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- https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Physical_Chemistry_(LibreTexts)/17%3A_Boltzmann_Factor_and_Partition_FunctionsThis page discusses how Statistical Mechanics connects microscopic atomic behavior to macroscopic properties like temperature and pressure, forming the basis for thermodynamics. It covers key concepts...This page discusses how Statistical Mechanics connects microscopic atomic behavior to macroscopic properties like temperature and pressure, forming the basis for thermodynamics. It covers key concepts such as the Boltzmann factor for particle distributions, the Boltzmann distribution for thermal equilibrium, and the role of heat capacity in linking energy to temperature. Partition functions are also mentioned for their role in describing system states.
- https://chem.libretexts.org/Bookshelves/Analytical_Chemistry/Instrumental_Analysis_(LibreTexts)/32%3A_Radiochemical_MethodsRadiochemical methods of analysis take advantage of the instability of some elemental isotopes, which decay through the release of alpha particles, beta particles, gamma rays, and/or X-rays, provide f...Radiochemical methods of analysis take advantage of the instability of some elemental isotopes, which decay through the release of alpha particles, beta particles, gamma rays, and/or X-rays, provide for a selective analysis for one analyte in a complex mixture of other species without the need for a prior separation. In this chapter we review the basics of radioactive decay and its direct application to samples, and two other methods of importance: neutron activation and isotope dilution.
- https://chem.libretexts.org/Bookshelves/Introductory_Chemistry/Introductory_Chemistry_(CK-12)/10%3A_The_Mole/10.01%3A_Avogadro's_NumberThis page explains Avogadro's number, 6.02 \times 10^{23}, which quantifies the number of representative particles in a mole, allowing chemists to measure atoms and molecules. It discusses the mol...This page explains Avogadro's number, 6.02 \times 10^{23}, which quantifies the number of representative particles in a mole, allowing chemists to measure atoms and molecules. It discusses the mole as the SI unit for substance amount, with representative particles being atoms for elements and molecules for compounds. Additionally, it mentions National Mole Day, celebrating this key chemistry concept.
- https://chem.libretexts.org/Courses/Western_Washington_University/Biophysical_Chemistry_(Smirnov_and_McCarty)/01%3A_Biochemical_Thermodynamics/1.05%3A_The_Boltzmann_Distribution_and_the_Statistical_Definition_of_EntropyIn this chapter we introduce the statistical definition of entropy as formulated by Boltzmann. This allows us to consider entropy from the perspective of the probabilities of different configurations ...In this chapter we introduce the statistical definition of entropy as formulated by Boltzmann. This allows us to consider entropy from the perspective of the probabilities of different configurations of the constituent interacting particles in an ensemble. This conception of entropy led to the development of modern statistical thermodynamics. For systems that can exchange thermal energy with the surroundings, the equilibrium probability distribution will be the Boltzmann distribution.
- https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Physical_Chemistry_(LibreTexts)/17%3A_Boltzmann_Factor_and_Partition_Functions/17.02%3A_The_Boltzmann_Distribution_represents_a_Thermally_Equilibrated_DistributionThis page explores the relationship between energy states and the total number of systems in an ensemble, highlighting the Boltzmann distribution's role in predicting system occupancy based on energy ...This page explores the relationship between energy states and the total number of systems in an ensemble, highlighting the Boltzmann distribution's role in predicting system occupancy based on energy levels. It introduces the molecular partition function, q, showing its dependence on temperature for determining thermally accessible states.
- https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Physical_Chemistry_(LibreTexts)/18%3A_Partition_Functions_and_Ideal_GasesThis page explores the treatment of dilute gases as ideal gas systems using ensemble theory and the molecular partition function. It covers translational partition functions, molecular states probabil...This page explores the treatment of dilute gases as ideal gas systems using ensemble theory and the molecular partition function. It covers translational partition functions, molecular states probabilities, and contributions of various energy types (translational, vibrational, rotational) to total molecular energy. Additionally, it discusses molecular symmetries and the equipartition principle's effects on heat capacities and structures of diatomic and polyatomic molecules.
- https://chem.libretexts.org/Bookshelves/Introductory_Chemistry/Introductory_Chemistry_(CK-12)/04%3A_Atomic_Structure/4.01%3A_Democritus'_Idea_of_the_AtomThis page discusses the philosophical debate on the nature of matter between ancient Greeks Aristotle and Democritus. Aristotle believed matter could be divided infinitely, while Democritus introduced...This page discusses the philosophical debate on the nature of matter between ancient Greeks Aristotle and Democritus. Aristotle believed matter could be divided infinitely, while Democritus introduced the idea of atoms as indivisible particles. Although Democritus's concepts lacked experimental support and were overshadowed by Aristotle's views for centuries, they eventually became foundational to modern science, taking about 2,000 years for acceptance.
- https://chem.libretexts.org/Bookshelves/Introductory_Chemistry/Introductory_Chemistry_(CK-12)/10%3A_The_Mole/10.08%3A_Mole_Road_MapThis page explains the "mole road map" in chemistry, which aids in understanding moles for calculations related to mass, particle number, and gas volume at STP. It presents a structured method for con...This page explains the "mole road map" in chemistry, which aids in understanding moles for calculations related to mass, particle number, and gas volume at STP. It presents a structured method for conversions and includes an example of calculating the volume of 79.3 g of neon gas, resulting in 88.0 L. The mole road map is emphasized as a valuable tool for systematic problem-solving in chemistry.
- https://chem.libretexts.org/Bookshelves/Introductory_Chemistry/Introductory_Chemistry_(CK-12)/10%3A_The_Mole/10.05%3A_Conversions_Between_Mass_and_Number_of_ParticlesThis page outlines Avogadro's contributions to gas laws, focusing on the connections between gas volume, particle count, and mass. It details the conversion of mass to the number of particles through ...This page outlines Avogadro's contributions to gas laws, focusing on the connections between gas volume, particle count, and mass. It details the conversion of mass to the number of particles through moles, featuring an example with 20 grams of chlorine gas (\ce{Cl_2}). The summary highlights the calculation methods and includes review questions to reinforce understanding of mass and particle conversions.
- https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Physical_Chemistry_(LibreTexts)/17%3A_Boltzmann_Factor_and_Partition_Functions/17.05%3A_Pressure_can_be_Expressed_in_Terms_of_the_Canonical_Partition_FunctionThis page explains the derivation of pressure from the canonical partition function in statistical mechanics, linking it to thermodynamic principles and the ideal gas law. It includes equations that r...This page explains the derivation of pressure from the canonical partition function in statistical mechanics, linking it to thermodynamic principles and the ideal gas law. It includes equations that relate average pressure to energy and the partition function, along with a thought experiment illustrating gas compression with a piston.
- https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Physical_Chemistry_(LibreTexts)/17%3A_Boltzmann_Factor_and_Partition_Functions/17.07%3A_Partition_Functions_of_Indistinguishable_Molecules_Must_Avoid_Over_Counting_StatesThis page discusses the partition function in statistical mechanics, comparing calculations for distinguishable and indistinguishable particles. Using a two-particle model, it shows that distinguishab...This page discusses the partition function in statistical mechanics, comparing calculations for distinguishable and indistinguishable particles. Using a two-particle model, it shows that distinguishable particles have four states, leading to a squared partition function. In contrast, indistinguishable particles have three states, requiring a modification to the partition function through a factor of N! to prevent overcounting.
