The vapour pressure of solution having 2 grams of solute X (molar mass-32) in 100 grans of CS2 (vapour pressure-854 torr) is 848.9 torr. The molecular formula of the solute is ?
To find the molecular formula of the solute, we can start by using Raoult's law, which states that the vapor pressure of an ideal solution is directly proportional to the mole fraction of the solute in the solution.
First, let's calculate the mole fraction of the solute in the solution:
Mole fraction of solute (X) = moles of X / total moles of solution
To find the moles of X, we need to convert the mass of X to moles using the molar mass:
moles of X = mass of X / molar mass of X
moles of X = 2 g / 32 g/mol
moles of X = 0.0625 moles
To find the total moles of the solution, we need to convert the mass of CS2 to moles using its molar mass:
moles of CS2 = mass of CS2 / molar mass of CS2
moles of CS2 = 100 g / 76.13 g/mol
moles of CS2 = 1.3124 moles
Now we can calculate the mole fraction:
Mole fraction of solute (X) = 0.0625 moles / (0.0625 moles + 1.3124 moles)
Mole fraction of solute (X) ≈ 0.0458
Now we can use Raoult's law to find the vapor pressure of the solute:
Vapor pressure of solute (X) = mole fraction of solute (X) * vapor pressure of pure solvent (CS2)
Vapor pressure of solute (X) = 0.0458 * 854 torr
Vapor pressure of solute (X) ≈ 39.1 torr
Since the given vapor pressure of the solution is 848.9 torr, we can deduce that the remaining vapor pressure is from the solvent CS2:
Vapor pressure of solvent (CS2) = total vapor pressure - vapor pressure of solute (X)
Vapor pressure of solvent (CS2) = 848.9 torr - 39.1 torr
Vapor pressure of solvent (CS2) ≈ 809.8 torr
Now, let's calculate the mole fraction of the solvent:
Mole fraction of solvent (CS2) = Vapor pressure of solvent (CS2) / vapor pressure of pure solvent (CS2)
Mole fraction of solvent (CS2) = 809.8 torr / 854 torr
Mole fraction of solvent (CS2) ≈ 0.9484
Finally, to determine the molecular formula of the solute, we need to calculate the ratio of moles of the solute (X) to the moles of the empirical formula. If the ratio is a whole number, it represents the molecular formula; otherwise, we need to find the multiple.
The empirical formula represents the simplest ratio of elements in a compound.
Given that the solute has molar mass 32 g/mol, we assume that the empirical formula has one mole of the element.
moles of empirical formula = mass of solute / molar mass of solute
moles of empirical formula ≈ 2 g / 32 g/mol
moles of empirical formula ≈ 0.0625 moles
Now we can calculate the mole ratio:
Mole ratio = moles of solute (X) / moles of empirical formula
Mole ratio ≈ 0.0625 moles / 0.0625 moles
Mole ratio ≈ 1
Since the mole ratio is 1, it means that the empirical formula is the same as the molecular formula. Therefore, the molecular formula of the solute is X.
To determine the molecular formula of the solute, we need to use the concept of Raoult's law, which governs the vapor pressure of solutions. According to Raoult's law, the vapor pressure of a solution is equal to the mole fraction of the solvent multiplied by the vapor pressure of the pure solvent.
Given:
Mass of solute X = 2 grams
Molar mass of solute X = 32 g/mol
Mass of solvent CS2 = 100 grams
Vapor pressure of pure CS2 = 854 torr
Vapor pressure of the solution = 848.9 torr
First, we need to calculate the mole fraction of the solute X in the solution.
1. Calculate the moles of solute X:
moles of solute X = mass of solute X / molar mass of solute X
moles of solute X = 2 g / 32 g/mol
moles of solute X = 0.0625 mol
2. Calculate the moles of solvent CS2:
moles of solvent CS2 = mass of solvent CS2 / molar mass of CS2
moles of solvent CS2 = 100 g / 76 g/mol
moles of solvent CS2 = 1.316 mol
3. Calculate the mole fraction of solute X:
mole fraction of solute X = moles of solute X / (moles of solute X + moles of solvent CS2)
mole fraction of solute X = 0.0625 mol / (0.0625 mol + 1.316 mol)
mole fraction of solute X = 0.0455
Now, let's use Raoult's law to find the vapor pressure of solute X in the solution.
Vapor pressure of solute X = mole fraction of solute X * vapor pressure of pure CS2
Vapor pressure of solute X = 0.0455 * 854 torr
Vapor pressure of solute X = 38.97 torr
Since the given vapor pressure of the solution is 848.9 torr, and we calculated the vapor pressure of solute X to be 38.97 torr, the remaining vapor pressure must be due to the solvent CS2.
Remaining vapor pressure = Vapor pressure of the solution - Vapor pressure of solute X
Remaining vapor pressure = 848.9 torr - 38.97 torr
Remaining vapor pressure = 809.93 torr
Considering that the vapor pressure of the solvent CS2 is 809.93 torr, we can conclude that the molecular formula of the solute X is the same as that of the solvent CS2, which is CS2.
You don't say if the solute is volatile or non-volatile. I assume it is volatile. Since X is used for mole fraction, I will change the unknown compound to Y.
mols Y = 2/32 = ?
mols CS2 = 100/76 = ?
total molsl = ? + ? = ?
Then XCS2 = mols CS2/total mols = ?
XY</sub) = mols Y/total mols = ?
The pressure due to CS2 is
pCS2 = XCS2 * PoCS2 = ?
Total Psolution = 848.9
pY = 848.9-pCS2
Finally,
pY = Xy*PoY
Solve for Y po (vapor pressure Y). look it up in tables to find the compound. Post your work if you get stuck.