Question

question 2
most of the worlds maple syrup comes form quebec, canada. sap is evaporated from maple trees until it reaches 66% by mass sucrose. what is the vapor pressure of a 66% aqueous solution of sucrose (mm = 342.30g/mol) at 100°c. assume the solution behaves ideally. the normal vapor pressure of water is 1.00 atm (mm = 18.02g/mol).
○ 0.102 atm
○ 0.91 atm
○ 0.0927 atm
○ 9.71 atm
clear selection

Explanation:

Step1: Define mass of components

Assume 100g of solution. Then mass of sucrose ($m_{sucrose}$) = 66g, mass of water ($m_{water}$) = 100 - 66 = 34g.

Step2: Calculate moles of each component

Moles of sucrose ($n_{sucrose}$) = $\frac{m_{sucrose}}{MM_{sucrose}}$ = $\frac{66g}{342.30g/mol}$ ≈ 0.1928 mol.
Moles of water ($n_{water}$) = $\frac{m_{water}}{MM_{water}}$ = $\frac{34g}{18.02g/mol}$ ≈ 1.887 mol.

Step3: Calculate mole fraction of water ($X_{water}$)

$X_{water}$ = $\frac{n_{water}}{n_{water} + n_{sucrose}}$ = $\frac{1.887}{1.887 + 0.1928}$ ≈ $\frac{1.887}{2.0798}$ ≈ 0.907.

Step4: Apply Raoult's Law

Raoult's Law: $P_{solution}$ = $X_{solvent} \times P^0_{solvent}$.
Here, solvent is water, so $P_{solution}$ = $X_{water} \times P^0_{water}$ = 0.907 × 1.00 atm ≈ 0.91 atm.

Answer:

0.91 atm