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- https://chem.libretexts.org/Courses/Los_Angeles_Trade_Technical_College/Analytical_Chemistry/2%3A_Analytical_Chemistry_2.0_(Harvey)/05%3A_Evaluating_Analytical_Data/5.04%3A_The_Distribution_of_Measurements_and_ResultsA population is the set of all objects in the system we are investigating. For our experiment, the population is all United States pennies in circulation. This population is so large that we cannot an...A population is the set of all objects in the system we are investigating. For our experiment, the population is all United States pennies in circulation. This population is so large that we cannot analyze every member of the population. Instead, we select and analyze a limited subset, or sample of the population.
- https://chem.libretexts.org/Bookshelves/Analytical_Chemistry/Instrumental_Analysis_(LibreTexts)/35%3A_Appendicies/35.03%3A_Critical_Values_for_t-TestIn the first approach we choose a value of α for rejecting the null hypothesis and read the value of t(α,ν) from the table below. In the second approach, we find the row in the tab...In the first approach we choose a value of α for rejecting the null hypothesis and read the value of t(α,ν) from the table below. In the second approach, we find the row in the table below that corresponds to the available degrees of freedom and move across the row to find (or estimate) the a that corresponds to texp=t(α,ν); this establishes largest value of α for which we can retain the null hypothesis.
- https://chem.libretexts.org/Courses/University_of_North_Carolina_Charlotte/CHEM_2141%3A__Survey_of_Physical_Chemistry/10%3A_Molecular_Spectroscopy/10.09%3A_Normal_Modes_in_Polyatomic_MoleculesThis page discusses normal modes as independent vibrational motions in molecules, defined by symmetries and their roles in IR and Raman spectroscopy. Molecules have 3N degrees of freedom, with nonline...This page discusses normal modes as independent vibrational motions in molecules, defined by symmetries and their roles in IR and Raman spectroscopy. Molecules have 3N degrees of freedom, with nonlinear and linear molecules having 3N-6 and 3N-5 vibrational degrees, respectively. Each vibrational mode acts as a harmonic oscillator, contributing to energy. Normal coordinates aid in analyzing vibrations by simplifying equations.
- https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Book%3A_Quantum_States_of_Atoms_and_Molecules_(Zielinksi_et_al)/06%3A_Vibrational_States/6.01%3A_Spatial_Degrees_of_Freedom_Normal_Coordinates_and_Normal_ModesThe motion of the atomic nuclei in a molecule is not as simple as translating each of the nuclei independently along the x, y, and z axes because the nuclei, which are positively charged, are coupled ...The motion of the atomic nuclei in a molecule is not as simple as translating each of the nuclei independently along the x, y, and z axes because the nuclei, which are positively charged, are coupled together by the electrostatic interactions with the electrons, which are negatively charged.
- https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Symmetry_(Vallance)/01%3A_Chapters/1.24%3A_Molecular_Vibrationsvibrational motions of polyatomic molecules are much more complicated than those in a diatomic. Since changing one bond length in a polyatomic will often affect the length of nearby bonds, we cannot c...vibrational motions of polyatomic molecules are much more complicated than those in a diatomic. Since changing one bond length in a polyatomic will often affect the length of nearby bonds, we cannot consider the vibrational motion of each bond in isolation; instead we talk of normal modes involving the concerted motion of groups of bonds. Group theory may be used to identify the symmetries of the translational, rotational and vibrational modes of motion of a molecule.
- https://chem.libretexts.org/Courses/Los_Angeles_Trade_Technical_College/Analytical_Chemistry/2%3A_Analytical_Chemistry_2.0_(Harvey)/15%3A_Developing_a_Standard_Method/15.3%3A_Validating_the_Method_as_a_Standard_MethodFor an analytical method to be useful, an analyst must be able to achieve results of acceptable accuracy and precision. Verifying a method, as described in the previous section, establishes this goal ...For an analytical method to be useful, an analyst must be able to achieve results of acceptable accuracy and precision. Verifying a method, as described in the previous section, establishes this goal for a single analyst. Another requirement for a useful analytical method is that an analyst should obtain the same result from day to day, and different labs should obtain the same result when analyzing the same sample. The process by which we approve method for general use is known as validation.
- https://chem.libretexts.org/Bookshelves/Analytical_Chemistry/Analytical_Chemistry_2.1_(Harvey)/04%3A_Evaluating_Analytical_Data/4.06%3A_Statistical_Methods_for_Normal_DistributionsThis page discusses the use of statistical tests to compare means and variances in analytical chemistry. Key methods include the t-test for comparing sample means, the F-test for variances, and signif...This page discusses the use of statistical tests to compare means and variances in analytical chemistry. Key methods include the t-test for comparing sample means, the F-test for variances, and significance tests for outliers like Dixon's Q-test, Grubb's test, and Chauvenet's criterion. The tests help determine if observed differences are significant or due to chance, aiding in validating analytical methods or identifying errors in analyses.
- https://chem.libretexts.org/Bookshelves/Analytical_Chemistry/Analytical_Chemistry_2.1_(Harvey)/16%3A_Appendix/16.04%3A_Critical_Values_for_t-TestThe page describes two approaches to interpreting a t-test once t_{exp} has been calculated. The first approach involves selecting an alpha value to reject the null hypothesis and comparing t_{exp} ag...The page describes two approaches to interpreting a t-test once t_{exp} has been calculated. The first approach involves selecting an alpha value to reject the null hypothesis and comparing t_{exp} against the critical t-values from a table. If t_{exp}) is greater, the null hypothesis is rejected.
- https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Physical_Chemistry_(LibreTexts)/18%3A_Partition_Functions_and_Ideal_Gases/18.07%3A_Vibrational_Partition_Functions_of_Polyatomic_Molecules_Include_the_Partition_Function_for_Each_Normal_CoordinateThis page explores the partition function of polyatomic molecules by approximating their energy through individual degrees of freedom. It explains translational, rotational, vibrational, and electroni...This page explores the partition function of polyatomic molecules by approximating their energy through individual degrees of freedom. It explains translational, rotational, vibrational, and electronic partition functions, with a focus on how normal modes describe vibrational motion. The vibrational energy and entropy relate to the potential energy surface's shape. For NO2 at 300 K, calculations indicate limited vibrational states, yielding a vibrational activity product of 1.
- https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Physical_Chemistry_(LibreTexts)/12%3A_Group_Theory_-_The_Exploitation_of_Symmetry/12.10%3A_Molecular_Motions_of_a_Molecule_can_be_Represented_by_a_Reducible_ReperesentationThis page explains how to determine the normal vibrational modes of polyatomic molecules, specifically using group theory with H2O as an example. It covers the 3N Cartesian basis for molecula...This page explains how to determine the normal vibrational modes of polyatomic molecules, specifically using group theory with H2O as an example. It covers the 3N Cartesian basis for molecular motions, focusing on the 9 elements of H2O.
- https://chem.libretexts.org/Courses/Lakehead_University/Analytical_I/4%3A_Evaluating_Analytical_Data/4.04%3A_The_Distribution_of_Measurements_and_ResultsA population is the set of all objects in the system we are investigating. For our experiment, the population is all United States pennies in circulation. This population is so large that we cannot an...A population is the set of all objects in the system we are investigating. For our experiment, the population is all United States pennies in circulation. This population is so large that we cannot analyze every member of the population. Instead, we select and analyze a limited subset, or sample of the population.
