Density of Aerogels

Aerogels are extremely light foams that look like clusters of bubbles or foam. They have been called the rarest form of matter, and have the lowest density of any material known.

They are strong (the Figure shows a brick supported by a nearly invisible aerogel), and they are incredibly good insulators. A MOVIE shows that if one side of a 6 mm aerogel blanket is heated to 1000 ° C, the other side can still be touched. Aerogels are also good at cushioning impact, and may be used to protect sensitive equipment like hard drives. Aerogels feel like styrofoam, but look like "frozen smoke".

The terms heavy and light are commonly used in two different ways. We refer to weight when we say that an adult is heavier than a child. On the other hand, something else is alluded to when we say that styrofoam is heavier than an aerogel. A small sample of styrofoam would obviously weigh less than a roomful of aerogel, but styrofoam is heavier in the sense that a piece of given size weighs more than the same-size piece of balsa.

What we are actually comparing is the mass per unit volume, that is, the density. In order to determine these densities, we might weigh a cubic centimeter of each material. If the styrofoam weighed 0.10 g and the aerogel 0.001 g, we could describe the density of styrofoam as 0.10 g cm^–3 and that of an aerogel as 0.001 g cm^–3. (Note that the negative exponent in the units cubic centimeters indicates a reciprocal. Thus 1 cm^–3 = 1/cm³ and the units for our densities could be written as g/cm³, or g cm^–3. In each case the units are read as grams per cubic centimeter, the per indicating division.) We often abbreviate "cm³" as "cc", and 1 cm³ = 1 mL exactly, by definition.

In general it is not necessary to weigh exactly 1 cm³ of a material in order to determine its density. We simply measure mass and volume and divide volume into mass:

\[\text{Density} = \dfrac{\text{mass}} {\text{volume}}\]

or

\[\rho = \dfrac{\text{m}} {\text{V}}\]

where ρ = density m = mass V = volume

Example \(\PageIndex{1}\): Density of Aerogel

Calculate the density of (a) a piece of aerogel whose mass is 0.0167 g and which, when submerged, increases the water level in a graduated cylinder by 13.9 ml; (b) a styrofoam cylinder of mass 1.3918 g, radius 0.750 cm, and height 5.25 cm.

Solution

a) Since the submerged metal displaces its own volume,

\[\text{Density} =\rho = \dfrac{\text{m}} {\text{V}} = \dfrac{0.0167 g} {13.9 mL} = \text {0.0012 g/mL or 0.0012 g mL}^{-1}\]

b) The volume of the cylinder must be calculated first, using the formula

\(\text{V} = \pi \text{r}^2 \text{h} = \text{3.142} \times \text{(0.750 cm)}^2 \times \text{5.25 cm} = \text{9.278 718 8 cm}^3\)

Then \[\rho = \dfrac{\text{m}} {\text{V}} = \dfrac{1.3918g} {9.278 718 8cm^{3}} = 0.150 \dfrac{g} {cm^{3}}\]

Table \(\PageIndex{1}\) Densities of Common Elements and Compounds

Substance	Density/g/cm^3 at 20^oC
Hydrogen gas	0.000089
Helium gas	0.00018
Air	0.00128
Aerogels	0.001 −0.002
styrofoam	0.03 - 0.12
Carbon Dioxide	0.001977
[| Sulfur hexafluoride]	0.006164
Argon	0.0018
[| Halon 1301]	.0066
grain alcohol	0.79
Water	1.00
Aluminum	2.7
Gold	17.31
osmium	22.61

Note

Note that unlike mass or volume, the density of a substance is independent of the size of the sample. Thus density is a property by which one substance can be distinguished from another. A sample of pure aluminum can be trimmed to any desired volume or adjusted to have any mass we choose, but its density will always be 2.70 g/cm³ at 20°C. The densities of some common pure substances are listed in the Table.

Tables and graphs are designed to provide a maximum of information in a minimum of space. When a physical quantity (number × units) is involved, it is wasteful to keep repeating the same units. Therefore it is conventional to use pure numbers in a table or along the axes of a graph. A pure number can be obtained from a quantity if we divide by appropriate units. For example, when divided by the units gram per cubic centimeter, the density of aluminum becomes a pure number 2.70:

\[\dfrac{\text{Density of aluminum}} {\text{1 g cm}^{-3}} = \dfrac{\text{2.70 g cm}^{-3}} {\text{1 g cm}^{-3}} = 2.70\]

Therefore, a column in a table or the axis of a graph is conveniently labeled in the following form:

\(\dfrac{\text{Quantity}}{\text{units}}\)

This indicates the units that must be divided into the quantity to yield the pure number in the table or on the axis. This has been done in the second column of the Table.

From ChemPRIME: 1.8: Density

Contributors and Attributions

• Ed Vitz (Kutztown University), John W. Moore (UW-Madison), Justin Shorb (Hope College), Xavier Prat-Resina (University of Minnesota Rochester), Tim Wendorff, and Adam Hahn.