Mixing ratio

Last updated May 04, 2021

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 (see concentration) or mass ratio (see stoichiometry).^[1]

In atmospheric chemistry and meteorology

Mole ratio

In atmospheric chemistry, mixing ratio usually refers to the mole ratior_i, which is defined as the amount of a constituent n_i divided by the total amount of all other constituents in a mixture:

r_{i}={\frac {n_{i}}{n_{\mathrm {tot} }-n_{i}}}

The mole ratio is also called amount ratio.^[2] If n_i is much smaller than n_tot (which is the case for atmospheric trace constituents), the mole ratio is almost identical to the mole fraction.

Mass ratio

In meteorology, mixing ratio usually refers to the mass ratio of water $\zeta$ , which is defined as the mass of water $m_{\mathrm {H2O} }$ divided by the mass of dry air ( $m_{\mathrm {air} }-m_{\mathrm {H2O} }$ ) in a given air parcel:^[3]

\zeta ={\frac {m_{\mathrm {H2O} }}{m_{\mathrm {air} }-m_{\mathrm {H2O} }}}

The unit is typically given in $\mathrm {g} \,\mathrm {kg} ^{-1}$ . The definition is similar to that of specific humidity.

Mixing ratio of mixtures or solutions

Two binary solutions of different compositions or even two pure components can be mixed with various mixing ratios by masses, moles, or volumes.

The mass fraction of the resulting solution from mixing solutions with masses m₁ and m₂ and mass fractions w₁ and w₂ is given by:

w={\frac {w_{1}m_{1}+w_{2}m_{1}r_{m}}{m_{1}+m_{1}r_{m}}}

where m₁ can be simplified from numerator and denominator

w={\frac {w_{1}+w_{2}r_{m}}{1+r_{m}}}

and

r_{m}={\frac {m_{2}}{m_{1}}}

is the mass mixing ratio of the two solutions.

By substituting the densities ρ_i(w_i) and considering equal volumes of different concentrations one gets:

w={\frac {w_{1}\rho _{1}(w_{1})+w_{2}\rho _{2}(w_{2})}{\rho _{1}(w_{1})+\rho _{2}(w_{2})}}

Considering a volume mixing ratio r_V(21)

w={\frac {w_{1}\rho _{1}(w_{1})+w_{2}\rho _{2}(w_{2})r_{V}}{\rho _{1}(w_{1})+\rho _{2}(w_{2})r_{V}}}

The formula can be extended to more than two solutions with mass mixing ratios

r_{m1}={\frac {m_{2}}{m_{1}}}\quad r_{m2}={\frac {m_{3}}{m_{1}}}

to be mixed giving:

w={\frac {w_{1}m_{1}+w_{2}m_{1}r_{m1}+w_{3}m_{1}r_{m2}}{m_{1}+m_{1}r_{m1}+m_{1}r_{m2}}}={\frac {w_{1}+w_{2}r_{m1}+w_{3}r_{m2}}{1+r_{m1}+r_{m2}}}

Volume additivity

The condition to get a partially ideal solution on mixing is that the volume of the resulting mixture V to equal double the volume V_s of each solution mixed in equal volumes due to the additivity of volumes. The resulting volume can be found from the mass balance equation involving densities of the mixed and resulting solutions and equalising it to 2:

V={\frac {(\rho _{1}+\rho _{2})V_{\mathrm {s} }}{\rho }},V=2V_{\mathrm {s} }

implies

{\frac {\rho _{1}+\rho _{2}}{\rho }}=2

Of course for real solutions inequalities appear instead of the last equality.

Solvent mixtures mixing ratios

Mixtures of different solvents can have interesting features like anomalous conductivity (electrolytic) of particular lyonium ions and lyate ions generated by molecular autoionization of protic and aprotic solvents due to Grotthuss mechanism of ion hopping depending on the mixing ratios. Examples may include hydronium and hydroxide ions in water and water alcohol mixtures, alkoxonium and alkoxide ions in the same mixtures, ammonium and amide ions in liquid and supercritical ammonia, alkylammonium and alkylamide ions in ammines mixtures, etc....

Related Research Articles

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. A concentration can be any kind of chemical mixture, but most frequently solutes and solvents in solutions. The molar (amount) concentration has variants such as normal concentration and osmotic concentration.

In chemistry, the mole fraction or molar fraction (x_i) is defined as unit of the amount of a constituent, n_i divided by the total amount of all constituents in a mixture, n_tot:.This expression is given below:-

Stoichiometry is the calculation of reactants and products in chemical reactions in chemistry.

Relative density, or specific gravity, is the ratio of the density of a substance to the density of a given reference material. Specific gravity for liquids is nearly always measured with respect to water at its densest ; for gases, the reference is air at room temperature. The term "relative density" is often preferred in scientific usage.

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

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 number of moles of solute present in 1 kg 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 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. In his publication about the quantity of gases absorbed by water, he described the results of his experiments:

… water takes up, of gas condensed by one, two, or more additional atmospheres, a quantity which, ordinarily compressed, would be equal to twice, thrice, &c. the volume absorbed under the common pressure of the atmosphere.

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⋅dm⁻³ in SI unit. A solution with a concentration of 1 mol/L is said to be 1 molar, commonly designated as 1 M. To avoid confusion with SI prefix mega, which has the same abbreviation, small caps ᴍ or italicized M are also used in journals and textbooks.

The density of air or atmospheric density, denoted ρ, is the mass per unit volume of Earth's atmosphere. Air density, like air pressure, decreases with increasing altitude. It also changes with variation in atmospheric pressure, temperature and humidity. At 101.325 kPa (abs) and 15°C, air has a density of approximately 1.225 kg/m³, about 1/1000 that of water according to ISA.

In chemistry, an ideal solution or ideal mixture is a solution in which the gas phase exhibits thermodynamic properties analogous to those of a mixture of ideal gases. The enthalpy of mixing is zero as is the volume change on mixing by definition; the closer to zero the enthalpy of mixing is, the more "ideal" the behaviour of the solution becomes. The vapor pressure of the solution obeys either Raoult's law or Henry's law, and the activity coefficient of each component is equal to one.

The equilibrium constant of a chemical reaction is the value of its reaction quotient at chemical equilibrium, a state approached by a dynamic chemical system after sufficient time has elapsed at which its composition has no measurable tendency towards further change. For a given set of reaction conditions, the equilibrium constant is independent of the initial analytical concentrations of the reactant and product species in the mixture. Thus, given the initial composition of a system, known equilibrium constant values can be used to determine the composition of the system at equilibrium. However, reaction parameters like temperature, solvent, and ionic strength may all influence the value of the equilibrium constant.

Air–fuel ratio (AFR) is the mass ratio of air to a solid, liquid, or gaseous fuel present in a combustion process. The combustion may take place in a controlled manner such as in an internal combustion engine or industrial furnace, or may result in an explosion.

A premixed flame is a flame formed under certain conditions during the combustion of a premixed charge of fuel and oxidiser. Since the fuel and oxidiser—the key chemical reactants of combustion—are available throughout a homogeneous stoichiometric premixed charge, the combustion process once initiated sustains itself by way of its own heat release. The majority of the chemical transformation in such a combustion process occurs primarily in a thin interfacial region which separates the unburned and the burned gases. The premixed flame interface propagates through the mixture until the entire charge is depleted. The propagation speed of a premixed flame is known as the flame speed which depends on the convection-diffusion-reaction balance within the flame, i.e. on its inner chemical structure. The premixed flame is characterised as laminar or turbulent depending on the velocity distribution in the unburned pre-mixture.

In chemistry, the mass fraction of a substance within a mixture is the ratio $of the mass of that substance to the total mass of the mixture. Expressed as a formula, the mass fraction is:$

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 when all of that component is added to the solution, per mole of component added. 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 thermodynamics, the volume of a system is an important extensive parameter for describing its thermodynamic state. The specific volume, an intensive property, is the system's volume per unit of mass. Volume is a function of state and is interdependent with other thermodynamic properties such as pressure and temperature. For example, volume is related to the pressure and temperature of an ideal gas by the ideal gas law.

In chemistry, the mass concentration $ρ i$ is defined as the mass of a constituent $m i$ divided by the volume of the mixture $V$ .

The simple chemical reacting system (SCRS) is one of the combustion models for computational fluid dynamics. This model helps us to determine the process of combustion which is a vital phenomenon used in many engineering applications like aircraft engines, internal combustion engines, rocket engines, industrial furnaces, and power station combustors. The simple chemical reacting system (SCRS) refers the global nature of the combustion process considering only the final species concentrations. The detailed kinetics of the process is generally neglected and it postulates that combustion does proceed via a global one-step without intermediates. Infinitely fast chemical reaction is assumed with oxidants reacting in stoichiometric proportions to form products. SCRS considers the reaction to be irreversible i.e. rate of reverse reaction is presumed to be very low.

In combustion, a Burke–Schumann flame is a type of diffusion flame, established at the mouth of the two concentric ducts, by issuing fuel and oxidizer from the two region respectively. It is named after S.P. Burke and T.E.W. Schumann, who were able to predict the flame height and flame shape using their simple analysis of infinitely fast chemistry in 1928 at the First symposium on combustion.

References

↑ IUPAC , Compendium of Chemical Terminology , 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) " mixing ratio ". doi : 10.1351/goldbook.M03948
↑ "Pure and Applied Chemistry, 2008, Volume 80, No. 2, pp. 233-276". Iupac.org. 2016-06-14. Retrieved 2016-06-30.
↑ Whiteman, D.N. (2015). Encyclopedia of Atmospheric Sciences (Second Edition, Volume 3 ed.). Elsevier Ltd. p. 298. ISBN 978-0-12-382225-3.

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[1] IUPAC , Compendium of Chemical Terminology , 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) " mixing ratio ". doi : 10.1351/goldbook.M03948

[2] "Pure and Applied Chemistry, 2008, Volume 80, No. 2, pp. 233-276". Iupac.org. 2016-06-14. Retrieved 2016-06-30.

[3] Whiteman, D.N. (2015). Encyclopedia of Atmospheric Sciences (Second Edition, Volume 3 ed.). Elsevier Ltd. p. 298. ISBN 978-0-12-382225-3.

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v t e Solutions
Solution	Ideal solution Aqueous solution Solid solution Buffer solution Flory–Huggins Mixture Suspension Colloid Phase diagram Phase separation Eutectic point Alloy Saturation Supersaturation Serial dilution Dilution (equation) Apparent molar property Miscibility gap
Concentration and related quantities	Molar concentration Mass concentration Number concentration Volume concentration Normality Molality Mole fraction Mass fraction Isotopic abundance Mixing ratio Ternary plot
Solubility	Solubility equilibrium Total dissolved solids Solvation Solvation shell Enthalpy of solution Lattice energy Raoult's law Henry's law Solubility table (data) Solubility chart
Solvent	(Category) Acid dissociation constant Protic solvent Inorganic nonaqueous solvent Solvation List of boiling and freezing information of solvents Partition coefficient Polarity Hydrophobe Hydrophile Lipophilic Amphiphile Lyonium ion Lyate ion