# Is density important in chemical reactions

## density

The density of a body \$ \ rho \$ (Rho), for better differentiation from other volume-related quantities such as energy or charge density Mass density called, is the fraction of its mass \$ \, m \$ (in the numerator) and its volume \$ \, V \$ (in the denominator), i.e. \$ \ rho = \ frac {m} {V} \$, and thus a quotient quantity im According to DIN 1313. It is often used in Grams per cubic centimeter = Kilograms per liter = Tons per cubic meter specified; The SI unit formed without prefixes becomes less common Kilograms per cubic meter used. Density is a characteristic of the material of the body and is independent of its shape and size.

In general (without density anomaly), solid and liquid substances expand with increasing temperature, so that their density decreases; gaseous ones are even stronger if they can expand against constant external pressure and are not enclosed in a rigid vessel.

With -density Compound words also denote other quantities that are related to the volume, but sometimes also to an area, a length, a frequency interval or other (examples under Other terms of density below).

### Differentiation from other terms

• The density (mass / volume) must not match the specific weight (specific gravity) be confused. While with the density the Dimensions is in relation to the volume, for the specific weight, instead of the mass, the Weight force (Force / volume).
• The relativ density is the ratio of the density to the density of a standard, i.e. a dimensionless quantity.

These differences are defined in DIN 1306 Density; Terms, information.

### Density of solutions

The sum of the mass concentrations of the constituents of a solution gives the density of the solution by dividing the sum of the masses of the constituents by the volume of the solution.

\$ \ rho = \ frac {1} {V} \ sum_i m_i = \ frac {\ sum_i \ rho_i V_i} {V} \, \$

The \$ m_i \$ are the individual partial masses, \$ V_i \$ the individual partial volumes and V the total volume.

### Special terms of density in technology

• Densityρ0, absolute density, true density, skeleton density (volume without voids), see solid cubic meters
• Bulk densityρ, geometric density, volume density, apparent density (of a porous body, including cavities), cf.
• Cullet density ρ, apparent density (including pores, excluding cavities)
• Bulk densityρSch a mixture with a fluid including air
• Grain density, hectolitre weight (logistics)
• Potential densityσθ (Oceanography)
• Sealing compressible materials: compacting density, tapping density, filling density, tamping density, volume density of asphalt
• Sintered density of sintered materials

As a dimensionless comparison variable:

### Sizes per unit area

(Recommended designation according to DIN 5485: -Area density or -cover)

### Sizes per unit of length

(Recommended designation according to DIN 5485: -length density, covering or - hangings)

• Line charge density
• Capacity coverage
• Inductance coating

### Location-dependent density

\$ \ Mathrm dm \$ denotes the mass in a certain control volume \$ \ mathrm dV \$. If the mass is constantly distributed, a border crossing can be carried out; d. H. one lets the control volume become smaller and smaller and so the mass density \$ \ rho (\ mathbf x) \$ can be passed through

\$ \ mathrm dm = \ rho (\ mathbf x) \, \ mathrm dV \$

define. The function \$ \ rho: \ R ^ 3 \ to \ R \$ is also called Density field designated.

For a homogeneous body, the mass density of which has the value \$ \ rho_0 \$ everywhere in its interior, the total mass \$ m \$ is the product of density and volume \$ V \$, i.e. it applies

\$ m = \ rho_0 \, V \ ,. \$

In the case of inhomogeneous bodies, the total mass is more generally the volume integral over the mass density

\$ m = \ int_V \ rho (\ mathbf x) \, \ mathrm dV \ ,. \$

The density results from the masses of the atoms that make up the material and from their spacing. In a homogeneous material, for example in a crystal, the density is the same everywhere. It usually changes with temperature and, in the case of compressible materials (such as gases), with pressure. Therefore, for example, the density of the atmosphere is location-dependent and decreases with altitude.

The reciprocal of the density becomes specific volume and plays a role primarily in the thermodynamics of gases and vapors. The ratio of the density of a substance to the density under normal conditions is called the relative density.

In the first edition of DIN 1306 Density and weight; Terms from August 1938, the density in today's sense was called medium density standardized and the location-dependent density in a point as density simply defined: “The density (without the addition of 'mean') in a point of a body is the limit value towards which the mean density in a volume containing the point strives, if one thinks it reduced so much that it becomes small compared to the dimensions of the body, but still remains large against the structural units of its material. ”In the August 1958 issue, the medium density in density renamed with the explanation: "Mass, weight and volume are determined on a body whose dimensions are large compared to its structural components."

### Density determination by buoyancy

Attacking forces on the immersed body

According to Archimedes' principle, a body completely immersed in a liquid or gas experiences a buoyancy force that corresponds to the weight of the volume of the displaced liquid. About the two strangers density and volume two measurements are required to determine.

If you immerse any body with the volume VK completely in two liquids or gases with the known densities ρ1 and ρ2 one, so he experiences the different, resulting weight forces F.G1 or. F.G2. The resulting forces can be measured using a simple scale. The density you are looking for ρK can be determined as follows.

Based on the formula for the weight of the body and the buoyancy forces F.Ai:

\$ F_ {G} = V_K \ cdot \ rho_K \ cdot g \$,
\$ F_ {Ai} = V_K \ cdot \ rho_i \ cdot g \$

the two scales measure the weight forces for the masses immersed in the liquid (or gas) 1 or 2

\$ \, F_ {Gi} = F_G- | F_ {Ai} | \$

One eliminates the volume from the two equations for i = 1.2 VK, after a few simple mathematical transformations you get the solution:

\$ \ \ rho_K = \ frac {F_ {G1} \ cdot \ rho_2 - F_ {G2} \ cdot \ rho_1} {F_ {G1} -F_ {G2}} \$

If one density is much smaller than the other, \$ \ \ rho_1 \ ll \ rho_2 \ ,, \$ for example for air and water, the formula simplifies to:

\$ \ \ rho_K = \ frac {F_ {G1}} {F_ {G1} -F_ {G2}} \ cdot \ rho_2 \$

If you only have one liquid, for example water with density \$ \ rho_W \$, you can use the above method as follows:

Body weight before immersion:

\$ F_ {G} = V_K \ cdot \ rho_K \ cdot g \$,

Weight (reduced) of the body after (complete) immersion, whereby the volume \$ V_K \$ is displaced (this is measured either by the overflow from the full vessel or in the measuring cylinder):

\$ F_ {Gr} = V_K \ cdot \ rho_K \ cdot g - F_ {A} = V_K \ cdot g (\ rho_K - \ rho_W) \$,

so after forming

\$ \ rho_K = \ rho_W + \ frac {F_ {Gr}} {V_k \ cdot g} \$

Archimedes used this method to determine the density of the crown of a king who doubted whether it was really made of pure gold (ρK = 19320 kg / m3.)

On the buoyancy measurement to determine the density of liquids are based on the hydrometer (spindle) and the Mohr balance.

### Other measurement methods

• Pycnometer, determination of the density of solids or liquids by measuring the displaced liquid volumes
• Isotope method, density determination by radiation absorption.
• Flexural vibrator, density determination by vibration measurement

A simple estimate of the density can be obtained using the Girolami method.

### Table values

Table values ​​for the density of various substances can be found in the following articles:

### literature

• DIN 1306 Density; Terms, information