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Ch.1 - Chemical Tools: Experimentation & Measurement
Chapter 1, Problem 15

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

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

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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.
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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.
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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.
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Related Practice
Textbook Question
A scientist uses an uncalibrated pH meter and measures the pH of a rainwater sample four times. A different pH meter was calibrated using several solutions with known pH. The true pH of the rain was found by the calibrated pH meter to be 5.12. What can be said about the level of accuracy and precision of the uncalibrated pH meter? (LO 1.14) (a) The uncalibrated pH meter is accurate and precise. (b) The uncalibrated pH meter is neither accurate nor precise. (c) The uncalibrated pH meter is accurate but not precise. (d) The uncalibrated pH meter is precise but not accurate.
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Textbook Question
Perform the calculation, and report the answer to the correct number of significant figures. (LO 1.16) (a) 1.5 * 10^-4 (b) 1.55 * 10^-4 (c) 1.547 * 10^-4 (d) 1.5473 * 10^-4
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Textbook Question
A person runs at a pace of 6.52 mi/hr. How long does it take the person to run a 15.0 km race? (1 mi = 1.61 km) (LO 1.17) (a) 85.7 min (b) 222 min (c) 50.0 min (d) 93.4 min
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Textbook Question
Which block in each of the following drawings of a balance is more dense, red or green? Explain.
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Textbook Question
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