Question

Trichloroethane, \(\mathrm{C}_{2} \mathrm{H}_{3} \mathrm{Cl}_{3}\) is used as a degreaser (solvent for waxes and oils). Its density is \(1.435 \mathrm{~g} / \mathrm{mL}\) and its vapor pressure at \(20^{\circ} \mathrm{C}\) is \(124 \mathrm{~mm} \mathrm{Hg}\). (a) How many mL will vaporize in an evacuated \(1.50-\mathrm{L}\) flask at \(20^{\circ} \mathrm{C} ?\) (b) A 3.00-mL sample is poured into an evacuated 1.5 - \(\mathrm{L}\) flask at \(20^{\circ} \mathrm{C}\). Will all the liquid vaporize? If not, what is the pressure in the flask? (c) A similar 3.00 -mL sample is poured into an evacuated \(20.00-\mathrm{L}\) flask at \(20^{\circ} \mathrm{C}\). What physical state(s) is/are in the flask?

Short answer

In summary, under the given conditions: (a) About 0.9311 mL of trichloroethane will vaporize in a 1.50-L flask at 20°C. (b) Not all the liquid will vaporize in a 1.5-L flask, leaving both liquid and gaseous trichloroethane, with a pressure of 0.1632 atm after vaporization. (c) All the liquid will vaporize in a 20.0-L flask at 20°C, resulting in only gaseous trichloroethane in the flask.

Step-by-step solution

Part (a): Calculate the moles of trichloroethane and the amount of vapor produced.

We have a \(1.50-L\) flask and want to know the volume in mL of trichloroethane that will vaporize at \(20^{\circ}\mathrm{C}\). First, we'll convert the temperature from Celsius to Kelvin: \(T = 20^{\circ}\mathrm{C} + 273.15 = 293.15\mathrm{K}\). Next, we'll convert the given vapor pressure to atmospheres: \(P = \frac{124\,\text{mm}\,\text{Hg}}{760\,\text{mm}\,\text{Hg}/\mathrm{atm}} = 0.1632\,\text{atm}\). Using the Ideal Gas Law, we can find the number of moles (n) of trichloroethane that will vaporize: \(PV=nRT \Rightarrow n=\frac{PV}{RT} = \frac{0.1632\,\text{atm}\times 1.50\,\text{L}}{0.0821\,\text{L}\,\text{atm}\, \text{K}^{-1}\,\text{mol}^{-1}\times 293.15\,\text{K}} \approx 0.0100\,\text{mol}\) Now, we'll use the formula: mass = moles \(\times\) molar_mass and density = mass/volume to find the volume of vapor produced: \(V = \frac{0.0100\,\text{mol}\times 133.4\,\text{g/mol}}{1.435\,\text{g/mL}} \approx 0.9311\,\text{mL}\). So, approximately \(0.9311\,\text{mL}\) of trichloroethane will vaporize in the 1.50-L flask at 20°C.

Part (b): Calculate the moles of trichloroethane and determine if it will all vaporize

We have 3.00 mL of trichloroethane in a \(1.5\,\text{L}\) flask. First, we'll find the moles of trichloroethane in the liquid: \(\text{moles} = \frac{\text{mass}}{\text{molar_mass}} = \frac{3.00\,\text{mL}\times 1.435\,\text{g/mL}}{133.4\,\text{g/mol}} \approx 0.0323\,\text{mol}\) Using the ideal gas law, let's calculate how many moles of trichloroethane will vaporize at 0.1632 atm: \(P V= n R T \Rightarrow n=\frac{PV}{RT} = \frac{0.1632\,\text{atm}\times 1.50\,\text{L}}{0.0821\,\text{L}\,\text{atm}\, \text{K}^{-1}\,\text{mol}^{-1}\times 293.15\,\text{K}} \approx 0.0100\,\text{mol}\) Since 0.0323 mol > 0.0100 mol, not all the liquid will vaporize. The remaining trichloroethane in the liquid state is \(0.0323 - 0.0100 = 0.0223\) mol. Now, we'll find the new pressure in the flask after vaporization: \(P = \frac{nRT}{V} = \frac{0.0100\,\text{mol}\times 0.0821\,\text{L}\,\text{atm}\, \text{K}^{-1}\,\text{mol}^{-1}\times 293.15\,\text{K}}{1.5\,\text{L}} \approx 0.1632\,\mathrm{atm}\) The pressure in the flask after vaporization is 0.1632 atm.

Part (c): Calculate the new pressure after vaporization and determine the physical state(s)

We have 3.00 mL of trichloroethane in a \(20.0\,\text{L}\) flask. Let's calculate how many moles of trichloroethane will vaporize at 0.1632 atm: \(PV=nRT \Rightarrow n=\frac{PV}{RT} = \frac{0.1632\,\text{atm}\times 20.00\,\text{L}}{0.0821\,\text{L}\,\text{atm}\, \text{K}^{-1}\,\text{mol}^{-1}\times 293.15\,\text{K}} \approx 0.1334\,\text{mol}\) Since 0.0323 mol < 0.1334 mol, all the liquid will vaporize in the \(20.0\,\text{L}\) flask at 20°C, and the physical state in the flask will be a gas.

Key concepts

Vapor Pressure Calculation

Vapor pressure is a critical concept in thermodynamics and chemistry that refers to the pressure exerted by a vapor when it's in equilibrium with its condensed phases (solid or liquid) at a given temperature. Understanding how to calculate vapor pressure is vital, as it determines whether a substance will remain as a liquid or turn into gas under specific conditions.

Let's dive into a practical application of vapor pressure calculation by revisiting the provided exercise. We determined whether trichloroethane would vaporize completely in different flask sizes at a constant temperature. First, we calculated the vapor pressure of the substance and then used the Ideal Gas Law to find the amount of trichloroethane that will vaporize.

To make the exercise more accessible, remember that the conversion from Celsius to Kelvin is always essential since the Ideal Gas Law requires absolute temperature. Also, converting pressure units to atmospheres simplifies the use of the gas constant, R. Lastly, ensure you understand the relationship between moles, mass, and density to calculate the volume accurately.

Ideal Gas Law

The Ideal Gas Law is a cornerstone of gas behavior, encapsulated in the equation: \(PV = nRT\). This law relates the pressure (P), volume (V), moles of gas (n), temperature (T in Kelvin), and the gas constant (R).

In the context of the textbook solution, the Ideal Gas Law allowed us to conclude how much trichloroethane vapor would form in varying flask volumes. When applying the Ideal Gas Law, it's crucial to use consistent units, especially for pressure (atmospheres) and volume (liters), and to plug in the correct value for R based on these units (0.0821 L·atm·K^-1·mol^-1).

Remember:

• The Ideal Gas Law assumes an ideal gas where particles have no volume and no intermolecular forces, which works well for many practical situations despite real gases deviating slightly at high pressures or low temperatures.
• The inputs (P, V, n, T) must be in the proper units to avoid calculation errors.

Phase Changes

Phase change is the transformation of matter from one state (solid, liquid, gas) to another due to changes in temperature or pressure. Common phase changes include melting, freezing, vaporization, condensation, sublimation, and deposition.

In our textbook problem, we examined how trichloroethane changes from liquid to gas (vaporization) inside containers of different volumes at the same temperature. By calculating the molar amount that will vaporize using the vapor pressure and comparing it to the initial amount, we identified if the substance would fully transition to the gaseous phase or remain as a combination of liquid and gas.

Useful Tips:

• During phase changes, the temperature of a substance doesn’t change until the entire material has transformed into the new phase.
• To predict whether a phase change will occur, comparing the available space (volume of the flask) to the amount of substance that can vaporize (calculated via the Ideal Gas Law) is necessary.