Chemistry

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Volumetric mass density

Density

Definition

Variations

Calculating Density

The density (ρ) of a chemical species can be calculated by dividing the mass (m) of this chemical species by the volume (V) it occupies, which can be expressed by the formula:

ρ = m / V

Example: 400 mL of acetone has a mass of 316.4 g; therefore, the density of acetone corresponds to the ratio of the mass of this sample (m = 316.4 g) by its volume (V = 0.400 L):

ρ (acetone) = 316.4: 0.400
ρ (acetone) = 791 g / L

Important, it is necessary to verify used units, if for example the mass is in kilogram and the volume in cubic centimeter then the density is in kilogram per cubic centimeter.

Units

For liquids and gases, the density is often expressed in grams per liter (unit rated g / L or g.L^-1).
For solids, units used are often grams per cubic decimeter (g / dm³ or g.dm^-3) or kilogram per cubic meter (kg /m³ or kg.m^-3).

Conversion

Density is a composite quantity (it is defined as the ratio of two other quantities) and it cannot be directly converted as it is possible for some units such as meter, gram or liter for which we can use a conversion chart.

The international method of conversion is to decompose the density as a ratio of mass and volume (even if no value is given and even if no particular sample of matter is referred to). Once decomposition is done, we convert the mass into its new unit (following the usual method of mass conversion), then we convert the volume. Thus, it only remains to calculate the density once again with the new values ​​of mass and volume, which result corresponds to the expression of the density in its new unit.

Example: Conversion of the density of an olive oil (ρ (oil) = 915 g / L) in kilograms per deciliter.

It can be considered ρ (oil) which is the ratio of a mass m = 915 g by a volume V = 1 L.
Mass conversion: 915g = 0.915kg
Volume conversion: 1L = 10 dL
Calculation of the density in its new unit: ρ (oil) = 0.915: 10
ρ (oil) = 0.0915 kg / dL

Equivalent units

Some units are equivalent which means that the density has the same values ​​when these units are used. In particular:

• Kilogram per liter (Kg / L), gram per milliliter (g / mL), kilogram per cubic decimeter (kg / dm³) and gram per cubic centimeter (g / cm³) are equivalent: 1 kg / L = 1 g / L = 1 kg / dm³ = 1 g / cm³

• The grams per liter (g / L), milligram per milliliter (mg / mL), gram per cubic decimeter (kg / dm³) and milligram per cubic centimeter (g / cm³) are equivalent: 1 g / L = 1 mg / mL = 1 g / dm³ = 1 mg / cm³

Explanation
the density corresponds to the ratio of the mass per volume unit therefore if the mass and the volume are multiplied or divided by the same number then the ratio does not change. Example:
1 kg / L = 1 kg / 1 L
= 1000 g / 1000 mL
= 1 g / 1mL
= 1 g / mL

Finding mass with density

If we modify the formula allowing to calculate the density it is possible to express mass with the help of other quantities:

ρ = m / V
ρ x V = m
m = ρ x V

Therefore, the mass of a substance is defined as the product of its volume by its density provided that the coherence of the units is respected.
Example: an 8 dm3 cylinder is made of copper with a density ρ = 8.96 g / cm³
According to the previous relation m = ρ x V. ρ is known but in order to verify the relation it is necessary to convert the volume in cm³: V = 8 dm³ = 8000 cm³.
By replacing in the previous formula we obtain:
m = 8.96 x 8000
m = 71,680
i.e. m = 71.7 kg Therefore, our copper cylinder has a mass of 71.7 kg.

Finding a volume with density

If we modify the formula that allows us to calculate the density, it is possible to express the volume with the helps of the other quantities:

ρ = m / V
ρ x V = m

V = m / ρ

The volume of a substance corresponds to the ratio of its mass by its density, provided, to respect the coherence of the units.

Example
A container contains 200 g of ethanol with a density ρ = 789 g / L
V = m / ρ
In this formula each size can be replaced by its value
V = 200/789
V = 0.253 L

Use the volumetric mass density to calculate a density

The density and the volumetric mass density are associated with the density of a chemical species by the density of water under the same conditions:

d = ρ (chemical species) / ρ (water)

Therefore: ρ (chemical species) = d x ρ (water)

If the density of water is expressed in some units such as kg / L, g / mL, kg / dm³ or in g / cm³  then its value is 1 and :
ρ (chemical species) = d x 1
ρ (chemical species) = d

Density of a gas

When a gas can be considered as "Ideal", i.e. under conditions where the interactions between its molecules remain limited (which excludes high pressures and temperatures), its density can be expressed as a function of its temperature, its pressure and its molar mass.

According to the ideal gas relation:

PV = n x R X T

n the number of moles constituting the gas; can be expressed as the ratio of its mass and of its density (n = m / M)

PV = (m × R × T) / M

P x V x M = m x R x T

P x M = (m / V) x R X T

The term m / V corresponds to the density (ρ)

P x M = ρ x R x T

ρ = (P x M) / (R x T)

The density of a gas is proportional to the pressure and to its molar mass, it is inversely proportional to the temperature.
If we consider a situation where a gas is at ambient temperature (20 ° C = 293.15 ° K) and at normal pressure (P = 1 atm = 101325 Pa) then the relation becomes:

ρ = (101325 x M) / (8.3144 x 293.15)

ρ = 41.57 x M (in the case where the molar mass is expressed in grams per mol and the density in grams per cubic meter)

ρ = 0.04157 x M (in the case where the molar mass is expressed in grams per mol and the density in grams per liter)

Using this formula, we can deduce the molar mass of different gases at 20 ° C and under a pressure of one atmosphere.

Examples:

- For the molar mass of dihydrogen M = 2 g / mol, ρ = 0.04157 x 2, ρ (dihydrogen) = 0.0831 g / L
- For dioxygen with a molar mass M = 32 g / mol, ρ = 0.04157 x 32, ρ (dihydrogen) = 1.33 g / L
- For the dinitrogen of molar mass M = 28 g / mol, ρ = 0.04157 x 28, ρ (dihydrogen) = 1.16 g / L
- For carbon dioxide of molar mass M = 44 g / mol, ρ = 0.04157 x 44, ρ (dihydrogen) = 1.83 g / L

Some densities

• Dry air at 0 ° C, under an atmosphere (at sea level): 1,29 g / l
• Steel: 7850 kg / m³ - 7.850 / dm³ (this is an average value because the steel content is variable)
• Pure water: 1,000 kg / L at 4 ° C under one atmosphere pressure.

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