Equations and Diagrams Set 10
Flory-Fox equation
A more precise, molecular-level derivation of this equation has been developed by Alessio Zaccone and Eugene Terentjev, which is based on a molecular-level model of the temperature-dependent shear modulus G of glassy polymers
Stiff diagram
A polygonal shape is created from four parallel horizontal axes extending on either side of a vertical zero axis on this diagram plotting cation and anion concentrations in water samples
Flory-Fox equation
Alessio Zaccone and Eugene Terentjev's molecular-level derivation of this equation sets the glass transition temperature inversely proportional to the thermal expansion coefficient in the glass state
Flory-Fox equation
Differential scanning calorimetry is the most common technique used to verify the molar mass dependence of this equation
Stiff diagram
Like Maucha and Piper diagrams, this diagram is used to graphically represent the major cationic and anionic species in a sample of water
Ragone plot
Lithium-ion capacitors and electric double layer capacitors (EDLCs) are plotted on the right side of this graph, while fuel cells and batteries are plotted on the left side
Ragone plot
The amount of time in hours during which an energy-storing device can be operated at its rated power is given as the ratio between the y-axis and x-axis of this plot
water retention curve
The instantaneous profile method uses soil moisture content to determine the van Genuchten parameters, which are used to create this curve
Ragone plot
The logarithmic specific energy in kilowatt-hours per kilogram is plotted on the y-axis against the logarithmic specific power in watts per kilogram on this plot
van Krevelen diagram
The thermal maturity of kerogen increases toward the origin on this diagram
water retention curve
The van Genuchten model sets the shape of this curve equal to the residual water content plus a term whose numerator is the difference between saturated and residual water content
Ragone plot
The vertical axis of this plot describes how much energy is available per unit mass, while the horizontal axis shows how quickly that energy can be delivered
Mitscherlich's law
This approximate law of isomorphism suggests that compounds which contain the same number of atoms and have similar structures exhibit similar crystal forms
Mitscherlich's law
This approximate law of isomorphism suggests that crystals composed of the same number of similar elements tend to demonstrate isomorphism
water retention curve
This curve is the relationship between the water content θ and the matric soil water potential ψ measured in hectopascals
water retention curve
This curve is used to predict soil water storage, plant water supply or field capacity, and soil aggregate stability
water retention curve
This curve plots the matric potential ψ on the y-axis against soil moisture content θ on the x-axis
Stiff diagram
This diagram can be used to help visualize ionically related waters from which a flow path can be determined or, if the flow path is known, to show how the ionic composition of a water body changes over space or time
van Krevelen diagram
This diagram cross-plots the hydrogen:carbon atomic ratio as a function of the oxygen:carbon atomic ratio
Stiff diagram
This diagram is created by plotting the equivalent concentration of the cations to the left of the center axis and anions to the right for a sample of water
van Krevelen diagram
This diagram is used to assess the origin and maturity of kerogen and petroleum
Stiff diagram
This diagram is widely used by hydrogeologists and geochemists to display the major cation and anion composition in milliequivalents per liter of a water sample
Urey-Bigeleisen-Mayer equation
This equation can be expressed by relating the equilibrium constant to the product of partition function ratios, namely the translational, rotational, vibrational, and sometimes electronic partition functions
Flory-Fox equation
This equation describes the dependence of glass transition temperature on free volume, which in turn is dependent on the average molecular weight of the polymer sample
Cahn-Hilliard equation
This equation describes the process of phase separation, by which the two components of a binary fluid spontaneously separate and form domains pure in each component
Hertz-Knudsen equation
This equation describes the sticking of gas molecules on a surface by expressing the time rate of change of the concentration of molecules on the surface as a function of the pressure of the gas and other parameters
Hertz-Knudsen equation
This equation in surface chemistry describes the rate of evaporation with respect to a flat surface
Urey-Bigeleisen-Mayer equation
This equation predicts isotope effects and the approximate equilibrium isotope fractionation in an isotope exchange reaction
Flory-Fox equation
This equation relates molecular weight to the class transition temperature of a polymer system
Flory-Fox equation
This equation sets the glass transition temperature equal to the maximum glass transition temperature that can be achieved at a theoretical infinite molecular weight minus the empirical parameter K over the number-averaged molecular weight
Cahn-Hilliard equation
This equation sets the partial time derivative of the fluid concentration c equal to the diffusion coefficient D times the Laplacian ∇^2 of the chemical potential in n dimensions
Cahn-Hilliard equation
This equation sets ∂c/∂t = D∇^2(c^3 − c − γ∇^2c), where c is the fluid concentration, D is the diffusion coefficient, ∇^2 is the Laplace operator, and (c^3 − c − γ∇^2c) is the chemical potential
Ostwald's dilution law
This law is a relationship between the dissociation constant K sub d and the degree of dissociation α of a weak electrolyte
Ostwald's dilution law
This law relates the molar conductivity of a weak electrolyte at a given to the molar conductivity at infinite dilution
Ostwald's dilution law
This law sets the degree of dissociation of a weak electrolyte directly proportional to the square root of dilution in an application of the law of mass action
Ostwald's dilution law
This law sets the degree of dissociation α of a weak electrolyte equal to the square root of the dissociation constant K sub d over the total electrolyte concentration c naught
Ostwald's dilution law
This law sets the dissociation constant K sub d equal to the square of the degree of association α times the total electrolyte concentration c naught over one minus α
Kopp-Neumann law
This law sets the specific heat C of a compound equal to the sum of the heat capacities and mass fractions of the constituents
Kopp-Neumann law
This law states that the molecular heat capacity of a solid compound is the sum of the atomic heat capacities of the elements composing it
Kopp-Neumann law
This law states that the specific heat of a solid compound is equal to the sum of the heat capacities for each constituent weighted by its mass fraction
Stark-Einstein law
This photochemical equivalence law states that every photon that is absorbed will cause a primary chemical or physical reaction
Stark-Einstein law
This photochemical equivalence law states that for every mole of a substance that reacts, an equivalent mole of photons are absorbed
Stark-Einstein law
This photochemical equivalence law states that photons can only interact with one molecule at a time
Ragone plot
This plot is used for comparing the energy density of various energy-storing devices such as batteries
Ragone plot
This plot shows that the power density or specific power of a battery always trades off with energy density or specific energy
Grotthuss-Draper law
This principle of photochemical activation states that only that light which is absorbed by a system can bring about a photochemical change
Grotthuss-Draper law
This principle of photochemical activation states that only the light absorbed by a substance or substances is effective in bringing about chemical change
Ostwald's step rule
This rule describes the formation of polymorphs and states that usually the less stable polymorph crystallizes first
Ostwald's step rule
This rule states that polymorph crystallization passes through multiple states of decreasing energy
Cahn-Hilliard equation
When one phase is significantly more abundant, this equation can show the phenomenon known as Ostwald ripening, where the minority phase forms spherical droplets adsorbed through diffusion into the larger ones
