What type of percentage concentration is derived by dividing the volume of solute?

Aqueous Solutions - Molarity

An aqueous solution consists of at least two components, the solvent (water) and the solute (the stuff dissolved in the water). Usually one wants to keep track of the amount of the solute dissolved in the solution. We call this the concentrations. One could do by keeping track of the concentration by determining the mass of each component, but it is usually easier to measure liquids by volume instead of mass. To do this measure called molarity is commonly used. Molarity (M) is defined as the number of moles of solute (n) divided by the volume (V) of the solution in liters.

It is important to note that the molarity is defined as moles of solute per liter of solution, not moles of solute per liter of solvent. This is because when you add a substance, perhaps a salt, to some volume of water, the volume of the resulting solution will be different than the original volume in some unpredictable way. To get around this problem chemists commonly make up their solutions in volumetric flasks. These are flasks that have a long neck with an etched line indicating the volume. The solute (perhaps a salt) is added to the flask first and then water is added until the solution reaches the mark. The flasks have very good calibration so volumes are commonly known to at least four significant figures.

Example #1 :

Molarity Calculation

The equation for calculating Molarity from the moles and volume is very simple. Just divide moles of solute by volume of solution.

What is the molarity (with the correct numbers of significant figures) of a 0.40 moles of NaCl dissolved in 0.250 liters?

Answer

Example #2 :

Making Dilutions

A solution can be made less concentrated by dilution with solvent. If a solution is diluted from V1 to V2, the molarity of that solution changes according to the equation:

The volume units must be the same for both volumes in this equation. In general, M1 usually refers to as the initial molarity of the solution. V1 refers to the volume that is being transferred. M2 refers to the final concentration of the solution and V2 is the final total volume of the solution.

Remeber that the number of moles of solute does not change when more solvent is added to the solution. Concentration, however, does change with the added amount of solvent. (illustration)

Don't forget this concept. You will use it again in acid-base equilibrium.

Dilution calculation example:

How do you prepare 100ml of 0.40M MgSO4 from a stock solution of 2.0M MgSO4?

Answer:

There are two solutions involved in this problem. Notice that you are given two concentrations, but only one volume. Solution #1 is the one for which you have only concentration - the solution that is already sitting on the shelf. Solution #2 is the one for which you have both concentration and volume - the solution that you are going to prepare.

At least until you are comfortable with this type of problem, it may be helpful to write out what numbers go with what letters in our equation.

M1 = 2.0M MgSO4 ; V1 = unknown
M2 = 0.40M MgSO4 ; V2 = 100ml

Chemical term for density of a component in a mixture

In chemistry, the mass concentration ρi (or γi) is defined as the mass of a constituent mi divided by the volume of the mixture V.[1]

ρ i = m i V {\displaystyle \rho _{i}={\frac {m_{i}}{V}}}

For a pure chemical the mass concentration equals its density (mass divided by volume); thus the mass concentration of a component in a mixture can be called the density of a component in a mixture. This explains the usage of ρ (the lower case Greek letter rho), the symbol most often used 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 litre of a solution usually contains either slightly more or slightly less than 1 litre of solvent because the process of dissolution causes volume of liquid to increase or decrease. Sometimes the mass concentration is called titre.

Notation

The notation common with mass density underlines the connection between the two quantities (the mass concentration being the mass density of a component in the solution), but it can be a source of confusion especially when they appear in the same formula undifferentiated by an additional symbol (like a star superscript, a bolded symbol or varrho).

Dependence on volume

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

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

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

Sum of mass concentrations - normalizing relation

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

ρ = ∑ i ρ i {\displaystyle \rho =\sum _{i}\rho _{i}\,}

Thus, for pure component the mass concentration equals the density of the pure component.

Units

The SI-unit for mass concentration is kg/m3 (kilogram/cubic metre). 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/decilitre).

Usage in biology

In biology, the "%" symbol 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). The notation is mathematically flawed because the unit "%" can only be used for dimensionless quantities. "Percent solution" or "percentage solution" are thus terms best reserved for "mass percent solutions" (m/m = m% = mass solute/mass total solution after mixing), or "volume percent solutions" (v/v = v% = 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.

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

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

In solutions, mass concentration is commonly encountered as the ratio of mass/[volume solution], or m/v. In water solutions containing relatively small quantities of dissolved solute (as in biology), such figures may be "percentivized" by multiplying by 100 a ratio of grams solute per mL solution. The result is given as "mass/volume percentage". Such a convention expresses mass concentration of 1 gram of solute in 100 mL of solution, as "1 m/v %".

Related quantities

Density of pure component

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

ρ i = ρ i ∗ V i V {\displaystyle \rho _{i}=\rho _{i}^{*}{\frac {V_{i}}{V}}\,}

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

Specific volume (or mass-specific volume)

Specific volume is the inverse of mass concentration only in the case of pure substances, for which mass concentration is the same as the density of the pure-substance:

ν = V m   = 1 ρ {\displaystyle \nu ={\frac {V}{m}}\ ={\frac {1}{\rho }}}

Molar concentration

The conversion to molar concentration ci is given by:

c i = ρ i M i {\displaystyle c_{i}={\frac {\rho _{i}}{M_{i}}}}

where Mi is the molar mass of constituent i.

Mass fraction

The conversion to mass fraction wi is given by:

w i = ρ i ρ {\displaystyle w_{i}={\frac {\rho _{i}}{\rho }}}

Mole fraction

The conversion to mole fraction xi is given by:

x i = ρ i ρ M M i {\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 bi is given by:

b i = ρ i M i ( ρ − ρ i ) {\displaystyle b_{i}={\frac {\rho _{i}}{M_{i}(\rho -\rho _{i})}}}

Spatial variation and gradient

The values of (mass and molar) concentration different in space triggers the phenomenon of diffusion.

References

1. ^ IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "mass concentration". doi:10.1351/goldbook.M03713

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