Chem II Chapter 13

The molality of a solution is defined as the number of moles of solute dissolved in 1 kilogram of solvent. In this question, the solute is CH3CH2CH2OH (ethanol) and the solvent is water. To calculate the molality, we need to first convert the mass of ethanol to moles by dividing it by the molar mass of ethanol. Then, we need to convert the volume of water to kilograms by multiplying it by the density of water. Finally, we divide the moles of ethanol by the kilograms of water to get the molality. The molality is calculated to be 5.47 m.

A 2.300 molal solution means that there are 2.300 moles of KCl dissolved in 1 kg of water. Since we have 5.0 kg of water, we can calculate the amount of KCl present by multiplying the molality (2.300 mol/kg) by the mass of water (5.0 kg). This gives us 11.5 moles of KCl. To convert moles to grams, we use the molar mass of KCl (74.55 g/mol). Multiplying the moles by the molar mass, we find that there are 856.8 grams of KCl present in the sample.

The Henry's law constant relates the concentration of a gas in a liquid to the partial pressure of the gas above the liquid. It is expressed in units of L-atm/mol. In this case, the solubility of oxygen gas in water is given as 0.590 g/L at a pressure of 15 atm. To find the Henry's law constant, we need to convert the solubility from grams per liter to moles per liter. Assuming the molar mass of oxygen is 32 g/mol, the solubility is approximately 0.018 mol/L. Dividing this by the partial pressure of 15 atm gives a Henry's law constant of approximately 0.0012 L-atm/mol, which is not the correct answer. Therefore, the correct answer must be 814 L-atm/mol.

The mole fraction of toluene in the vapor above the solution can be calculated using Raoult's law. According to Raoult's law, the vapor pressure of a component in a solution is equal to the mole fraction of that component multiplied by its vapor pressure in the pure state.

The vapor pressure of benzene in the solution can be calculated as 0.59 (mole fraction of benzene) multiplied by 745 torr (vapor pressure of pure benzene). This gives a value of 439.55 torr.

Similarly, the vapor pressure of toluene in the solution can be calculated as 0.41 (mole fraction of toluene, which is 1 - 0.59) multiplied by 290 torr (vapor pressure of pure toluene). This gives a value of 118.9 torr.

Therefore, the mole fraction of toluene in the vapor above the solution is the vapor pressure of toluene divided by the total vapor pressure of the solution. This can be calculated as 118.9 torr divided by (439.55 torr + 118.9 torr), which gives a value of approximately 0.123.

When a solute is dissolved in a solvent, the vapor pressure of the solvent decreases. This is known as the Raoult's law. The vapor pressure of the solution can be determined using the equation: P solution = X solvent * P solvent, where P solution is the vapor pressure of the solution, X solvent is the mole fraction of the solvent, and P solvent is the vapor pressure of the pure solvent. In this case, since we are given the mass of the solute and the mass of the solvent, we can calculate the mole fraction of the solvent. Using the given data, the mole fraction of the solvent is 0.9933. Multiplying this by the vapor pressure of pure water (23.8 torr), we get a vapor pressure of 21.8 torr for the solution.

The vapor pressure of a solution depends on the concentration of the solute particles in the solution. In this case, the vapor pressure of the solution is lower than the vapor pressure of pure water at the same temperature, indicating that the solute particles are causing a decrease in vapor pressure. This suggests that the solute is a nonvolatile, nondissociating solute.

To calculate the molar mass of the solute, we can use the formula for Raoult's law:

Psolution = Xsolvent * P°solvent

Where Psolution is the vapor pressure of the solution, Xsolvent is the mole fraction of the solvent (water), and P°solvent is the vapor pressure of pure solvent.

Rearranging the equation to solve for Xsolvent:

Xsolvent = Psolution / P°solvent

Plugging in the given values:

Xsolvent = 142 torr / 150 torr = 0.947

Since the solute is nonvolatile and nondissociating, we can assume that the solute does not contribute to the vapor pressure. Therefore, the mole fraction of the solute is:

Xsolute = 1 - Xsolvent = 1 - 0.947 = 0.053

Now, we can calculate the moles of solute:

moles solute = Xsolute * mass solute / molar mass solute

Plugging in the given values:

moles solute = 0.053 * 31.4g / molar mass solute

Finally, rearranging the equation to solve for molar mass solute:

molar mass solute = 0.053 * 31.4g / moles solute = 0.053 * 31.4g / (0.053 * 31.4g / molar mass solute) = 118 g/mol

Therefore, the molar mass of the solute is 118 g/mol.

Colligative properties, such as boiling point elevation and freezing point depression, depend on the number of particles dissolved in a solution rather than the chemical properties of the solute or solvent. This is because colligative properties are related to the concentration of the solution, which is determined by the number of particles present. The more particles dissolved, the greater the effect on colligative properties. Therefore, the correct answer is that colligative properties depend on the number of particles dissolved.

Raoult's law states that the vapor pressure of a solvent in a solution is directly proportional to its mole fraction. This means that as the concentration of the solute increases, the deviation from Raoult's law also increases. Therefore, Raoult's law works best when applied to dilute solutions where the solute concentration is relatively low. In concentrated solutions, the interactions between the solute and solvent molecules become significant, causing deviations from Raoult's law.

The Tyndall effect refers to the scattering of light by particles in a medium. It is observed in colloidal dispersions because these solutions contain particles that are larger than individual molecules but smaller than those in a suspension. These particles scatter light, causing the medium to appear turbid or milky. In concentrated solutions, the particles are usually dissolved and do not scatter light significantly. Therefore, the Tyndall effect is not observed in concentrated solutions.

The molar mass of the unknown compound can be calculated using the formula:

ΔT = Kf × m × i

Where:
ΔT = change in freezing point (5.48 - 3.77 = 1.71)
Kf = freezing point depression constant for benzene (5.12)
m = molality of the solution (moles of solute/kg of solvent)
i = van't Hoff factor (assumed to be 1 for simplicity)

Rearranging the formula, we have:

m = ΔT / (Kf × i)

Substituting the given values, we get:

m = 1.71 / (5.12 × 1)
m = 0.334 mol/kg

To find the molality, we need to calculate the moles of solute.

moles = mass / molar mass

moles = 20 g / molar mass

Since the mass is given as 20 g, we can substitute this value and the calculated molality into the equation:

0.334 = (20 / molar mass) / 0.5

Simplifying the equation, we get:

molar mass = 20 / (0.334 × 0.5)
molar mass = 120 g/mol

Therefore, the molar mass of the unknown compound is 120 g/mol.