The vapor pressure of water at 25 oC is 23.8 torr. Calculate the vapor pressure of a solution prepared by dissolving 35.0 g of urea [(NH2)2CO] in 75.0 g of water at 25 oC.
To calculate the vapor pressure of the solution, we can use the formula:
P_solution = P_water * X_water
Where P_solution is the vapor pressure of the solution, P_water is the vapor pressure of pure water, and X_water is the mole fraction of water in the solution.
First, let's calculate the number of moles of each component in the solution, which involves finding the molar mass of urea.
Urea (NH2)2CO has the following molecular composition: 1 Carbon, 4 Hydrogen, 2 Nitrogen, and 1 Oxygen.
C: 12.01 g/mol
H: 1.01 g/mol
N: 14.01 g/mol
O: 16.00 g/mol
Molar mass of urea = (1 × 12.01) + (4 × 1.01) + (2 × 14.01) + (16.00)
= 12.01 + 4.04 + 28.02 + 16.00
= 60.07 g/mol
Now, we can calculate the number of moles of urea and water in the solution.
Moles of urea = mass (g) / molar mass (g/mol) = 35.0 g / 60.07 g/mol = 0.582 moles
Moles of water = mass (g) / molar mass (g/mol) = 75.0 g / 18.02 g/mol = 4.16 moles
Next, we can find the mole fraction of water in the solution.
X_water = moles of water / (moles of water + moles of urea) = 4.16 / (4.16 + 0.582) = 4.16 / 4.742 = 0.877
Now, we can use the formula to find the vapor pressure of the solution.
P_solution = P_water * X_water
= 23.8 torr * 0.877
= 20.87 torr
Thus, the vapor pressure of the solution is approximately 20.87 torr at 25°C.
To calculate the vapor pressure of a solution, we can use Raoult's Law. 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.
Step 1: Calculate the moles of urea (solvent).
To calculate the moles, we need to know the molar mass of urea. The molar mass of urea ([(NH2)2CO]) is approximately 60.06 g/mol.
moles of urea = mass of urea / molar mass of urea
moles of urea = 35.0 g / 60.06 g/mol
moles of urea ≈ 0.583 mol
Step 2: Calculate the moles of water (solvent).
To calculate the moles, we need to know the molar mass of water (H2O). The molar mass of water is approximately 18.015 g/mol.
moles of water = mass of water / molar mass of water
moles of water = 75.0 g / 18.015 g/mol
moles of water ≈ 4.16 mol
Step 3: Calculate the mole fraction of the solvent (water).
The mole fraction (X) is the ratio of moles of solvent to the total moles of both solvent and solute.
mole fraction of water = moles of water / (moles of water + moles of urea)
mole fraction of water = 4.16 mol / (4.16 mol + 0.583 mol)
mole fraction of water ≈ 0.877
Step 4: Calculate the vapor pressure of the solution.
Now that we have the mole fraction of water (solvent) and the vapor pressure of pure water, we can use Raoult's Law to calculate the vapor pressure of the solution.
vapor pressure of the solution = mole fraction of water * vapor pressure of pure water
vapor pressure of the solution = 0.877 * 23.8 torr
vapor pressure of the solution ≈ 20.89 torr
Therefore, the vapor pressure of the solution prepared by dissolving 35.0 g of urea in 75.0 g of water at 25 oC is approximately 20.89 torr.
To calculate the vapor pressure of the solution, we need to consider the contribution of both the solvent (water) and the solute (urea) to the total vapor pressure. The vapor pressure of the solvent is given as 23.8 torr.
To solve this problem, we can use Raoult's law, which states that the vapor pressure of a solution is equal to the mole fraction of the solvent multiplied by the vapor pressure of the pure solvent.
Step 1: Calculate the moles of water and urea:
Molar mass of water (H2O) = 18.015 g/mol
Molar mass of urea [(NH2)2CO] = 60.055 g/mol
moles of water = mass of water / molar mass of water
moles of water = 75.0 g / 18.015 g/mol
moles of urea = mass of urea / molar mass of urea
moles of urea = 35.0 g / 60.055 g/mol
Step 2: Calculate the mole fraction of water:
mole fraction of water = moles of water / (moles of water + moles of urea)
Step 3: Calculate the vapor pressure of the solution:
vapor pressure of the solution = mole fraction of water × vapor pressure of pure water
Now let's calculate the values:
Step 1:
moles of water = 75.0 g / 18.015 g/mol = 4.16 mol
moles of urea = 35.0 g / 60.055 g/mol = 0.583 mol
Step 2:
mole fraction of water = 4.16 mol / (4.16 mol + 0.583 mol) = 0.877
Step 3:
vapor pressure of the solution = 0.877 × 23.8 torr
The vapor pressure of the solution prepared by dissolving 35.0 g of urea in 75.0 g of water at 25 oC is approximately 20.9 torr.