The Ideal Gas Law combines Boyle's Law, Charles's Law, and Gay-Lussac's Law into a single equation: PV = nRT, where P is pressure, V is volume, n is the number of moles of gas, R is the ideal gas constant, and T is temperature.

The change in internal energy of a system is equal to the heat added to the system minus the work done by the system.

The work done by a system is equal to the negative of the pressure times the change in volume.

The heat capacity of a substance is equal to the amount of heat required to raise the temperature of the substance by one degree Celsius.

The efficiency of a heat engine is equal to the work done by the engine divided by the heat added to the engine.

The entropy of a system is equal to the Boltzmann constant multiplied by the natural logarithm of the number of microstates of the system.

The Gibbs free energy of a system is equal to the enthalpy of the system minus the temperature of the system multiplied by the entropy of the system.

The Helmholtz free energy of a system is equal to the internal energy of the system minus the temperature of the system multiplied by the entropy of the system.

The chemical potential of a substance is equal to the partial derivative of the Gibbs free energy of the system with respect to the number of moles of the substance, at constant temperature and pressure.

The equilibrium constant of a chemical reaction is equal to the ratio of the concentrations of the products to the concentrations of the reactants, at equilibrium.

The van 't Hoff factor is equal to the ratio of the change in temperature of a solution to the molal boiling point elevation constant multiplied by the molality of the solution.

Raoult's law states that the total vapor pressure of a solution is equal to the sum of the vapor pressures of the pure components of the solution.

Henry's law states that the partial pressure of a gas in a solution is proportional to the mole fraction of the gas in the solution.

The Clausius-Clapeyron equation relates the vapor pressure of a liquid to its temperature.

The Nernst equation relates the electromotive force of a cell to the concentrations of the reactants and products of the cell reaction.