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

Short Answer

Expert verified
(a) The density of tetrachloroethylene can be calculated using the formula \(density = \frac{mass}{volume}\), which gives \(\rho = \frac{40.55 \mathrm{~g}}{25.0 \mathrm{~mL}} = 1.62 \mathrm{g/cm^3}\). Since this is greater than the density of water (\(1 \mathrm{g/cm^3}\)), tetrachloroethylene will not float on water. (b) To find the mass of the \(25.0-\mathrm{mL}\) sample of supercritical \(\mathrm{CO}_{2}\), we need to use the density formula: \(mass = density \times volume\). This gives \(m = 0.469 \mathrm{~g/cm^3} \times 25.0 \mathrm{~mL} = 11.7 \mathrm{~g}\) for the mass of the supercritical \(\mathrm{CO}_{2}\) sample.

Step by step solution

01

(a) Calculate the density of tetrachloroethylene

To find the density of tetrachloroethylene, we use the formula for density: \(density = \frac{mass}{volume}\) Given that the mass of the sample is \(40.55 \mathrm{~g}\) and its volume is \(25.0 \mathrm{~mL}\), we can find the density. Note that \(1 \mathrm{mL}\) is equal to \(1 \mathrm{cm^3}\).
02

(a) Determine if tetrachloroethylene will float on water

To determine if tetrachloroethylene will float on water, we can compare its density to the density of water. Since the density of water at room temperature is about \(1 \mathrm{g/cm^3}\), any material with a density lower than this value will float on water.
03

(b) Calculate the mass of a \(25.0-\mathrm{mL}\) sample of supercritical \(\mathrm{CO}_{2}\)

To find the mass of the \(25.0-\mathrm{mL}\) sample of supercritical \(\mathrm{CO}_{2}\), we need to use the density formula mentioned above: \(mass = density \times volume\) By rearranging the density formula and inputting the given values, we can find the mass of the sample.

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