Problem 35 - Chemistry The Central Science In Si Units

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 "supercritical fluid" that is a much safer dry-cleaning agent than tetrachloroethylene. At a certain pressure, the density of supercritical \(\mathrm{CO}_{2}\) is \(0.469 \mathrm{~g} / \mathrm{cm}^{3} .\) What is the mass of a 25.0-mL sample of supercritical \(\mathrm{CO}_{2}\) at this pressure?

Step-by-Step Solution

Answer

(a) Density of tetrachloroethylene: 1.622 g/mL; it will not float on water. (b) Mass of supercritical CO2: 11.725 g.

Step 1: Calculate the Density of Tetrachloroethylene

To find the density of tetrachloroethylene at 25°C, use the formula for density: \[\text{Density} = \frac{\text{Mass}}{\text{Volume}}\]Given that the mass of tetrachloroethylene is 40.55 g and the volume is 25.0 mL, we substitute these values into the formula:\[\text{Density} = \frac{40.55 \, \text{g}}{25.0 \, \text{mL}} = 1.622 \, \text{g/mL}\]

Step 2: Determine if Tetrachloroethylene Will Float on Water

Next, we need to compare the density of tetrachloroethylene with the density of water, which is approximately 1.00 g/mL at 25°C. Since tetrachloroethylene has a density of 1.622 g/mL, which is greater than the density of water, it will not float on water.

Step 3: Calculate the Mass of Supercritical CO2

Given that the density of supercritical CO2 is 0.469 g/cm³, we need to find the mass of a 25.0 mL sample. Since 1 mL = 1 cm³, we can use the density formula:\[\text{Mass} = \text{Density} \times \text{Volume} = 0.469 \, \text{g/cm}^3 \times 25.0 \, \text{cm}^3 = 11.725 \, \text{g}\]

Key Concepts

Tetrachloroethylene

Tetrachloroethylene, also known as perchloroethylene or PCE, is a volatile organic compound most widely used in the dry cleaning industry. It appears as a colorless liquid with a sweet smell. However, despite its efficacy in removing stains, it has been criticized due to its potential health risks.

PCE is under scrutiny because it can potentially cause cancer, leading to its gradual phase-out in favor of safer alternatives. It's crucial to handle it with care and follow safety guidelines to minimize exposure. It's heavier than water; thus, it will sink when introduced to a water body due to its higher density. Understanding these properties helps us make informed choices about using and substituting hazardous chemicals.

Supercritical CO2

Supercritical carbon dioxide (CO2) is an exciting form of CO2 that is neither entirely a gas nor a liquid but possesses properties of both. By maintaining CO2 above a certain pressure and temperature, it becomes a supercritical fluid. This state is achieved when the pressure is above 73.8 bar and the temperature is above 31.1°C.

Due to its unique properties, supercritical CO2 is an excellent solvent. It has a lower toxicity level compared to tetrachloroethylene, making it a safer alternative for applications like dry cleaning. Its ability to penetrate materials like a gas while dissolving substances like a liquid allows it to clean without leaving any harmful residues. The transition into supercritical form makes it a sustainable choice for industrial applications.

Density calculation

Density is an important physical property that relates the mass of an object to its volume. It is calculated using the formula:
\[\text{Density} = \frac{\text{Mass}}{\text{Volume}} \]
To determine the density of a substance, divide its mass (measured in grams) by its volume (measured in milliliters or cubic centimeters). This calculation is essential for understanding how substances behave when interacting with each other, such as whether a material will float or sink in water.

In the case of tetrachloroethylene, its density of 1.622 g/mL indicates that it is heavier than water, which is about 1.00 g/mL at room temperature. Conversely, supercritical CO2, with a density of 0.469 g/cm³, is less dense than water. Understanding density helps us predict the behavior of substances in various conditions.

Floating and sinking

The concepts of floating and sinking are mainly explained by comparing the densities of an object and the liquid it's placed in. Simply put, an object will float in a liquid if its density is less than the liquid's density.

Since density is defined as mass per unit volume, a denser substance will naturally want to settle below a less dense substance. This principle can help predict behavior in fluid environments. For example, knowing that water has a density of approximately 1.00 g/mL at standard room temperature, any material with a density less than this will float on water.

Tetrachloroethylene, having a density of 1.622 g/mL, will sink, while substances with lower densities, such as supercritical CO2's 0.469 g/cm³, will float on water. Recognizing these factors helps in making critical decisions in scientific and everyday applications.