1. If a gaseous sample contains 73% N2 by volume, what is the solubility of N2 in water at 25°C and 1.0 atm (kH in H2O at 25°C = 7.0 10-4 mol/Latm)?
2. Calculate the vapor pressure of a solution of 0.60 mol of cholesterol in 4.5 mol of toluene at 32°C. Pure toluene has a vapor pressure of 41 torr at 32°C. (Assume ideal behavior.)
3. The freezing point of benzene is 5.5°C. What is the freezing point of a solution of 8.10 g of naphthalene (C10H8) in 670. g of benzene (Kf of benzene = 4.90°C/m)?
4. In a study designed to prepare new gasoline-resistant coatings, a polymer chemist dissolves 6.111 g poly(vinyl alcohol) in enough water to make 100.0 mL of solution. At 25°C, the osmotic pressure of this solution is 0.272 atm. What is the molar mass of the polymer sample?
Someone please explain these questions?
Sure! I can help you with these questions. To solve each of these, we will need to use different concepts and formulas. Let's go through them one by one:
1. The first question is asking about the solubility of nitrogen gas (N2) in water. We are given the percentage of N2 in a gaseous sample. To find the solubility, we can use Henry's Law, which states that the solubility of a gas in a liquid is directly proportional to the partial pressure of the gas above the liquid. The equation is given as:
C = kH * P
Where C represents the concentration of the gas in the liquid (solubility), kH is the Henry's Law constant (given as 7.0 x 10-4 mol/Latm), and P is the partial pressure of the gas (given as 1.0 atm in this case).
We need to convert the given percentage of N2 by volume to a partial pressure by multiplying it by the total pressure of the gas sample. If the gas sample contains 73% N2 by volume, then the partial pressure of N2 would be 73% of the total pressure. If the total pressure is not given, we assume it to be 1 atm.
So, the partial pressure of N2 (P) would be 0.73 atm (73% of 1 atm). Plugging the values into the Henry's Law equation:
C = (7.0 x 10-4 mol/Latm) * (0.73 atm)
Calculating this will give you the solubility of N2 in water at 25°C and 1.0 atm.
2. The second question involves calculating the vapor pressure of a solution. We are given the number of moles of cholesterol and toluene present in the solution, as well as the vapor pressure of pure toluene at 32°C (41 torr). To calculate the vapor pressure of the solution, we can use Raoult's Law, which states that the vapor pressure of a component in a solution is equal to the mole fraction of that component multiplied by its vapor pressure in its pure state.
The equation is given as:
P_solution = X_cholesterol * P_cholesterol + X_toluene * P_toluene
Where P_solution is the vapor pressure of the solution, X_cholesterol is the mole fraction of cholesterol, P_cholesterol is the vapor pressure of cholesterol, X_toluene is the mole fraction of toluene, and P_toluene is the vapor pressure of toluene.
To calculate the mole fractions, divide the number of moles of each component by the total number of moles in the solution. Then, plug in the values into the Raoult's Law equation to find the vapor pressure of the solution.
3. The third question is about the freezing point of a solution. We are given the freezing point of benzene (5.5°C), as well as the mass of naphthalene and benzene in the solution and the freezing point depression constant (Kf) of benzene.
The equation to calculate the freezing point depression is given as:
ΔT = Kf * m
Where ΔT is the change in freezing point, Kf is the freezing point depression constant, and m is the molality (moles of solute per kilogram of solvent). To calculate the molality, we need to convert the given masses of naphthalene and benzene into moles and find the total moles of the solution. Then, divide the moles of naphthalene by the mass of benzene in kilograms to find the molality.
Plugging in the values into the freezing point depression equation will give you the change in freezing point. To find the freezing point of the solution, subtract the change in freezing point from the freezing point of the pure solvent.
4. The fourth question involves calculating the molar mass of a polymer sample using the osmotic pressure of the solution. We are given the mass of poly(vinyl alcohol) and the volume of the solution, as well as the osmotic pressure.
The equation to calculate the molar mass of the polymer is given as:
M = (RT) / P
Where M is the molar mass, R is the ideal gas constant, T is the temperature in Kelvin, and P is the osmotic pressure.
To use this equation, convert the given temperature to Kelvin and the osmotic pressure to atm. Then, plug in the values into the molar mass equation to calculate the molar mass of the polymer sample.