The vapor pressure of water is 23.8 torr. at 25 degrees C. Determine the mass of glucose (molar mass 180g/mol) needed to add to 500g of water to change the vapor pressure to 23.1 torr.
To solve this problem, we can use Raoult's law, which states that the vapor pressure of a solution is equal to the vapor pressure of the solvent multiplied by the mole fraction of the solvent. We can set up the equation as follows:
P_total = P_water * X_water
Where:
P_total = total vapor pressure of the solution
P_water = vapor pressure of pure water
X_water = mole fraction of water
First, we need to calculate the mole fraction of water.
Mole fraction of water (X_water) = moles of water / total moles
To find the moles of water, we need to use the given mass and the molar mass of water.
Moles of water = mass of water / molar mass of water
Mass of water = 500g
Molar mass of water = 18g/mol
Moles of water = 500g / 18g/mol = 27.78 mol
Now, let's find the moles of glucose needed to change the vapor pressure.
Moles of glucose = (P_total - P_water) / P_water
P_total = 23.1 torr
P_water = 23.8 torr
Moles of glucose = (23.1 torr - 23.8 torr) / 23.8 torr = -0.0294 mol
Since the mole fraction of glucose (X_glucose) is equal to 1 - X_water:
X_glucose = 1 - X_water = 1 - (moles of water / total moles)
X_glucose = 1 - (27.78 mol / (27.78 mol - 0.0294 mol)) = 1 - (27.78 mol / 27.75 mol) = 0.999
Next, we need to calculate the mass of glucose using the mole fraction and the molar mass of glucose.
Mass of glucose = moles of glucose * molar mass of glucose
Molar mass of glucose = 180g/mol
Mass of glucose = (-0.0294 mol) * (180g/mol) = -5.292g
Since mass cannot be negative, we can conclude that no mass of glucose is needed to change the vapor pressure to 23.1 torr.
To determine the mass of glucose needed to change the vapor pressure of water, we need to use Raoult's law, which relates the vapor pressure of a solution to the mole fraction of the solute.
Raoult's law 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. Mathematically, it can be expressed as:
P = Xsolute * Psolvent
where P is the vapor pressure of the solution, Xsolute is the mole fraction of the solute, and Psolvent is the vapor pressure of the pure solvent.
Given:
Vapor pressure of water (Psolvent) = 23.8 torr
Vapor pressure of the solution (P) = 23.1 torr
We can rearrange Raoult's law to solve for Xsolute:
Xsolute = P / Psolvent
Substituting the values, we get:
Xsolute = 23.1 torr / 23.8 torr
Xsolute = 0.970
Now, we can use Xsolute to find the number of moles of glucose (solute) needed to achieve this mole fraction. Since we have 500g of water, we can calculate the moles of water using its molar mass:
moles of water = mass of water / molar mass of water
moles of water = 500g / 18g/mol (molar mass of water)
moles of water = 27.778 mol
As per Raoult's law, the mole fraction of the solute is equal to the moles of the solute divided by the sum of moles of solvent and solute:
Xsolute = moles of solute / (moles of solvent + moles of solute)
Since we want to calculate the mass of glucose (solute), we need to rearrange the equation to solve for the moles of the solute:
moles of solute = Xsolute * moles of solvent / (1 - Xsolute)
moles of solute = 0.970 * 27.778 mol / (1 - 0.970)
moles of solute = 0.970 * 27.778 mol / 0.030
moles of solute = 899.85 mol
Finally, we can calculate the mass of glucose using its molar mass:
mass of glucose = moles of solute * molar mass of glucose
mass of glucose = 899.85 mol * 180 g/mol (molar mass of glucose)
mass of glucose = 161,970 g or approximately 162 kg
Therefore, approximately 162 kg of glucose is needed to add to 500 g of water to change the vapor pressure to 23.1 torr.
555.6
Psoln = XH2O*PoH2O
Solve for XH2O
XH2O = (moles H2O/total moles)
Plug in X, n for H2O and n for glucose and solve for n glucose, then
grams glucose = moles x molar mass.
Post your work if you get stuck.