(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?

검증된 단계별 안내

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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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

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.