 # Chemistry

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## Volumetric mass density

### Density

Density or “volumetric mass density” is often noted "ρ" (Greek letter rhô).

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 (C2H6O).

### 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).

### 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 / 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 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 / dm
3 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. Science class Mechanics lessons Water Water on Earth Changes of state in the nature: the water cycle Water in human body Test for water Properties of water in different states States of matter States of matter and its changes Boiling water Water: freezing and melting Changes of state: mass and volume Molecules in different states of matter Mixtures and solutions Heterogeneous mixtures Homogeneous mixtures Decantation Centrifugation Filtration Vaporization of water Distillation Chromatography Dissolving a solid in water Conservation of mass on dissolving Miscibility in water Mass and volume Volume and its units Measuring volume with a graduated cylinder Mass and its units Measuring the mass of a liquid Mass of a liter of water Volumetric mass density Air and atmosphere Earth's atmosphere protect us Pressure Atoms and molecules Molecules Molecules in mixtures and pure substances Molecules and states of matter Atoms Composition of molecules Constituents of the atoms The electrical neutrality of the atom Combustions Basics of combustion The combustion of carbon The combustion of butane Atoms and chemical reactions Chemical reactions Chemical equations Law of conservation of mass Chemical synthesis Metals Most common metals How to distinguish metals ? Corrosion of metals Electrical conductivity of solid materials Electrons and free electrons Electric current in metals Ions The conductivity of aqueous solutions Aqueous solutions and ions The direction of movement of ions Formation of ions Tests for ions Acidic and basic solutions pH of aqueous solutions Ions in acidic and basic solutions Dilution of acids and bases Composition of hydrochloric acid Chemical reaction between iron and hydrochloric acid Electrochemical cells and chemical energy Chemical reaction beteween a copper sulphate solution and zinc Copper sulfate and zinc battery Basics of electrochemical cell