Ch.1 - Introduction: Matter, Energy, and Measurement

Brown - Chemistry: The Central Science 15th Edition

Brown15th EditionChemistry: The Central ScienceISBN: 9780137542970Not the one you use?Change textbook

Brown 15th Edition

Ch.1 - Introduction: Matter, Energy, and Measurement

Problem 37b

Chapter 1, Problem 37b

(b) Carbon dioxide (CO₂) is a gas at room temperature and pressure. However, carbon dioxide can be put under pressure to become a 'supercritical fluid' that is a much safer dry-cleaning agent than tetrachloroethylene. At a certain pressure, the density of supercritical CO₂ is 0.469 g/cm³. What is the mass of a 25.0-mL sample of supercritical CO₂ at this pressure?

Verified step by step guidance

Identify the given values: density of supercritical CO_2 is 0.469 g/cm^3 and the volume of the sample is 25.0 mL.

Recall the formula for mass using density and volume: \( \text{mass} = \text{density} \times \text{volume} \).

Substitute the given values into the formula: \( \text{mass} = 0.469 \, \text{g/cm}^3 \times 25.0 \, \text{mL} \).

Note that 1 mL is equivalent to 1 cm^3, so the units are consistent and will cancel appropriately.

Perform the multiplication to find the mass of the supercritical CO_2 sample.

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Key Concepts

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

Density

Density is defined as mass per unit volume, typically expressed in grams per cubic centimeter (g/cm³). It is a crucial property that helps determine how much mass is contained in a given volume of a substance. In this question, the density of supercritical CO₂ is provided, allowing us to calculate the mass of a specific volume of the substance.

Supercritical Fluids

Supercritical fluids occur when a substance is subjected to temperature and pressure above its critical point, resulting in unique properties that are distinct from gases and liquids. Supercritical CO₂, for example, can dissolve materials like a liquid while maintaining the diffusivity of a gas, making it useful in applications such as dry cleaning. Understanding this concept is essential for grasping the context of the question.

Mass Calculation

Mass calculation involves using the formula mass = density × volume. In this scenario, knowing the density of supercritical CO₂ and the volume of the sample allows us to compute the mass. This fundamental relationship is key to solving the problem presented in the question.

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