Undergraduate
  1. General chemistry  1.1. Introduction to Chemistry  1.2. Atomic Structure  1.2.1. Subatomic particles  1.2.2. Atomic Model  1.2.3. Quantum numbers  1.2.4. Electron Configuration  1.2.5. Periodic trends  1.2.6. Isotopes and their applications  1.3. Chemical bond  1.3.1. Ionic bond  1.3.2. Covalent bonds  1.3.3. Metal Bond  1.3.4. Hybridization  1.3.5. Molecular geometry and VSEPR theory  1.3.6. Bond polarity and dipole moment  1.4. Stoichiometry  1.4.1. Mole concept  1.4.2. Empirical and molecular formula  1.4.3. Limiting reactant and excess reactant  1.4.4. Percent Yield and Purity  1.4.5. Dilution calculation  1.5. States of matter  1.5.1. Gas Laws  1.5.2. Matter and Intermolecular Forces  1.5.3. Solid and Crystal Structures  1.5.4. Phase diagram  1.5.5. Plasma and supercritical fluid  1.6. Chemical reactions  1.6.1. Types of Chemical Reactions  1.6.2. Balancing Chemical Equations  1.6.3. Thermochemical reactions  1.6.4. Reaction energy profiles  1.7. Solutions and Mixtures  1.7.1. Concentration units  1.7.2. Syndrome properties  1.7.3. Solubility and Solubility Rules  1.7.4. Henry's Law and Raoult's Law  1.7.5. Partition coefficient  1.8. Chemical equilibrium  1.8.1. Law of mass action  1.8.2. Le Chatelier's principle  1.8.3. Reaction quotient  1.8.4. To use this online calculator for Equilibrium Constant, enter Equilibrium Constant (Eq.) and hit the calculate button. Here is how the Equilibrium Constant calculation can be explained with given input values -> 0.05 = 0.05/0.  1.8.5. Acid-base balance  1.9. Acids and bases  1.9.1. Arrhenius, Brønsted–Lowry, and Lewis definitions  1.9.2. pH and pOH  1.9.3. Acid-base titration  1.9.4. Buffer Solution  1.9.5. Acid-base indicator  1.9.6. Polyprotic Acids and Bases  1.10. Electrochemistry  1.10.1. redox reactions  1.10.2. Galvanic and Electrolytic Cells  1.10.3. Nernst equation  1.10.4. Electrolysis  1.10.5. Faraday's laws of electrolysis  1.11. Thermodynamics  1.11.1. Laws of Thermodynamics  1.11.2. Enthalpy, entropy and Gibbs free energy  1.11.3. Spontaneity of reactions  1.11.4. Thermodynamic cycles (Hess's law, Carnot cycle)  1.12. Kinetics  1.12.1. Rate law and reaction order  1.12.2. Activation Energy and Catalyst  1.12.3. Collision theory  1.12.4. Reaction mechanism  1.12.5. Transition state theory
  2. Organic chemistry  2.1. Structure and relationships  2.1.1. Hybridisation in Carbon Compounds  2.1.2. Resonance and aromatization  2.1.3. Molecular orbitals  2.1.4. Inductive and mesomeric effects  2.2. Hydrocarbons  2.2.1. Hydrocarbons  2.2.2. Alkene  2.2.3. Alkynes  2.2.4. Aromatic compounds  2.2.5. Cycloalkanes and Conformation  2.3. Functional Group  2.3.1. Alcohols and phenols  2.3.2. Ethers and epoxides  2.3.3. Aldehyde and ketone  2.3.4. Carboxylic acids and derivatives  2.3.5. Amin  2.3.6. Esters and amides  2.3.7. Thiols and sulfides  2.4. Stereoscopic  2.4.1. Isomerism in Stereochemistry  2.4.2. Chirality and optical activity  2.4.3. Structural analysis  2.4.4. Diastereomers and Enantiomers  2.5.1. Substitution reactions  2.5.2. Elimination reactions  2.5.3. Addition reactions  2.5.4. Radical reactions  2.5.5. Rearrangement reactions  2.5.6. Pericyclic Reactions  2.6. Spectroscopy and structural analysis  2.6.1. Infrared Spectroscopy  2.6.2. Nuclear magnetic resonance spectroscopy  2.6.3. Mass Spectrometry  2.6.4. UV-visible spectroscopy  2.6.5. X-ray crystallography  2.7. Polymer chemistry  2.7.1. Addition and Condensation Polymers  2.7.2. Polymerization mechanism  2.7.3. Biodegradable Polymer  2.7.4. Conducting and smart polymers
  3. Inorganic chemistry  3.1. Coordination chemistry  3.1.1. Ligands and coordination compounds  3.1.2. Crystal field theory  3.1.3. Molecular Orbital Theory in Coordination Compounds  3.1.4. Jahn–Taylor distortion  3.2. Main Group Chemistry  3.2.1. Alkali and alkaline earth metals  3.2.2. Halogens and Noble Gases  3.2.3. Transition metals and their complexes  3.2.4. Lanthanides and Actinides  3.3. Solid state chemistry  3.3.1. Crystal lattices and unit cells  3.3.2. Defects in solids  3.3.3. Electrical and magnetic properties  3.3.4. Superconductivity  3.4. Bio-inorganic chemistry  3.4.1. Metal ions in biology  3.4.2. Enzymatic reactions with metals  3.4.3. Metal poisoning and detoxification  3.4.4. Metalloproteins and Metalloenzymes
  4. Physical chemistry  4.1. Quantum Chemistry  4.1.1. Wave–particle duality  4.1.2. Schrödinger Equation  4.1.3. Quantum Numbers and Orbitals  4.1.4. Atomic and molecular spectroscopy  4.2. Statistical mechanics  4.2.1. Maxwell–Boltzmann distribution  4.2.2. Partitioning functions  4.2.3. Bose–Einstein and Fermi–Dirac statistics  4.3. Chemical thermodynamics  4.3.1. Gibbs Free Energy  4.3.2. Phase transition  4.3.3. Thermodynamic efficiency  4.4. Surface chemistry  4.4.1. Absorption and Catalysis  4.4.2. Colloids and Emulsions
  5. Analytical Chemistry  5.1. Classical methods  5.1.1. Gravimetric Analysis  5.1.2. titrimeter  5.2. Instrumental methods  5.2.1. Chromatography  5.2.2. Spectroscopy  5.2.3. Electroanalytical methods  5.2.4. X-ray diffraction
  6. Industrial Chemistry  6.1. Petrochemistry  6.2. Chemical engineering principles  6.3. Green Chemistry  6.4. Pharmaceuticals and Drug Synthesis
  7. Biochemistry  7.1. Carbohydrates  7.2. Proteins and enzymes  7.3. Lipids and membranes  7.4. Nucleic acids  7.5. Metabolism and Bioenergetics  7.6. Enzyme kinetics and mechanism

Undergraduate → General chemistry → Electrochemistry → Introduction to Chemistry ↓


Nernst equation


The Nernst equation is an important formula in electrochemistry that allows us to calculate the electric potential of a cell under non-standard conditions. It is named after the German chemist Walther Nernst, who developed the equation. This equation is important for understanding how batteries work, predicting the direction of electrochemical reactions, and much more.

Understanding electrochemical cells

Before diving into the Nernst equation, it's important to understand what electrochemical cells are. An electrochemical cell is a device that generates electrical energy from a chemical reaction or facilitates a chemical reaction through the introduction of electrical energy.

An electrochemical cell has two electrodes: the anode and the cathode. These electrodes are immersed in the electrolyte. A simple way to think about an electrochemical cell is to imagine two beakers connected by a salt bridge. One beaker contains the anodic component where oxidation occurs, and the other beaker contains the cathodic component where reduction occurs.

Anode(oxidation) ---- Salt bridge ---- Cathode(reduction)

Cell potential and standard cell potential

The potential difference between these two electrodes is known as the cell potential or electromotive force (EMF). Cell potential is a measure of a cell's ability to produce energy. Under standard conditions (1 M concentration, 1 atm pressure, and 25°C), this potential is known as the standard cell potential, denoted as E°.

The formula for calculating the standard cell potential is:

E°_cell = E°_cathode - E°_anode

where E°_cathode and E°_anode are the standard electrode potentials for the cathode and anode, respectively.

Nernst equation

Standard potentials provide important reference values, but real cells often operate under non-standard conditions. This is where the Nernst equation comes in. The Nernst equation allows us to calculate the cell potential under any conditions.

E_cell = E°_cell - (RT/nF) * ln(Q)

Here's what each symbol represents:

  • E_cell is the cell potential under non-standard conditions.
  • E°_cell is the standard cell potential.
  • R is the universal gas constant (8.314 J/(mol K)).
  • T is the temperature in Kelvin.
  • n is the number of moles of electrons transferred in the reaction.
  • F is the Faraday constant (about 96485 C/mol).
  • Q is the reaction quotient, a measure of the ratio of products and reactants at any given time.

Simplified Nernst equation at room temperature

At room temperature (about 298 K), the Nernst equation can be simplified by substituting the values of R and F, yielding the more familiar form:

E_cell = E°_cell - (0.0592/n) * log(Q)

The logarithm used here is base 10. This form is often used in class because it simplifies calculations, especially with calculators. This simplified equation is especially useful for galvanic cells operating around standard temperature.

Example 1: Calculation at 298 K

Consider a cell reaction where n = 2 and E°_cell = 1.1 V. Let the reaction quotient Q = 0.01. Calculate E_cell.

E_cell = 1.1 - (0.0592/2) * log(0.01)
E_cell = 1.1 - 0.0296 * log(0.01)
e_cell = 1.1 - 0.0296 * (-2)
e_cell = 1.1 + 0.0592
E_cell = 1.16 V

Therefore, under these conditions, the cell potential is 1.16 volts.

Reaction quotient Q

The reaction quotient Q is a measure that helps adjust standard cell potentials for non-standard conditions. It is expressed as:

Q = [C]^c [D]^d / [A]^a [B]^b

where [A], [B], [C], and [D] represent the molar concentrations of the reactants and products, and a, b, c, and d are their respective stoichiometric coefficients.

Anode Cathode

Effect of concentration and temperature

The Nernst equation shows us that the concentrations of reactants and products, as well as temperature, can profoundly affect the cell potential. If the concentration of reactants increases, the potential also increases, promoting the forward reaction. Conversely, if the concentration of products increases, it lowers the potential, promoting the reverse reaction.

Temperature also plays an important role. As temperature increases, the kinetic energy of molecules increases, which can affect the potential. However, temperature effects are often less obvious than concentration changes, especially within moderate temperature ranges such as room temperature.

Example 2: Effect of increasing product concentration

Suppose we have a reaction where initially Q = 0.1 and E°_cell = 1.5 V and n=2. Calculate E_cell after increasing the product concentration so that Q = 10.

E_initial = 1.5 - (0.0592/2) * log(0.1)
E_initial = 1.5 - 0.0296 * (-1)
E_initial = 1.5 + 0.0296
E_initial = 1.5296 V

E_final = 1.5 - (0.0592/2) * log(10)
E_final = 1.5 - 0.0296 * 1
E_final = 1.5 - 0.0296
E_final = 1.4704 V

As observed, increasing the product concentration decreases the cell potential from 1.53 V to 1.47 V.

Applications of the Nernst equation

The Nernst equation is widely used in various scientific and engineering fields. Its applications are as follows:

  • Batteries: Predicting how a battery's capacity changes as it is discharged.
  • Electrolytic cells: Determining the minimum potential required to produce non-spontaneous reactions.
  • Chemistry and biochemistry: Processes such as photosynthesis and respiration can be better understood using the Nernst equation.
  • Environmental science: Studying redox reactions in the natural environment, such as reactions that affect water quality.

Limitations of the Nernst equation

Although the Nernst equation is powerful, it still has its limitations:

  • Ideal conditions: Conditions close to ideality are assumed, which may not always be true.
  • Concentration range: Works best for situations where the concentration is neither too low nor too high.
  • Temperature Sensitivity: Precise temperature changes require advanced modifications.

Conclusion

Understanding the Nernst equation is an important part of mastering electrochemistry. It ties together key concepts such as cell potential, reaction quotient, and the effects of non-standard conditions. Mastering this equation provides a deep understanding of how chemical energy is converted into electrical energy and vice versa, with far-reaching implications for technology and natural processes.

When delving deeper into electrochemistry, keep in mind the fundamental concepts behind the Nernst equation. With practice, the calculations become intuitive, and this empowers exploration into more complex and fascinating chemical systems.


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Nernst equation

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