Statistical mechanics is the part of physical chemistry that allows the prediction of thermodynamic properties from the data provided by quantum mechanics. Thus, from microscopic properties of matter (quantum) macroscopic properties such as entropy, heat capacities, internal energy, surface tension, viscosity,... can be obtained.
Statistical thermodynamics assumes that matter is made up of a large number of microscopic components that individually obey quantum mechanics, but collectively obey statistical laws. Statistical thermodynamics establishes a connection between the microscopic description and the macroscopic description of nature.
Based on the results at the molecular level that are obtained with quantum mechanics, statistical thermodynamics calculates directly observable properties.