4.3 Concentration Cells and Membrane Potentials

Concentration cells harness ion concentration differences to generate electric potential. These cells consist of two half-cells with the same electrolyte at different concentrations, connected by electrodes of the same material. The Nernst equation quantifies the relationship between cell potential and ion concentrations.

Membrane potentials are electrical differences across biological membranes, crucial for nerve impulses and cellular processes. They result from selective ion permeability and unequal ion distribution. Factors like ion concentrations, membrane permeability, and ion pumps influence membrane potentials, described by the Goldman-Hodgkin-Katz equation.

Concentration Cells

Principles of concentration cells

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• Concentration cells generate electric potential from differences in ion concentration between two half-cells
  • Both half-cells contain the same electrolyte at different concentrations (HCl, NaCl)
  • Electrodes in both half-cells are made of the same material (Ag, Pt)
• Half-cell with higher ion concentration acts as the anode, while the lower concentration half-cell acts as the cathode
• Electrons flow from anode to cathode through an external circuit, driven by the concentration gradient
• Electric potential generated depends on the ratio of ion concentrations in the two half-cells
  • Higher concentration ratio leads to a larger potential difference

Nernst equation for cell potentials

• Nernst equation relates concentration cell potential to ion concentrations in the two half-cells
  • $E = E^0 - \frac{RT}{nF} \ln \frac{[C]_1}{[C]_2}$
    • $E$ = cell potential at non-standard conditions
    • $E^0$ = standard cell potential
    • $R$ = universal gas constant (8.314 J/mol·K)
    • $T$ = absolute temperature (K)
    • $n$ = number of electrons transferred
    • $F$ = Faraday's constant (96,485 C/mol)
    • $[C]_1$ and $[C]_2$ = ion concentrations in the two half-cells
• Cell potential is directly proportional to the logarithm of the concentration ratio
  • Doubling the concentration ratio increases potential by $\frac{RT}{nF} \ln 2$
• Nernst equation allows calculation of cell potential at any given concentration ratio and temperature

Membrane Potentials

Membrane potentials in biology

• Membrane potentials are electrical potential differences across biological membranes (cell membranes)
  • Arise from selective permeability of the membrane to specific ions (Na⁺, K⁺, Cl⁻)
  • Unequal ion distribution creates concentration and electrical gradients across the membrane
• Membrane potentials are crucial for various biological processes
  • Transmission of nerve impulses in neurons
  • Regulation of ion and molecule transport across cell membranes
  • Muscle contraction and cellular homeostasis maintenance
• Resting membrane potential is the steady-state potential when the cell is not stimulated
  • Typically negative inside the cell relative to outside (−70 mV in neurons)

Factors affecting membrane potentials

• Several factors influence the magnitude and stability of membrane potentials
  1. Ion concentrations
     • Concentrations of Na⁺, K⁺, and Cl⁻ inside and outside the cell determine electrochemical gradients driving membrane potential
  2. Membrane permeability
     • Selective permeability to specific ions, controlled by ion channels and transporters, affects membrane potential
  3. Ion pumps
     • Active transport mechanisms (Na⁺/K⁺ ATPase pump) maintain ion concentration gradients by pumping ions against their electrochemical gradients
  4. Membrane capacitance
     • Lipid bilayer of the membrane acts as a capacitor, storing electrical charge and influencing rate of change of membrane potential
• Goldman-Hodgkin-Katz equation describes the relationship between ion concentrations, permeabilities, and membrane potential at equilibrium
  • $V_m = \frac{RT}{F} \ln \frac{P_{K}[K^+]_o + P_{Na}[Na^+]_o + P_{Cl}[Cl^-]_i}{P_{K}[K^+]_i + P_{Na}[Na^+]_i + P_{Cl}[Cl^-]_o}$
    • $V_m$ = membrane potential
    • $P_K$, $P_{Na}$, $P_{Cl}$ = membrane permeabilities to K⁺, Na⁺, and Cl⁻
    • $[X]_o$ and $[X]_i$ = concentrations of ion X outside and inside the cell