Problem 35 - Chemistry The Central Science

Question

(a) A sample of tetrachloroethylene, a liquid used in dry cleaning that is being phased out because of its potential to cause cancer, has a mass of 40.55 \(\mathrm{g}\) and a volume of 25.0 \(\mathrm{mL}\) at \(25^{\circ} \mathrm{C}\) . What is its density at this temperature? Will tetrachloroethylene float on water? (Materials that are less dense than water will float.) (b) Carbon dioxide \(\left(\mathrm{CO}_{2}\right)\) is a gas at room temperature and pressure. However, carbon dioxide can be put under pressure to become a usupercritical fluid" that is a much safer dry-cleaning agent than tetrachlorosthvlene, At a certain pressure, the density of super critical \(\mathrm{CO}_{2}\) is 0.469 \(\mathrm{g} / \mathrm{cm}^{3} .\) What is the mass of a 25.0 \(\mathrm{-mL}\) sample of supercritical \(\mathrm{CO}_{2}\) at this pressure?

Step-by-Step Solution

Answer

The density of tetrachloroethylene at \(25^{\circ} \mathrm{C}\) is \(1.622 \, \frac{\text{g}}{\text{mL}}\), and since it is denser than water, it will not float on water. The mass of a 25.0 mL sample of supercritical CO2 at the given pressure is 11.725 g.

Step 1: Calculate the density of tetrachloroethylene

We are given the mass and volume of tetrachloroethylene. We can use the formula for density to find its value: Density = \(\frac{Mass}{Volume}\) We can plug in the given values to obtain the density: Density = \(\frac{40.55 \,\text{g}}{25.0 \,\text{mL}}\) Now, we calculate the density: Density = \(1.622 \, \frac{\text{g}}{\text{mL}}\)

Step 2: Compare density with water

To determine if tetrachloroethylene will float on water, we must compare its density with the density of water. The density of water is approximately \(1.0 \, \frac{\text{g}}{\text{mL}}\) at \(25^{\circ} \mathrm{C}\). Since the density of tetrachloroethylene (\(1.622 \, \frac{\text{g}}{\text{mL}}\)) is greater than the density of water (\(1.0 \, \frac{\text{g}}{\text{mL}}\)), it will not float on water.

Step 3: Calculate the mass of supercritical CO2

We are given the density and volume of supercritical CO2, and we need to calculate its mass. We can rearrange the density formula to get the desired value: Mass = Density × Volume Plugging in the given values, we can calculate the mass of supercritical CO2: Mass = \(0.469 \, \frac{\text{g}}{\text{cm}^3} \times 25.0 \,\text{mL}\) (Note that \(1 \, \text{mL} = 1 \, \text{cm}^3\).) Now, we calculate the mass: Mass = \(11.725 \, \text{g}\) Therefore, a 25.0 mL sample of supercritical CO2 at the given pressure has a mass of 11.725 g.

Key Concepts

Tetrachloroethylene

Tetrachloroethylene is a chemical compound widely used in the dry cleaning industry due to its ability to dissolve organic materials efficiently. Known as perchloroethylene, or "perc," this clear liquid has found extensive use in cleaning and degreasing activities. However, its usage is being reconsidered, primarily due to health concerns like its classification as a potential carcinogen. Subsequently, safer alternatives are sought in various sectors including dry cleaning. When it comes to density, tetrachloroethylene features a density of approximately 1.622 g/mL at 25°C. This density value means it is denser than water (which has a density of about 1.0 g/mL at the same temperature), and therefore, tetrachloroethylene will sink when placed in water rather than float. Understanding this property is essential in applications requiring separation of substances based on their density differences.

Supercritical Fluids

Supercritical fluids are fascinating states of matter that occur beyond critical points of temperature and pressure. A supercritical fluid exhibits properties of both gases and liquids, acting as a solvent like a liquid but diffusing through materials like a gas. This unique characteristic makes them incredibly versatile and valuable in various applications, including in the replacement of traditional dry-cleaning solvents. Carbon dioxide ( CO_{2} ) can become a supercritical fluid, providing an environmentally friendly alternative to chemicals like tetrachloroethylene. Supercritical CO_{2} offers a safer and non-toxic option, as it is not flammable and can penetrate materials effectively without damaging them. Companies use supercritical CO_{2} in supercritical extraction, where it helps to separate components based on their solubility in the fluid. Supercritical fluids are increasingly adopted in various industries due to their tunable properties and environmentally benign nature.

Carbon Dioxide

Carbon dioxide, represented chemically as CO_{2} , is a colorless gas vital for life on Earth. At room temperature and pressure, CO_{2} remains a gas and is produced by combustion processes, cellular respiration, and volcanic eruptions. It plays a crucial role in the ecological cycle as plants absorb it for photosynthesis and release oxygen in return. When subjected to high pressure and temperature, carbon dioxide transforms into supercritical fluid. In this state, CO_{2} exhibits a density of 0.469 g/cm³ at certain pressure conditions, making it suitable for dry cleaning and other industrial applications. One advantage of using supercritical CO_{2} is that it doesn't leave harmful residues or potential pollutants when the cleaning process is complete. Converting CO_{2} to a supercritical form for various applications is not only effective but also aids in reducing the environmental footprint left by more traditional methods. This makes it a preferred choice for those looking to align with sustainable practices.