Key Equations in General Chemistry

Nernst Equation

The Nernst equation is used to calculate the cell potential of an electrochemical cell under non-standard conditions. It relates the standard cell potential to the concentrations (or partial pressures) of the reactants and products.

• Equation:

• Variables:

  • = cell potential under non-standard conditions

  • = standard cell potential

  • = ideal gas constant

  • = temperature in Kelvin

  • = number of moles of electrons transferred

  • = Faraday's constant

  • = reaction quotient

• Example: Calculating the cell potential for a galvanic cell with non-standard concentrations.

Two-Point Arrhenius Equation

The Arrhenius equation describes how the rate constant () of a reaction depends on temperature and activation energy. The two-point form allows calculation of at two different temperatures.

• Equation:

• Variables:

  • , = rate constants at temperatures and

  • = activation energy

  • = ideal gas constant

  • , = temperatures in Kelvin

• Example: Determining how a reaction rate changes with temperature.

Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation is used to estimate the pH of a buffer solution, relating pH to the acid dissociation constant and the ratio of conjugate base to acid.

• Equation:

• Variables:

  • = acidity of the solution

  • = negative log of the acid dissociation constant

  • = concentration of conjugate base

  • = concentration of acid

• Example: Calculating the pH of a buffer made from acetic acid and sodium acetate.

Rydberg Equation

The Rydberg equation predicts the wavelengths of spectral lines in hydrogen and hydrogen-like atoms.

• Equation:

• Variables:

  • = wavelength of emitted/absorbed light

  • = Rydberg constant

  • , = principal quantum numbers ()

• Example: Calculating the wavelength of light emitted during an electron transition in hydrogen.

Gibbs Free Energy Equations

Gibbs free energy () determines the spontaneity of a reaction. Several equations relate to equilibrium constant () and cell potential ().

• Standard Gibbs Free Energy:

• Relationship to Cell Potential:

• General Gibbs Free Energy:

• Variables:

  • = Gibbs free energy

  • = ideal gas constant

  • = temperature in Kelvin

  • = equilibrium constant

  • = moles of electrons

  • = Faraday's constant

  • = standard cell potential

  • = reaction quotient

• Example: Determining if a reaction is spontaneous at a given temperature.

Integrated Rate Laws

Integrated rate laws describe how reactant concentration changes over time for reactions of different orders.

• Zero Order:

• First Order:

• Second Order:

• Variables:

  • = concentration at time

  • = initial concentration

  • = rate constant

  • = time

• Example: Calculating how much reactant remains after a certain time for a first-order reaction.

Total Energy Equation

The total energy equation in thermodynamics relates the change in internal energy to heat and work. Both and are used interchangeably.

• Equation:

• Variables:

  • = change in internal energy

  • = heat

  • = work

• Example: Calculating the internal energy change when a system absorbs heat and does work.

Table of Fundamental Constants

The following constants are essential for calculations in general chemistry:

Example: These constants are used in equations such as the ideal gas law, electrochemistry, quantum mechanics, and thermodynamics.