Determine the mass in grams of glucose (180.2 g/mol) needed to prepare a solution with a vapor pressure of 40.8 mmHg. The glucose is dissolved in 575g of water at 35C. The vapor pressure of pure water at 35C is 42.2 mmHg.
Please help me, I don't know what to start with or even what equation this requires
Given VP(H₂O) = 42.2-mmHg @35ᵒC & Needed VP(Soln) = 40.8-mmHg
VP(Solution) = VP(solvent) – ΔVP(solvent)
ΔVP(solvent) = X(solute)∙VP(solvent)
(42.2-mmHg – 40.8-mmHg) = [(m/180.2)/(m/180.2) + (575/18)]∙42.2-mmHg ; m = mass glucose (g)
Solving for mass of glucose => *m = 198.2-grams needed to effect a drop in VP of 1.4-mmHg in solvent VP.
*Verify by substituting m = 198.2-g into ΔVP = [(m/180.2)/(m/180.2) + (575/18)]∙42.2-mm => 1.4-mmHg drop in VP of solvent => Final VP(Solution) = 42.2-mmHg – 1.4-mmHg = 40.8-mmHg.
Psoln = Xsolvent*Posolvent
Substitute and solve for Xsolute
Then Xsolute = mols solvent)/(mols solvent)+(mols solute)
Solve for mols solute and convert to grams solute. Post your work if you get stuck.
To determine the mass of glucose needed to prepare a solution with a specific vapor pressure, we can use Raoult's Law, which states that the vapor pressure of a solvent above a solution is directly proportional to the mole fraction of the solvent present. The equation for Raoult's Law is:
P = X_solvent * P_solvent
where P is the vapor pressure of the solution, X_solvent is the mole fraction of the solvent, and P_solvent is the vapor pressure of the pure solvent.
In this case, the solvent is water, and the solute is glucose. We are given the vapor pressure of pure water (P_solvent = 42.2 mmHg), the desired vapor pressure of the solution (P = 40.8 mmHg), and the mass of water (575 g).
To find the mole fraction of water, we need to calculate the moles of water and glucose present in the solution. We can use the following equations:
moles of water = mass of water / molar mass of water
moles of glucose = mass of glucose / molar mass of glucose
Then, the mole fraction of water (X_water) is given by:
X_water = moles of water / (moles of water + moles of glucose)
Finally, we can rearrange Raoult's Law to solve for the mass of glucose:
mass of glucose = (P * mass of water) / (X_water * P_solvent)
Now let's calculate the mass of glucose needed:
1. Calculate the moles of water:
moles of water = mass of water / molar mass of water = 575g / 18.015 g/mol ≈ 31.89 moles
2. Calculate the moles of glucose:
moles of glucose = mass of glucose / molar mass of glucose = ?
Since we don't have the value for the mass of glucose yet, we'll solve for the unknown mass in the next step.
3. Calculate the mole fraction of water:
X_water = moles of water / (moles of water + moles of glucose)
4. Use Raoult's Law to solve for the mass of glucose:
mass of glucose = (P * mass of water) / (X_water * P_solvent) = (40.8 mmHg * 575g) / ((31.89 moles / (31.89 moles + moles of glucose)) * 42.2 mmHg)
Now you can substitute the values into the equation and solve for the mass of glucose needed.