Calculate the volume of solution that has a vapour pressure of 31.27 mbar and contains 84.3g of sucrose, at a temperature of 25.0C. The vapour pressure of pure water at 25.0C is 31.7mbar, the density of water is 1.00g/mL, and assume no change in volume occurs upon dissolution.
Psoln = XH2O*PoH2O
You know Psoln and PoH2O; solve for XH2O.
Then
XH2O = nH2O/(nH2O+nsucrose)
You know XH2O and nsucrose, solve for nH2O. Convert mols H2O to grams H2O then use density to convert to mL H2O.
n sucrose = grams sucrose/molar mass sucrose.
To calculate the volume of the solution, we first need to determine the mole fraction of sucrose in the solution.
Step 1: Calculate the mole fraction of sucrose.
The mole fraction of sucrose (Xsucrose) can be calculated using the formula:
Xsucrose = moles of sucrose / total moles of solute.
Since we know the mass of sucrose (84.3g) and its molar mass (342.3 g/mol), we can calculate the moles of sucrose as follows:
moles of sucrose = mass of sucrose / molar mass of sucrose
= 84.3g / 342.3 g/mol
Step 2: Calculate the total moles of solute.
The total moles of solute can be calculated using the mole fraction of sucrose formula:
total moles of solute = moles of sucrose / Xsucrose
Since the mole fraction of sucrose is equal to 1 (since we are considering only sucrose as solute), the total moles of solute is the same as the moles of sucrose in this case.
total moles of solute = moles of sucrose
Step 3: Calculate the volume of the solution.
The volume of the solution can be calculated using the following formula:
volume of solution = mass of solute / density of water
Since the volume of water is assumed to remain constant upon dissolution, the volume of solution will be equal to the volume of water.
volume of solution = mass of sucrose / density of water
Let's plug in the values:
moles of sucrose = 84.3g / 342.3 g/mol
≈ 0.2463 mol
volume of solution = mass of sucrose / density of water
= 84.3g / 1.00 g/mL
≈ 84.3 mL
Therefore, the volume of the solution is approximately 84.3 mL.
To calculate the volume of the solution, you'll need to use the formula for the vapor pressure lowering caused by a solute in a solvent.
The formula is:
ΔP = Xsolute * Psolvent
Where ΔP is the vapor pressure lowering, Xsolute is the mole fraction of the solute, and Psolvent is the vapor pressure of the pure solvent.
First, we need the mole fraction of the solute (sucrose) in the solution.
To find the moles of sucrose, use the formula:
moles = mass / molar mass
The molar mass of sucrose is approximately 342.3 g/mol.
moles sucrose = 84.3 g / 342.3 g/mol = 0.246 mol
Next, we need the moles of water in the solution.
To find the moles of water, use the formula:
moles = volume * density / molar mass
The volume of water can be calculated by converting the given mass of sucrose to an equivalent volume of water using the density of water.
volume water = mass sucrose * (1 mL / 1 g) = 84.3 mL
Now, calculate the moles of water:
moles water = volume water * (1 g/mL) / 18.015 g/mol = 4.675 mol
To calculate the mole fraction of the solute, divide the moles of sucrose by the total moles of solute and water:
Xsolute = moles sucrose / (moles sucrose + moles water)
Xsolute = 0.246 mol / (0.246 mol + 4.675 mol) = 0.0501
Now, use the formula for vapor pressure lowering to find the vapor pressure of the solution:
ΔP = Xsolute * Psolvent
ΔP = 0.0501 * 31.7 mbar = 1.59 mbar
Finally, to find the volume of the solution, divide the vapor pressure lowering by the difference in vapor pressures between pure water and the solution:
volume = ΔP / (Ppure - Psolution)
volume = 1.59 mbar / (31.7 mbar - 31.27 mbar) = 127 mL
Therefore, the volume of the solution is 127 mL.