## Density

Solids Density (ρs) is the density of the solid soil particles only in units of mass per volume e.g., (g/cm³), or (g cm⁻³). Often in texts the greek letter rho (ρ) is a shorthand symbol for density and, s, is for solids.

The Particle Density equals the Weight of the Solids divided by the Volume of the Solids. Or said another way the dividend "Weight of the Solids" and divisor "Volume of the Solids" yields "Particle Density" as the quotient.
$$\frac{Weight\,of\,Solids}{Volume\,of\,Solids} = Particle\,Density$$

In mathematical shortcut symbols, or icons, the relationship is presented as:

$\genfrac{}{}{0.1ex}{}{\text{W}{}_{\text{s}}}{\text{V}{}_{\text{s}}}={\rho }_{\text{s}}$  where ρ is density, W is weight, V is volume, and s is solids.

The reader is cautioned to mind the defined variables in equations representing physical and chemical relationships. The variable representing the definition is not as important as the definition, and eventually the representation of the relationships conveyed. As an example ρs is defined as ρp (density of particles) in some textbooks. In some instances a capitol D is used instead of ρ to represent density itself, likely in an effort to not hunt down how to use greek letters in the presentation system. No matter the symbols, or icons, used to represent the defined, it is the relationships they represent that matter.

Ranges of particle density values for typical soil materials differs for inorganic and organics. For inorganic materials ρs is 2.60 to 2.75 $\genfrac{}{}{0.1ex}{}{\text{g}}{\text{cm}{}^{3}}$ ( $\text{Al}=\genfrac{}{}{0.1ex}{}{\text{27 g}}{\text{mol}}$ ; $Si=\genfrac{}{}{0.1ex}{}{\text{28 g}}{\text{mol}}$ ; and Fe =  $\genfrac{}{}{0.1ex}{}{\text{56 g}}{\text{mol}}$ ). If the precise aggregated mean of the particle density of size separates for a mineral sample is not known the particle density of quartz, 2.65 $\genfrac{}{}{0.1ex}{}{\text{g}}{\text{cm}{}^{3}}$ , is often assumed to be the most probable value. For organic materials ρs is 0.90 to 1.30 $\genfrac{}{}{0.1ex}{}{\text{g}}{\text{cm}{}^{3}}$ (C = 12 $\genfrac{}{}{0.1ex}{}{\text{g}}{\text{mol}}$ ; O = 16 $\genfrac{}{}{0.1ex}{}{\text{g}}{\text{mol}}$ ; and H = 1 $\genfrac{}{}{0.1ex}{}{\text{g}}{\text{mol}}$ ).

The aggregate ρs is affected by the kind of minerals or rock (e.g., iron is heavier than aluminum) and the proportion of organic matter to mineral (inorganic) material.

The individual particle ρs is not affected by texture or soil structure (arrangement of soil solids).

Bulk Densityb) is a measure of the weight of the soil per unit volume ( $\genfrac{}{}{0.1ex}{}{\text{g}}{\text{cm}{}^{3}}$ ). The bulk density volume includes both solids and pore space. Usually reported as the weight of oven-dry soil following heating to 110℃.

$\text{Bulk Density}=\left(\genfrac{}{}{0.1ex}{}{\text{Weight of Solids}}{\text{Volume of Solids + Voids}}\right)$

ρb = Ms/Vt where b is for bulk (sampled with pores intact), and t is total (pores and solids) and the particle solids are s.

The ρs values for most mineral (inorganic) soils are 1.20 to 1.40 g/cm³ and for organic soils 0.10 to 0.25 g/cm³. Recall that the density of water (ρw), at STP, is 1.00 g/cm³.

Bulk Density is affected by:

1. Particle density
2. Texture because it affects total porosity; ρb(sand) > ρb(clay)
3. Soil structure because it affects porosity
4. Concentration of organic matter – affects the average ρs and porosity
5. Cultivation – tends to result in both compaction and destruction of organic matter

Think about number two above. It is counter intuitive to some learners because most people equate infiltration speed with greater porosity.

Infiltration is also impacted by the pore size distribution. Larger pores can transmit water more readily than smaller pores due to waters interaction with the solid surfaces and resulting turbulent flow. Sands favor the larger pore sizes.

Bulk density and porosity are inversely related. For any soil horizon as bulk density goes up, porosity goes down.

Bulk density is affected by particle density. Texture affects total soil porosity (see Soil Porosity) where ρb sand is greater than ρb of clay. Soil structure also affects porosity and, therefore, bulk density. Aggregation of particles, or soil structure, affects porosity by favoring an increase in macropores (see Particle Arraignment).

Concentration of organic matter affects average ρs and porosity. Cultivation tends to result in both compaction and destruction of organic matter thus increasing bulk density.

Be cautious here as average particle density and ‘textural classes’ are not necessarily similar. Textural classes determined in laboratory analysis is done so after removing evaporites, iron (oxy)hydroxides, and organic matter, salts, or evaporites. When using the phrase 'average particle density' the meaning may be including organic matter, salts, and salts, e.g., increase in organic matter content decreases average particle density of the soil.

Evaporite
Operationally defined as minerals that form readily by precipitation during the evaporation, or desiccation, of a solution and that have solubilities higher than that of gypsum $$\left(CaSO_4\thinspace ·\thinspace 2\thinspace H_2O\right)$$. Also, in the glossary.