How many grams of the nonelectrolyte sucrose (molar mass -342 g / mole) must be added to 450 grams of water (molar mass 18.0 g / mole) to change the vapor pressure to 745 mm Hg at 100
How many grams of sucrose Akerla (molar mass -342 g / mol) must be added to 450 grams of water (molar mass 18.0 g / mol) to change the vapor pressure to 745 mm Hg at 100
vapor pressure is related to mole fraction
moles sucrose=massSucrose/342
moles water=450/18
total moles add them
745/760=molessucrose/total moles
solve for massSucrose
To determine how many grams of sucrose need to be added, we need to use Raoult's Law, which states that the vapor pressure of a solvent above a solution is equal to the mole fraction of the solvent multiplied by the vapor pressure of the pure solvent.
First, we need to calculate the mole fraction of the solvent (water) in the solution. The mole fraction (X) is the ratio of the moles of the solvent to the total moles of solute and solvent.
To calculate the mole fraction of water:
Molar mass of water (H2O) = 18.0 g/mol
First, we'll convert the given mass of water (450 g) to moles using the molar mass:
Moles of water = mass / molar mass = 450 g / 18.0 g/mol = 25 moles
Next, we'll calculate the mole fraction of water:
X_water = moles of water / (moles of water + moles of sucrose)
X_water = 25 moles / (25 moles + moles of sucrose)
According to Raoult's Law, the vapor pressure of pure water at 100°C is 760 mm Hg.
Now, we can use the given vapor pressure (745 mm Hg) to determine the mole fraction of water in the solution:
745 mm Hg = X_water × 760 mm Hg
To solve for X_water:
X_water = 745 mm Hg / 760 mm Hg = 0.979
Now we can solve for the mole fraction of sucrose (X_sucrose):
X_sucrose = 1 - X_water = 1 - 0.979 = 0.021
Finally, we'll use the mole fraction of sucrose to determine the number of moles of sucrose (n_sucrose) required:
moles of sucrose = X_sucrose × (moles of water + moles of sucrose)
moles of sucrose = 0.021 × (25 moles + moles of sucrose)
Since we don't know the value of moles of sucrose, we'll rearrange the equation to solve for it:
moles of sucrose - 0.021 × moles of sucrose = 0.021 × 25
0.979 × moles of sucrose = 0.52125
moles of sucrose = 0.52125 / 0.979
Now we can calculate the grams of sucrose needed using the molar mass of sucrose (342 g/mol):
grams of sucrose = moles of sucrose × molar mass
grams of sucrose = (0.52125 / 0.979) × 342 g/mol
To calculate the grams of sucrose needed, we'll substitute the values:
grams of sucrose = 0.53148 × 342 g/mol ≈ 181.68 g
Therefore, approximately 181.68 grams of sucrose need to be added to change the vapor pressure to 745 mm Hg at 100°C.
To calculate the grams of sucrose (nonelectrolyte) that needs to be added to 450 grams of water in order to change the vapor pressure, we need to use Raoult's law equation:
P = Xsolvent * Psolvent
Where:
P is the vapor pressure of the mixture
Xsolvent is the mole fraction of the solvent (water)
Psolvent is the vapor pressure of the pure solvent
In this case, we want to change the vapor pressure to 745 mm Hg at 100°C. The vapor pressure of pure water at this temperature is approximately 760 mm Hg.
Let's calculate the mole fraction of the solvent:
Moles of water = mass of water / molar mass of water
Moles of water = 450 g / 18.0 g/mol
Moles of water = 25 mol
The mole fraction of the solvent, Xsolvent, is given by:
Xsolvent = Moles of water / (Moles of water + Moles of solute)
Now, we need to rearrange Raoult's law equation to solve for the moles of solute:
Moles of solute = (P / Psolvent - 1) * Moles of water
Substituting the given values:
Moles of solute = (745 mm Hg / 760 mm Hg - 1) * 25 mol
Moles of solute = (-0.0197) * 25 mol
Moles of solute = -0.493 mol
Since we cannot have a negative number of moles, it means that we do not need to add any sucrose to the water in order to achieve a vapor pressure of 745 mm Hg at 100°C.