BackEssential Equations and Constants in General Chemistry
Study Guide - Smart Notes
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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:
Constant | Symbol | Value | Units |
|---|---|---|---|
Ideal Gas Constant | R | 8.314 | J mol-1 K-1 |
Faraday's Constant | F | 96,485 | C mol-1 |
Avogadro's Number | NA | 6.022 × 1023 | mol-1 |
Planck's Constant | h | 6.626 × 10-34 | J s |
Speed of Light | c | 2.998 × 108 | m s-1 |
Example: These constants are used in equations such as the ideal gas law, electrochemistry, quantum mechanics, and thermodynamics.
