Density

Absolute density is an intensive property that measures the concentration of mass per unit volume of a substance.

$$\boxed{\rho = \frac{m}{V}}$$

where:

• $\rho$: Absolute density [kg/m³ (SI)]
• $m$: Mass of the substance [g, kg]
• $V$: Volume occupied [cm³, m³, L]

• Solids and liquids: g/cm³, g/mL, kg/L, lb/ft³
• Gases: g/L, kg/m³ (at standard conditions)

$$1 \text{ g/cm}^3 = 1000 \text{ kg/m}^3 = 1 \text{ kg/L}$$

$$1 \text{ lb/ft}^3 = 16.0185 \text{ kg/m}^3$$

Densities measured at standard conditions (P = 1 atmosphere and T = 0°C)

Substance	S.I. (kg/m³)	Common (g/cm³)
Cork	240	0.24
Wood	500	0.50
Paper	700	0.70
NaCl	2160	2.16
Cu	8920	8.92
Au	19300	19.3
Os	22400	22.4
Lead	11300	11.3
Glass	2600	2.6
Brick (average)	1900	1.9
Hard Rubber	1200	1.2

Substance	S.I. (kg/m³)	Common (g/cm³)
Chloroform	1500	1.50
Ethyl Alcohol	780	0.78
Oil	800	0.80
Seawater	1040	1.04
Milk	1030	1.03
Blood	1060	1.06
Bromine	3120	3.12
Mercury	13600	13.6
Glycerin	1260	1.26
Sulfuric Acid	1840	1.84
Gasoline (approx.)	670	0.67

Substance	S.I. (kg/m³)	Common (g/L)
H₂	0.09	0.09
Air	1.29	1.29
O₂	1.43	1.43
CO₂	1.98	1.98

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For homogeneous or heterogeneous mixtures, the density is calculated as:

$$\boxed{\rho_M = \frac{m_{\text{total}}}{V_{\text{total}}} = \frac{m_A + m_B + m_C + \cdots}{V_A + V_B + V_C + \cdots}}$$

When each component occupies the same volume:

$$\rho_M = \frac{\rho_1 + \rho_2 + \cdots + \rho_n}{n}$$

Example: Mixture of 3 liquids with equal volumes:

$$\rho_M = \frac{\rho_1 + \rho_2 + \rho_3}{3}$$

When each component has the same mass:

$$\rho_M = \frac{n}{\frac{1}{\rho_1} + \frac{1}{\rho_2} + \cdots + \frac{1}{\rho_n}}$$

Example: Mixture of 2 substances with equal masses:

$$\rho_M = \frac{2}{\frac{1}{\rho_1} + \frac{1}{\rho_2}} = \frac{2\rho_1\rho_2}{\rho_1 + \rho_2}$$

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Relative density (ρᵣ or SG) is a dimensionless quantity that compares the density of a substance to a standard reference.

$$\boxed{\rho_r = SG = \frac{\rho_{\text{substance}}}{\rho_{\text{reference}}}}$$

State	Reference Substance	Conditions	Reference Density
Solids and liquids	Pure water	4°C and 1 atm	$1.000 \text{ g/cm}^3$
Gases	Dry air	S.T.P. (0°C, 1 atm)	$1.2929 \text{ g/L}$

• SG < 1: The substance is less dense than the reference (floats)
• SG = 1: Density equal to the reference
• SG > 1: The substance is denser than the reference (sinks)

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An intensive property that relates the weight of a substance to its volume.

$$\boxed{\gamma = \frac{W}{V} = \frac{mg}{V} = \rho g}$$

• International System (SI): N/m³
• Technical System: kgf/m³

$$\gamma = \rho \times g$$

Where $g = 9.80665 \text{ m/s}^2$ (standard acceleration of gravity)

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Relationship between the specific weight of a substance and that of the reference substance.

$$\boxed{\gamma_r = \rho_r = SG}$$

Proof:

$$\gamma_r = \frac{\gamma_{\text{subst}}}{\gamma_{\text{ref}}} = \frac{\rho_{\text{subst}} g}{\rho_{\text{ref}} g} = \frac{\rho_{\text{subst}}}{\rho_{\text{ref}}} = \rho_r$$

Density of chemical elements under laboratory conditions, expressed in $\frac{g}{cm^3}$ (elements with a density greater than osmium or iridium only have a theoretical density: superheavy radioactive elements are produced in quantities too low or decay too rapidly to allow measurement):

Density of the elements at their melting point in $\frac{g}{cm^3}$: