). The freezing of water is favored by enthalpy ( — AH) but disfavored by entropy (— AS). Below 0°C, the enthalpy term AH dominates the entropy term TAS in the Gibbs free-energy equation, so freezing is spontaneous. Above 0°C, the entropy term dominates the enthalpy term, so melting is spontaneous. At 0°C, the entropy and enthalpy terms are in balance. 

Nature prefers a lower enthalpy state. To accomplish this, energy must be lost. This means that nature prefers a AH (-). Nature also prefers states of increased entropy and chaos. Therefore, nature prefers AS (+). Substituting into the Gibbs Free Energy equation (and remembering that the temperature is in Kelvin so that there can be no zeros or negative values) ... 

O H WH According to the Gibbs Free Energy equation, AG = AH - TAS, the favored decrease in enthalpy (AH is -) and the favored increase in entropy (AS is +) AG will have a negative value. 

A similar expression is also obtained from the Gibbs free energy equation when pressure approaches zero. If the partial differentiation inside the integral is determined from an equation of state (EOS), then t/real can be calculated. For example, (777) from the van der Waals EOS is... 

The advantage of the application of the law of mass action is that the equilibrium exchange constant allows the calculation of other thermodynamic parameters, namely, the Gibbs free energy (Equation 1.84) ... 

Hopefully, you will recall that we can express the overall change in entropy in terms of parameters describing changes within the system alone, using (for a fixed pressure and temperature) the Gibbs free energy, Equation 10-21 in the preceding section (AG = -TA AZf-TAS). 

It should also be noted that in an elimination reaction, two molecules react to give three new molecules. In contrast, for a substitution reaction, two molecules react to form two new molecules. The change in entropy (AS °) is therefore greater for an elimination reaction. From the Gibbs free energy equation (see Section 4.9.1), AS0 is multiplied by the temperature (T), and the larger the TAS° term, the more favourable AG°. 

To evaluate reactions that take place at the electrode at a fundamental level, we first consider a thermodynamic perspective. Any thermodynamic analysis of a chemical reaction begins with the Gibbs free energy equation (1), which relates cell potentials directly to free energy... 

For the case of nucleation on porous membranes, if Equation 10.13 is applied to Equation 10.25, after appropriate arrangements, the surface term of the Gibbs free energy (Equation 10.26) for a nucleus formation is... 

Whether or not a chemical reaction will proceed spontaneously is determined by the change in standard free energy (AG" ). The standard free energy is calculated from the change in enthalpy (H" ) and the change in entropy (S" ) by the Gibbs free energy equation AG° = AH - TAS This calcrdation assumes that the reaction is done under standard conditions in solution with a concentration of 1 M and at 298.15 K. 

Or third, the AAHs and AASs are linearly related to each other for both the reference reaction and the new reaction. That is, for each reaction, as AH goes up AS increases also. In other words, they scale proportionately. In this scenario, the enthalpy and entropy compensate for each other, because in the Gibbs free energy equation (AG = AH - TAS) the enthalpy and entropy terms have opposite algebraic signs. 

Using the Gibbs free energy equation (AG = AH - TAS ) in combination with Eq. 8.64 leads to Eq. 8.65. Now the proportionality constant is seen to have units of temperature, and is referred to as the isokinetic or isoequilibrium temperature for kinetic or thermodynamic LFERs, respectively. 

Kd. The advantages of using the dissociation constant becomes clear when we consider the relationship between Kd and key kinetic as well as thermodynamic properties. As described above, Kd is linked not only to the Gibbs free energy (Equation 13.1) but also to the on and off rates (/Con, Aoff) of a ligand as Equation 13.6 defines. 

Similarly, from the definition of the Gibbs free energy. Equation (1.30),... 

Consider the combined first and second laws in terms of the Gibbs free energy, Equation (2.21). How many Maxwell reciprocal relations can be obtained from this equation Write each of them and comment on their physical significance. 

Why Because elimination reactions are entropically favored over substitution reactions (because the products are greater in number than the reactants). Hence AS° in the Gibbs free-energy equation, AG° = AH° T AS° is significant, and AS° will be increased by higher temperature since T is a coefficient, leading to a more negative (favorable) AG°. 

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