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In chemistry, the standard state for a solution is 1 $M$ (see Table 17.2 ). This means that each solute concentration expressed in molarity is divided by 1 $M$. In biological systems, however, we define the standard state for the $\mathrm{H}^{+}$ ions to be $1 \times 10^{-7}$ $M$ because the physiological $\mathrm{pH}$ is about 7 Consequently, the change in the standard Gibbs free energy according to these two conventions will be different involving uptake or release of $\mathrm{H}^{+}$ ions, depending on which convention is used. We will therefore replace $\Delta G^{\circ}$ with $\Delta G^{\circ \prime},$ where the prime denotes that it is the standard Gibbs freeenergy change for a biological process. (a) Consider the reaction $A+B \longrightarrow C+x H^{+}$ where $x$ is a stoichiometric coefficient. Use Equation (17.13) to derive a relation between $\Delta G^{\circ}$ and $\Delta G^{\circ \prime},$ keeping in mind that $\Delta G$ is the same for a process regardless of which convention is used. Repeat the derivation for the reverse process: $\mathbf{C}+x \mathbf{H}^{+} \longrightarrow \mathbf{A}+\mathbf{B}$(b) $\mathrm{NAD}^{+}$ and $\mathrm{NADH}$ are the oxidized and reduced forms of nicotinamide adenine dinucleotide, two key compounds in the metabolic pathways. For the oxidation of NADH: $\mathrm{NADH}+\mathrm{H}^{+} \longrightarrow \mathrm{NAD}^{+}+\mathrm{H}_{2}$ $\Delta G^{\circ}$ is $-21.8 \mathrm{kJ} / \mathrm{mol}$ at $298 \mathrm{K}$. Calculate $\Delta G^{\circ}.$ Also calculate $\Delta G$ using both the chemical and biological conventions when $[\mathrm{NADH}]=1.5 \times 10^{-2}$ $M,\left[\mathrm{H}^{+}\right]=3.0 \times 10^{-5} M,[\mathrm{NAD}]=4.6 \times 10^{-3} M,$ and $P_{\mathrm{H}_{2}}=0.010 \mathrm{atm}.$

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a. $\Delta G^{o}=\Delta G^{o^{\prime}}-\mathrm{xRTln}\left(\frac{1}{1 x 10^{-7}}\right)$b. $\Delta G=-10.3 \mathrm{kJ} / \mathrm{mol}$

Chemistry 102

Chapter 17

Entropy, Free Energy, and Equilibrium

Thermodynamics

University of Kentucky

University of Toronto

Lectures

00:42

In thermodynamics, the zeroth law of thermodynamics states that if two systems are in thermal equilibrium with a third system, they are also in thermal equilibrium with each other.

01:47

A spontaneous process is one in which the total entropy of the universe increases. In a spontaneous process, the system will move from an ordered state to a disordered state, such as from ice to water, or from a solid to a gas. The concept of spontaneity was introduced by Rudolf Clausius in 1850.

02:06

In chemistry, the standard…

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