Mass concentration (chemical)

In chemistry, the mass concentration ρ_i (or γ_i) is defined as the mass of a constituent m_i divided by the volume of the mixture V.

ρ ρ i=miV{displaystyle rho _{i}={frac {m_{i}}{V}}

For a pure chemical, the mass concentration is equal to its density (mass divided by volume); therefore, the mass concentration of a component in a mixture can be called the density of a component in a mixture. This explains the use of ρ (the lowercase Greek letter rho), the most widely used symbol for density.

Definition and properties

The volume V in the definition refers to the volume of the solution, not the volume of the solvent. One liter of a solution usually contains a little more or a little less than 1 liter of solvent because the dissolving process causes the volume of the liquid to increase or decrease. Sometimes the mass concentration is called the titer.

Notation

The notation common with mass density emphasizes the connection between the two quantities (mass concentration being the mass density of a component in solution), but it can be a source of confusion, especially when they appear in the same formula without being differentiated by an additional symbol (such as a superscript star, bold symbol, or rho).

Volume dependency

The mass concentration depends on the variation of the volume of the solution mainly due to thermal expansion. In small temperature intervals the dependence is:

ρ ρ i=ρ ρ i(T0)1+α α Δ Δ T{displaystyle rho _{i}={frac {rho _{ileft(T_{0}right)}}{1+alpha Delta T}}}}}}}}

where ρ_i(T0) is the mass concentration at a reference temperature, α is the coefficient of thermal expansion of the mixture.

Sum of mass concentrations - normalization relation

The sum of the mass concentrations of all the components (including the solvent) gives the density ρ of the solution:

ρ ρ =␡ ␡ iρ ρ i{displaystyle rho =sum _{i}rho _{i},}

Therefore, for the pure component, the mass concentration is equal to the density of the pure component.

Units

The SI unit for mass concentration is kg/m³ (kilogram/cubic meter). This is the same as mg/mL and g/L. Another commonly used unit is g/(100 mL), which is identical to g/dL (gram/deciliter).

Use in biology

In biology, the symbol "%" it is sometimes used incorrectly to indicate mass concentration, also called "mass/volume percent". A solution with 1 g of solute dissolved in a final volume of 100 mL of solution would be labeled "1%" or "1% m/v" (mass/volume). The notation is mathematically flawed because the unit "%" can only be used for dimensionless quantities. Therefore, "percent solution" or "percent solution" are terms best reserved for "mass percent solutions" (m/m = m% = mass solute/mass total solution after mixing), or "percent solutions by volume" (v/v = v % = volume of solute per volume of total solution after mixing). The highly ambiguous terms "percent solution" and "percent solutions" without other qualifiers they continue to meet occasionally.

This common use of % to mean m/v in biology is because many biological solutions are dilute and based on water or an aqueous solution. Liquid water has a density of about 1 g/cm³ (1 g/mL). Thus, 100 mL of water is equal to approximately 100 grams. Therefore, a solution with 1 g of solute dissolved in a final volume of 100 mL of aqueous solution can also be considered at 1% m/m (1 g solute in 99 g of water). This approximation breaks down as the solute concentration increases (for example, in mixtures of water and NaCl). High solute concentrations are often not physiologically relevant, but are occasionally found in pharmacology, where mass per volume notation is still sometimes found. An extreme example is saturated potassium iodide solution (SSKI) which reaches a mass concentration of potassium iodide of 100 "%" m/v (1 gram KI per 1 ml of solution) only because the solubility of the dense KI salt is extremely high in water and the resulting solution is very dense (1.72 times denser than water).

Although there are examples to the contrary, it should be stressed that "units" Commonly used % w/v is grams per milliliter (g/mL). 1% m/v solutions are sometimes considered grams/100 mL, but this detracts from the fact that % m/v is g/mL; 1 g of water has a volume of about 1 mL (at standard temperature and pressure) and the mass concentration is said to be 100%. To make 10 mL of a 1% aqueous cholate solution, 0.1 grams of cholate is dissolved in 10 mL of water. Volumetric flasks are the most appropriate glassware for this procedure, as deviations from ideal solution behavior can occur with high solute concentrations.

In solutions, the mass concentration is commonly found as the ratio of mass/[volume solution], or m/v. In water solutions that contain relatively small amounts of dissolved solute (as in biology), these numbers can be "percentivized" by some of the numbers. multiplying by 100 a ratio of grams of solute per ml of solution. The result is given as "mass/volume percentage". Such a convention expresses the mass concentration of 1 gram of solute in 100 mL of solution, as "1 m/v %".

Related Quantities

Density of the pure component

The relationship between the mass concentration and the density of a pure component (mass concentration of mixtures of a single component) is:

ρ ρ i=ρ ρ i↓ ↓ ViV{displaystyle rho _{i}=rho _{i}{i}{frac {V_{i}}{V}}}{v}}}{,}

where ρ∗
i is the density of the pure component, V_i the volume of the pure component before mixing.

Specific volume (or specific volume of mass)

The specific volume is the inverse of the mass concentration only in the case of pure substances, for which the mass concentration is equal to the density of the pure substance:

.. =Vm=1ρ ρ {displaystyle nu ={frac {V}{m}}}{frac {1{rho }}}}}

Molar concentration

The conversion to molar concentration c_i is given by:

ci=ρ ρ iMi{displaystyle c_{i}={frac {rho _{i}}{M_{i}}}}}}}

where M_i is the molar mass of the constituent i.

Mass Fraction

The conversion to mass fraction w_i is given by:

wi=ρ ρ iρ ρ {displaystyle w_{i}={frac {rho _{i}}{rho }}}}}

Mole Fraction

The conversion to mole fraction x_i is given by:

xi=ρ ρ iρ ρ MMi{displaystyle x_{i}={frac {rho _{i}}}{rho }}{frac {M}{M_{i}}}}}}}{

where M is the average molar mass of the mixture.

Molality

For binary mixtures, the conversion to molality b_i is given by:

bi=ρ ρ iMi(ρ ρ − − ρ ρ i){displaystyle b_{i}={frac {rho _{i}}{M_{i}(rho -rho _{i})}}}}

Spatial variation and gradient

Different concentration values (mass and molar) in space trigger the phenomenon of diffusion.