Mass fraction (chemistry)

Last updated

In chemistry, the mass fraction of a substance within a mixture is the ratio (alternatively denoted ) of the mass of that substance to the total mass of the mixture. [1] Expressed as a formula, the mass fraction is:

Contents

Because the individual masses of the ingredients of a mixture sum to , their mass fractions sum to unity:

Mass fraction can also be expressed, with a denominator of 100, as percentage by mass (in commercial contexts often called percentage by weight, abbreviated wt.% or % w/w; see mass versus weight). It is one way of expressing the composition of a mixture in a dimensionless size; mole fraction (percentage by moles, mol%) and volume fraction (percentage by volume, vol%) are others.

When the prevalences of interest are those of individual chemical elements, rather than of compounds or other substances, the term mass fraction can also refer to the ratio of the mass of an element to the total mass of a sample. In these contexts an alternative term is mass percent composition. The mass fraction of an element in a compound can be calculated from the compound's empirical formula [2] or its chemical formula. [3]

Terminology

Percent concentration does not refer to this quantity. This improper name persists, especially in elementary textbooks. In biology, the unit "%" is sometimes (incorrectly) used to denote mass concentration, also called mass/volume percentage. A solution with 1 g of solute dissolved in a final volume of 100 mL of solution would be labeled as "1%" or "1% m/v" (mass/volume). This is incorrect because the unit "%" can only be used for dimensionless quantities. Instead, the concentration should simply be given in units of g/mL. Percent solution or percentage solution are thus terms best reserved for mass percent solutions (m/m, m%, or mass solute/mass total solution after mixing), or volume percent solutions (v/v, v%, or volume solute per volume of total solution after mixing). The very ambiguous terms percent solution and percentage solutions with no other qualifiers continue to occasionally be encountered.

In thermal engineering, vapor quality is used for the mass fraction of vapor in the steam.

In alloys, especially those of noble metals, the term fineness is used for the mass fraction of the noble metal in the alloy.

Properties

The mass fraction is independent of temperature until phase change occurs.

Mixing ratio

The mixing of two pure components can be expressed introducing the (mass) mixing ratio of them . Then the mass fractions of the components will be

The mass ratio equals the ratio of mass fractions of components:

due to division of both numerator and denominator by the sum of masses of components.

Mass concentration

The mass fraction of a component in a solution is the ratio of the mass concentration of that component ρi (density of that component in the mixture) to the density of solution .

Molar concentration

The relation to molar concentration is like that from above substituting the relation between mass and molar concentration:

where is the molar concentration, and is the molar mass of the component .

Mass percentage

Mass percentage is defined as the mass fraction multiplied by 100.

Mole fraction

The mole fraction can be calculated using the formula

where is the molar mass of the component , and is the average molar mass of the mixture.

Replacing the expression of the molar-mass products,

Spatial variation and gradient

In a spatially non-uniform mixture, the mass fraction gradient gives rise to the phenomenon of diffusion.

See also

Related Research Articles

<span class="mw-page-title-main">Concentration</span> Ratio of part of a mixture to the whole

In chemistry, concentration is the abundance of a constituent divided by the total volume of a mixture. Several types of mathematical description can be distinguished: mass concentration, molar concentration, number concentration, and volume concentration. The concentration can refer to any kind of chemical mixture, but most frequently refers to solutes and solvents in solutions. The molar (amount) concentration has variants, such as normal concentration and osmotic concentration. Dilution is reduction of concentration, e.g. by adding solvent to a solution. The verb to concentrate means to increase concentration, the opposite of dilute.

Density is a substance's mass per unit of volume. The symbol most often used for density is ρ, although the Latin letter D can also be used. Mathematically, density is defined as mass divided by volume:

<span class="mw-page-title-main">Fick's laws of diffusion</span> Mathematical descriptions of molecular diffusion

Fick's laws of diffusion describe diffusion and were first posited by Adolf Fick in 1855 on the basis of largely experimental results. They can be used to solve for the diffusion coefficient, D. Fick's first law can be used to derive his second law which in turn is identical to the diffusion equation.

In chemistry, the mole fraction or molar fraction, also called mole proportion or molar proportion, is a quantity defined as the ratio between the amount of a constituent substance, ni, and the total amount of all constituents in a mixture, ntot :

In chemistry and related fields, the molar volume, symbol Vm, or of a substance is the ratio of the volume occupied by a substance to the amount of substance, usually given at a given temperature and pressure. It is equal to the molar mass (M) divided by the mass density (ρ):

In chemistry, the molar mass of a chemical compound is defined as the ratio between the mass and the amount of substance of any sample of said compound. The molar mass is a bulk, not molecular, property of a substance. The molar mass is an average of many instances of the compound, which often vary in mass due to the presence of isotopes. Most commonly, the molar mass is computed from the standard atomic weights and is thus a terrestrial average and a function of the relative abundance of the isotopes of the constituent atoms on Earth. The molar mass is appropriate for converting between the mass of a substance and the amount of a substance for bulk quantities.

In chemical thermodynamics, activity is a measure of the "effective concentration" of a species in a mixture, in the sense that the species' chemical potential depends on the activity of a real solution in the same way that it would depend on concentration for an ideal solution. The term "activity" in this sense was coined by the American chemist Gilbert N. Lewis in 1907.

Molality is a measure of the number of moles of solute in a solution corresponding to 1 kg or 1000 g of solvent. This contrasts with the definition of molarity which is based on a specified volume of solution.

In physical chemistry, Henry's law is a gas law that states that the amount of dissolved gas in a liquid is directly proportional to its partial pressure above the liquid. The proportionality factor is called Henry's law constant. It was formulated by the English chemist William Henry, who studied the topic in the early 19th century.

Molar concentration is a measure of the concentration of a chemical species, in particular of a solute in a solution, in terms of amount of substance per unit volume of solution. In chemistry, the most commonly used unit for molarity is the number of moles per liter, having the unit symbol mol/L or mol/dm3 in SI unit. A solution with a concentration of 1 mol/L is said to be 1 molar, commonly designated as 1 M. Molarity is often depicted with square brackets around the substance of interest, for example the molarity of the hydrogen ion is depicted as [H+].

In chemistry, colligative properties are those properties of solutions that depend on the ratio of the number of solute particles to the number of solvent particles in a solution, and not on the nature of the chemical species present. The number ratio can be related to the various units for concentration of a solution such as molarity, molality, normality (chemistry), etc. The assumption that solution properties are independent of nature of solute particles is exact only for ideal solutions, which are solutions that exhibit thermodynamic properties analogous to those of an ideal gas, and is approximate for dilute real solutions. In other words, colligative properties are a set of solution properties that can be reasonably approximated by the assumption that the solution is ideal.

In chemistry and physics, the dimensionless mixing ratio is the abundance of one component of a mixture relative to that of all other components. The term can refer either to mole ratio or mass ratio.

In chemistry and fluid mechanics, the volume fraction φi is defined as the volume of a constituent Vi divided by the volume of all constituents of the mixture V prior to mixing:

In physics and engineering, mass flux is the rate of mass flow. Its SI units are kg m−2 s−1. The common symbols are j, J, q, Q, φ, or Φ, sometimes with subscript m to indicate mass is the flowing quantity. Mass flux can also refer to an alternate form of flux in Fick's law that includes the molecular mass, or in Darcy's law that includes the mass density.

<span class="mw-page-title-main">Mass attenuation coefficient</span>

The mass attenuation coefficient, or mass narrow beam attenuation coefficient of a material is the attenuation coefficient normalized by the density of the material; that is, the attenuation per unit mass. Thus, it characterizes how easily a mass of material can be penetrated by a beam of light, sound, particles, or other energy or matter. In addition to visible light, mass attenuation coefficients can be defined for other electromagnetic radiation, sound, or any other beam that can be attenuated. The SI unit of mass attenuation coefficient is the square metre per kilogram. Other common units include cm2/g and L⋅g−1⋅cm−1. Mass extinction coefficient is an old term for this quantity.

<span class="mw-page-title-main">Diffusion</span> Transport of dissolved species from the highest to the lowest concentration region

Diffusion is the net movement of anything generally from a region of higher concentration to a region of lower concentration. Diffusion is driven by a gradient in Gibbs free energy or chemical potential. It is possible to diffuse "uphill" from a region of lower concentration to a region of higher concentration, as in spinodal decomposition. Diffusion is a stochastic process due to the inherent randomness of the diffusing entity and can be used to model many real-life stochastic scenarios. Therefore, diffusion and the corresponding mathematical models are used in several fields beyond physics, such as statistics, probability theory, information theory, neural networks, finance, and marketing.

In thermodynamics, an apparent molar property of a solution component in a mixture or solution is a quantity defined with the purpose of isolating the contribution of each component to the non-ideality of the mixture. It shows the change in the corresponding solution property per mole of that component added, when all of that component is added to the solution. It is described as apparent because it appears to represent the molar property of that component in solution, provided that the properties of the other solution components are assumed to remain constant during the addition. However this assumption is often not justified, since the values of apparent molar properties of a component may be quite different from its molar properties in the pure state.

In chemistry, the mass concentrationρi is defined as the mass of a constituent mi divided by the volume of the mixture V.

The Kirkwood–Buff (KB) solution theory, due to John G. Kirkwood and Frank P. Buff, links macroscopic (bulk) properties to microscopic (molecular) details. Using statistical mechanics, the KB theory derives thermodynamic quantities from pair correlation functions between all molecules in a multi-component solution. The KB theory proves to be a valuable tool for validation of molecular simulations, as well as for the molecular-resolution elucidation of the mechanisms underlying various physical processes. For example, it has numerous applications in biologically relevant systems.

The shear viscosity of a fluid is a material property that describes the friction between internal neighboring fluid surfaces flowing with different fluid velocities. This friction is the effect of (linear) momentum exchange caused by molecules with sufficient energy to move between these fluid sheets due to fluctuations in their motion. The viscosity is not a material constant, but a material property that depends on temperature, pressure, fluid mixture composition, local velocity variations. This functional relationship is described by a mathematical viscosity model called a constitutive equation which is usually far more complex than the defining equation of shear viscosity. One such complicating feature is the relation between the viscosity model for a pure fluid and the model for a fluid mixture which is called mixing rules. When scientists and engineers use new arguments or theories to develop a new viscosity model, instead of improving the reigning model, it may lead to the first model in a new class of models. This article will display one or two representative models for different classes of viscosity models, and these classes are:

References

  1. IUPAC , Compendium of Chemical Terminology , 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006) " mass fraction ". doi : 10.1351/goldbook.M03722
  2. Formula from Mass Composition.
  3. "How to Calculate Mass Percent Composition". ThoughtCo. Retrieved 2018-01-05.