(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 drycleaning 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 \(25.0-\mathrm{mL}\) sample of supercritical \(\mathrm{CO}_{2}\) at this pressure?

Step by step solution

01

Find the density of tetrachloroethylene

The formula for density is: $$ \text{Density} = \frac{\text{Mass}}{\text{Volume}} $$ Given mass = \(40.55\mathrm{~g}\), and volume = \(25.0\mathrm{~mL}\), we can find the density of tetrachloroethylene at \(25^{\circ}\mathrm{C}\) as follows: $$ \text{Density} = \frac{40.55\mathrm{~g}}{25.0\mathrm{~mL}} $$

02

Calculate the density of tetrachloroethylene

Using the provided data: $$ \text{Density} = \frac{40.55\mathrm{~g}}{25.0\mathrm{~mL}}=1.62 \mathrm{~g/mL} $$ So, the density of tetrachloroethylene at \(25^{\circ}\mathrm{C}\) is \(1.62\mathrm{~g/mL}\).

03

Determine if tetrachloroethylene will float on water

Water has a density of approximately \(1.0\mathrm{~g/mL}\). Since the density of tetrachloroethylene is \(1.62\mathrm{~g/mL}\), which is higher than the density of water, tetrachloroethylene will NOT float on water.

04

Find the mass of a \(25.0\mathrm{~mL}\) sample of supercritical \(\mathrm{CO}_{2}\)

We are given the density of supercritical \(\mathrm{CO}_{2}\) as \(0.469\mathrm{~g/cm^3}\). We also know that \(1 \mathrm{~mL} = 1 \mathrm{~cm^3}\). Therefore, the density of supercritical \(\mathrm{CO}_{2}\) can also be expressed as \(0.469\mathrm{~g/mL}\). Given the volume of the supercritical \(\mathrm{CO}_{2}\) sample as \(25.0\mathrm{~mL}\), we need to find its mass. Use the density formula and rearrange to solve for mass: $$ \text{Mass} = \text{Density} \times \text{Volume} $$ Plug in the known values for density and volume: $$ \text{Mass} = 0.469 \mathrm{~g/mL} \times 25.0\mathrm{~mL} $$

05

Calculate the mass of the supercritical \(\mathrm{CO}_{2}\) sample

Using the provided data: $$ \text{Mass} = 0.469 \mathrm{~g/mL} \times 25.0\mathrm{~mL} = 11.725\mathrm{~g} $$ So, the mass of a \(25.0\mathrm{~mL}\) sample of supercritical \(\mathrm{CO}_{2}\) at the given pressure is \(11.725\mathrm{~g}\).

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