Order of Magnitude

(noun)

An order of magnitude is the class of scale or magnitude of any amount, where each class contains values of a fixed ratio to the class preceding it.

Related Terms

Examples of Order of Magnitude in the following topics:

  • Scientific Notation

    • In order to go between scientific notation and decimals, the decimal point is moved the number of spaces indicated by the exponent.
    • Another way of writing this expression, as seen on calculators and computer programs, is to use E to represent "times ten to the power of."
    • Scientific notation enables comparisons between orders of magnitude.
    • As seen above, scientific notation uses base 10, and if a number is an order of magnitude greater than another, it is 10 times larger.
    • For example, 4.759 x 106 is 3 orders of magnitude bigger than 5 x 103; it is 8 orders of magnitude bigger than 2.56 x 10-2.

  • Acid Dissociation Constant (Ka)

    • The acid dissociation constant (Ka) is the measure of the strength of an acid in solution.
    • The acid dissociation constant (Ka) is a quantitative measure of the strength of an acid in solution.
    • As with all equilibrium constants, the value of Ka is determined by the concentrations (in mol/L) of each aqueous species at equilibrium.
    • Due to the many orders of magnitude spanned by Ka values, a logarithmic measure of the acid dissociation constant is more commonly used in practice.
    • The larger the value of pKa, the smaller the extent of dissociation.

  • Reactions of Coordination Compounds

    • In chemistry, a coordination or metal complex consists of an atom or ion (usually metallic) and a surrounding array of bound molecules or anions known as ligands or complexing agents.
    • Many metal-containing compounds consist of coordination complexes.
    • Polydentate (multiple bonded) ligands consist of several donor atoms, several of which are bound to the central atom or ion.
    • One important indicator of reactivity is the rate of degenerate exchange of ligands.
    • For example, the rate of interchange of the coordinate water in [M(H2O)6]n+ complexes varies over 20 orders of magnitude.

  • Solutions and Heats of Hydration

    • In order for any chemical reaction to proceed, it must be thermodynamically favorable.
    • The dissolution of an ionic solid MX in water can be thought of as a sequence of two processes:
    • The value of Hsolution is dependent upon the magnitudes of Hhydration and Hlattice energy of the solute.
    • The average time an ion spends in a hydration shell is about two to four nanoseconds, which is about two orders of magnitude longer than the lifetime of an individual H2O–H2O hydrogen bond.
    • A hot solution results when the heat of hydration is much greater than the lattice energy of the solute.

  • Spin-Spin Splitting

    • The magnitude of J, usually given in units of Hz, is magnetic field independent.
    • The splitting patterns shown above display the ideal or "First-Order" arrangement of lines.
    • Two examples that exhibit minor 2nd order distortion are shown below (both are taken at a frequency of 90 MHz).
    • The magnitude of the observed spin-splitting depends on many factors and is given by the coupling constant J (units of Hz).
    • To make use of a calculator that predicts first order splitting patterns, click the following link (http://www.colby.edu/chemistry/NMR/jmmset.html).

  • Regioselectivity and Lewis Acid Catalysis

    • In order to extend this treatment to account for different relative orientations of reactants, it is necessary to evaluate the magnitude of the HOMO and LUMO orbitals at each atom.
    • This orbital magnitude is usually represented by a coefficient, derived from the wave equations for the pi-orbitals.
    • Of course, the phase signs change to designate an increasing number of nodes.
    • A qualitative representation of the relative magnitude of terminal orbital coefficients for the HOMO and LUMO orbitals of alkenes (dienophiles) and dienes substituted in this common manner are in the first diagram below.
    • If the two ends of the dienophile each have a carbonyl substituent, as in the case of quinones and anhydrides, then Lewis acid catalysis may change the regioselectivity of the cycloaddition.

  • Predicting Spontaneous Direction of a Redox Reaction

    • The direction of a redox reaction depends on the relative strengths of the oxidants and reductants in a solution.
    • The sign of the standard electrode potential indicates in which direction the reaction must proceed in order to achieve equilibrium.
    • The positive Eo value indicates that at STP this reaction must proceed to the right in order to achieve equilibrium.
    • Neither the relative strengths of the oxidizing or reducing agents nor the magnitude of the potential will change.
    • In order to predict if two reactants will take part in a spontaneous redox reaction, it is important to know how they rank in an electrochemical series.

  • The Arrhenius Equation

    • What is "decaying" here is not the concentration of a reactant as a function of time, but the magnitude of the rate constant as a function of the exponent –Ea /RT.
    • What is the significance of this quantity?
    • Depending on the magnitudes of Ea and the temperature, this fraction can range from zero, where no molecules have enough energy to react, to unity, where all molecules have enough energy to react.
    • While "barrier-less" reactions, which have zero activation energy, have been observed, these are rare, and even in such cases, molecules will most likely need to collide with the right orientation in order to react.
    • Plot of ln(k) versus 1/T for the decomposition of nitrogen dioxide

  • Interference and Diffraction

    • In chemistry, the applications of interference to light are the most relevant to the study of matter.
    • The principle of superposition of waves states that when two or more waves are incident on the same point, the total displacement at that point is equal to the vector sum of the displacements of the individual waves.
    • If a crest of a wave meets a crest of another wave of the same frequency at the same point, then the magnitude of the displacement is the sum of the individual magnitudes; this is known as constructive interference.
    • If a crest of one wave meets a trough of another wave, then the magnitude of the displacements is equal to the difference in the individual magnitudes; this is known as destructive interference.
    • If the difference between the phases is intermediate between these two extremes, then the magnitude of the displacement of the summed waves lies between the minimum and maximum values.

  • Predicting if a Metal Will Dissolve in Acid

    • The classic example is of zinc displacing copper:
    • If you immerse a piece of metallic zinc in a solution of copper sulfate, the surface of the zinc quickly becomes covered with a coating of finely divided copper.
    • Similar comparisons of other metals have made it possible to arrange them in order of their increasing electron-donating, or reducing, power.
    • Each half-cell is associated with a potential difference whose magnitude depends on the nature of the particular electrode reaction and on the concentrations of the dissolved species.
    • In order to express them in a uniform way, we follow the rule that half-cell potentials are always defined for the reduction direction.