
Density
Density
or “volumetric mass density” is often noted "ρ"
(Greek letter rh?.
The
name of the chemical species or its empirical formula (where there is
no ambiguity) are usually mentioned in parentheses. For example, the
ethanol density is noted ρ
(ethanol) or ρ
(C_{2}H_{6}O).
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Definition
The
density of a chemical species is the mass per volume unit of that
species.
For
example, depending on the chosen unit, the density of the water
corresponds to the mass of water in one liter of water or one cubic
meter of water or one cubic centimeter of water etc.
Variations
The
density of a substance depends on conditions in which it is found, it
varies with temperature and pressure, especially for gases, but it is
also true for liquids and solids:
•
At constant
pressure, when the temperature of a substance increases, it expands;
it occupies a larger volume and consequently its density decreases.
•
At constant
temperature, if the pressure increases, a substance becomes
compressed; it occupies a smaller volume and therefore its density
increases.
This
relation between density, temperature and pressure specifies under
which conditions the value of the density is given, but most often,
when no precision is provided, this implies that one refers to the
ambient conditions (pressure of 1 atmosphere and temperature of 25 ?C for which the density of the water is 1,00 kg / L).
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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 / dm^{3}
or g.dm^{3})
or kilogram per cubic meter (kg /m^{3}
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 / cm^{3})
are equivalent: 1 kg / L
=
1 g / L = 1 kg / dm^{3
}=
1 g / cm^{3}
 The grams
per liter (g / L), milligram per milliliter (mg / mL), gram per cubic
decimeter (kg / dm^{3})
and milligram per cubic centimeter (g / cm^{3})
are equivalent: 1 g / L = 1
mg / mL = 1 g / dm3 = 1 mg / cm^{3}
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
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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 dm^{3}
cylinder is made of copper with a density ρ = 8.96 g / cm^{3}
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 cm^{3}:
V = 8 dm^{3} = 8000 cm^{3}.
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 / dm^{3}
or in g / cm^{3} then its value is 1 and :
ρ
(chemical species) = d x 1
ρ
(chemical species) = d
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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 / m^{3}
 7.850 / dm^{3}
(this is an average value because the steel content is variable)
 Pure water:
1,000 kg / L at 4 ?C under one atmosphere pressure.
