Aerogels are transparent, low-density materials that are nearly 99.8% empty space and excellent insulators against hot and cold. The density of a silica-based aerogel is 3.0 mg/cm3. What is the density in units of g/m3? (LO 1.17) (a) 3.0 * 10-3 g/m3(b) 3.0 * 101 g/m3 (c) 3.0 g/m3(d) 3.0 * 103 g/m3

Verified step by step guidance

1. Convert the given density from mg/cm^3 to g/cm^3 by dividing by 1000, since 1 g = 1000 mg.
2. Recognize that 1 cm^3 is equivalent to 1 mL, and 1 m^3 is equivalent to 1,000,000 mL.
3. Convert the density from g/cm^3 to g/m^3 by multiplying by 1,000,000, since there are 1,000,000 cm^3 in 1 m^3.
4. Perform the multiplication to find the density in g/m^3.
5. Compare the calculated density with the given options to determine the correct answer.

Key Concepts

Density Conversion

Density is defined as mass per unit volume, typically expressed in units like grams per cubic centimeter (g/cm³) or grams per cubic meter (g/m³). To convert between these units, one must recognize that 1 g/cm³ is equivalent to 1000 g/m³. Therefore, understanding how to convert density from mg/cm³ to g/m³ is essential for solving the problem.

Unit Prefixes

Unit prefixes such as 'milli-' (m) and 'kilo-' (k) are used to denote specific powers of ten. For example, 'milli-' indicates a factor of 10^-3, meaning 1 mg is 0.001 g. Recognizing these prefixes helps in accurately converting measurements and understanding the scale of the values involved in the problem.

Aerogel Properties

Aerogels are unique materials characterized by their low density and high porosity, making them excellent insulators. Their structure, which consists mostly of air, contributes to their thermal insulating properties. Understanding the physical properties of aerogels can provide context for their applications and the significance of their density in practical scenarios.