What is the *change* in vapor pressure when74.30gfructose,C6H12O6, are added to182.5g water (H2O) at 298 K (vapor pressure of pure water at 298 K = 3.1690 kPa, molar mass offructose=180.156g/mol, molar mass of water = 18.02 g/mol)?

To calculate the change in vapor pressure when fructose is added to water, we can use Raoult's Law. Raoult's Law states that the vapor pressure of the solvent above a solution is proportional to the mole fraction of the solvent in the solution.

### Step 1: Calculate the number of moles of water and fructose.

**Moles of water (\(n_{\text{H2O}}\)):**

\[
n_{\text{H2O}} = \frac{\text{Mass of water}}{\text{Molar mass of water}} = \frac{182.5 \, \text{g}}{18.02 \, \text{g/mol}} \approx 10.13 \, \text{mol}
\]

**Moles of fructose (\(n_{\text{fructose}}\)):**

\[
n_{\text{fructose}} = \frac{\text{Mass of fructose}}{\text{Molar mass of fructose}} = \frac{74.30 \, \text{g}}{180.156 \, \text{g/mol}} \approx 0.4124 \, \text{mol}
\]

### Step 2: Calculate the mole fraction of water in the solution.

\[
\text{Mole fraction of water} \, (X_{\text{H2O}}) = \frac{n_{\text{H2O}}}{n_{\text{H2O}} + n_{\text{fructose}}} = \frac{10.13}{10.13 + 0.4124} \approx \frac{10.13}{10.5424} \approx 0.9603
\]

### Step 3: Apply Raoult's Law to find the new vapor pressure.

Raoult's Law:

\[
P_{\text{solution}} = X_{\text{H2O}} \times P_{\text{H2O}}^{\text{pure}}
\]

\[
P_{\text{solution}} = 0.9603 \times 3.1690 \, \text{kPa} \approx 3.043 \, \text{kPa}
\]

### Step 4: Calculate the change in vapor pressure.

\[
\Delta P = P_{\text{H2O}}^{\text{pure}} - P_{\text{solution}} = 3.1690 \, \text{kPa} - 3.043 \, \text{kPa} \approx 0.126 \, \text{kPa}
\]

**Answer:** The change in vapor pressure is approximately **0.126 kPa**.

Would you like further details or have any questions?

Here are 5 related questions you might find interesting:
1. How does the mole fraction affect vapor pressure in a solution?
2. What would happen if you increased the amount of fructose in the solution?
3. How does temperature affect the vapor pressure of water?
4. Can Raoult's Law be applied to all types of solutions?
5. How would the vapor pressure change if another non-volatile solute was added?

**Tip:** Raoult's Law works best for ideal solutions where interactions between all particles (solute-solvent and solvent-solvent) are similar.

Learn how to calculate the change in vapor pressure when 74.30g of fructose (C6H12O6) are added to 182.5g of water (H2O) at 298 K. Understand Raoult's Law and its application, with step-by-step calculations and explanations.

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