dimensional analysis

Examples of dimensional analysis in the following topics:

• Converting from One Unit to Another

  • Converting units using dimensional analysis makes working with large and small measurements more convenient.
  • Converting between metric units is called unit analysis or dimensional analysis.
  • Unit analysis is a form of proportional reasoning where a given measurement can be multiplied by a known proportion or ratio to give a result having a different unit or dimension.
  • If you had a sample of a substance with a mass of 0.0034 grams, and you wanted to express that mass in mg, you could use the following dimensional analysis.

• Strategy for General Problem Solving

  • You can also use dimensional analysis to convert between moles and grams.
  • Apply knowledge of dimensional analysis to convert between units in chemistry problems

• Electrolysis Stoichiometry

• Converting between Mass and Number of Moles

  • By recognizing the relationship between the molar mass (g/mol), moles (mol), and particles, scientists can use dimensional analysis convert between mass, number of moles and number of atoms very easily.

• Mass-to-Mole Conversions

  • Multiplying by the molar mass constant ensures that the calculation is dimensionally correct because atomic weights are dimensionless.
  • After the molar mass is determined, dimensional analysis can be used to convert from grams to moles.

• Converting between Moles and Atoms

  • Therefore, given the relationship 1 mol = 6.022 x 1023 atoms, converting between moles and atoms of a substance becomes a simple dimensional analysis problem.

• Cycloalkanes

  • The three dimensional shapes assumed by the common rings (especially cyclohexane and larger rings) are described and discussed in the Conformational Analysis Section.

• Conformational Stereoisomers

  • Structural formulas show the manner in which the atoms of a molecule are bonded together (its constitution), but do not generally describe the three-dimensional shape of a molecule, unless special bonding notations (e.g. wedge and hatched lines) are used.
  • The importance of such three-dimensional descriptive formulas became clear in discussing configurational stereoisomerism, where the relative orientation of atoms in space is fixed by a molecule's bonding constitution (e.g. double-bonds and rings).
  • In this section we shall extend our three-dimensional view of molecular structure to include compounds that normally assume an array of equilibrating three-dimensional spatial orientations, which together characterize the same isolable compound.

• Designating the Configuration of Chiral Centers

  • The sequence order of the substituent groups in lactic acid should be obvious, but the carvone example requires careful analysis.
  • In order to determine the true or "absolute" configuration of an enantiomer, as in the cases of lactic acid and carvone reported here, it is necessary either to relate the compound to a known reference structure, or to conduct a rather complex X-ray analysis on a single crystal of the sample.
  • In the example of carvone, shown above, the initial formula directed the lowest priority substituent (H) toward the viewer, requiring either a reorientation display or a very good sense of three-dimensional structure on the part of the reader.

• Isomers

  • Developing the ability to visualize a three-dimensional structure from two-dimensional formulas requires practice, and in most cases the aid of molecular models.
  • Combustion analysis yielded the ratio of carbon to hydrogen by measuring the amount of carbon dioxide and water produced, and a rough molecular weight was obtained from boiling point studies.
  • The first two compounds cannot be distinguished by the number of carbon signals; however, a careful analysis of the chemical shifts permits an assignment to be made.