As we saw in Chapter 18, the free energy (ΔG) of a reaction is related to the cell potential by

step 1 To find delta G for the transport of N .A. plus ions from the side of higher concentration to th

As we saw in Chapter 18, the free energy (ΔG) of a reaction...

As we saw in Chapter $18,$ the free energy $(\Delta G)$ of a reaction is related to the cell potential by the equation $\Delta G=-n F E .$ In Figure $P 21.5,$ two solutions of $\mathrm{Na}^{+}$ of different concentrations are separated by a semipermeable membrane. Calculate $\Delta G$ for the transport of $\mathrm{Na}^{+}$ from the side with higher concentration to the side with lower concentration. (Hint: See Problem 21.45.) (FIGURE CAN'T COPY)

Key Concepts

Free Energy (?G)

Free energy represents the maximum work obtainable from a process at constant temperature and pressure. In electrochemistry, a negative value indicates that the process, such as ion transport or a redox reaction, can occur spontaneously, and it quantifies the overall energy change, calculated by the relationship ?G = -n F E.

Cell Potential (E)

Cell potential is the electrical potential difference between two points in an electrochemical cell. It reflects the work done per charge transferred when a reaction occurs, and it directly relates to free energy changes in the system via the equation ?G = -n F E.

Nernst Equation

The Nernst equation provides a quantitative relation between the concentration gradient of ions and the resulting electrical potential difference across a membrane or cell. It is an essential tool for calculating the potential difference induced by non-standard conditions such as differing ion concentrations.

Concentration Gradient and Ion Transport

A concentration gradient refers to a difference in the amount of a substance between two regions. In the context of ion transport, this gradient drives the movement of ions across a semipermeable membrane, and the energy associated with this movement can be calculated using principles from thermodynamics and electrochemistry.

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