a student needs to prepare an aqueous solution of sucrose at a temperature of 20 degrees c with a vapor pressure of 15. 0 mm Hg. How many grams of sucrose (mm=342 g/mol) does she need if she uses 375 g H20? (the vapor pressure of water at 20 degrees c is 17.5 mm Hg)
Psoln = XH2O*PoH2O
15.0 torr = XH2O*17.5 torr
Solve for XH2O which gives you the mole fraction that H2O must be. I'll call that ??
[molesH2O/(moles H2O + moles sucrose)]=??
moles H2O = grams water/molar mass H2O, substitute this into the equation immediately above this (both numerator and denominator) and solve for moles sucrose.
Finally, moles sucrose = grams/molar mass sucrose.
Then check everything to make sure all of that gives you 15.0 torr.
Please send me the answer
To determine the grams of sucrose needed, we can use Raoult's law, which states that the vapor pressure of a solution is proportional to the mole fraction of the solvent and its vapor pressure in its pure form.
The mole fraction (X) of water can be calculated using the formula:
X(solvent) = moles of solvent / total moles of solute
First, let's calculate the number of moles of water (H2O):
moles of H2O = mass of H2O / molar mass of H2O
Since the molar mass of water (H2O) is approximately 18 g/mol:
moles of H2O = 375 g / 18 g/mol
moles of H2O = 20.83 mol
Next, let's calculate the mole fraction of water (X):
X(H2O) = moles of H2O / (moles of H2O + moles of sucrose)
To determine the moles of sucrose, we can use the ideal gas law:
PV = nRT
where P is the vapor pressure, V is the volume, n is the number of moles, R is the ideal gas constant (0.0821 L·atm/(mol·K)), and T is the temperature in Kelvin.
In this case, we need to be careful since we have a solution rather than a gas. However, since we are dealing with dilute solutions, we can assume the vapor pressure of water is not affected by the sucrose.
Therefore, the number of moles of sucrose can be calculated using the formula:
moles of sucrose = (vapor pressure of solution - vapor pressure of water) / vapor pressure of water * moles of H2O
Let's calculate the moles of sucrose:
moles of sucrose = (15.0 mm Hg - 17.5 mm Hg) / 17.5 mm Hg * 20.83 mol
moles of sucrose = -2.5 mm Hg / 17.5 mm Hg * 20.83 mol
moles of sucrose = -2.5/17.5 * 20.83 mol
moles of sucrose = -2.9836 mol
Please note that we encountered a negative value, which indicates that sucrose cannot be dissolved in water to achieve the given vapor pressure. This result suggests that the sucrose would precipitate rather than dissolve.
Therefore, there is no accurate way to determine the grams of sucrose needed to prepare the desired solution.