To calculate the expected vapor pressure of the solution, we will use Raoult's Law, which states that the vapor pressure of a component in a solution is equal to the vapor pressure of the pure component multiplied by its mole fraction in the solution.
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Determine Moles of Solute (Citric Acid):
- The molar mass of citric acid (C6H8O7) is approximately \( 192.13 , \text{g/mol} \).
- Given that we have 5 tonnes of citric acid:
- Convert tonnes to grams: \( 5 , \text{tonnes} = 5,000 , \text{kg} = 5,000,000 , \text{g} \).
- Calculate moles of citric acid: \[ \text{Moles of citric acid} = \frac{5,000,000 , \text{g}}{192.13 , \text{g/mol}} \approx 26040.7 , \text{mol} \]
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Determine Moles of Solvent (Water):
- The density of water is approximately \( 1 , \text{g/mL} \), so for \( 20 , \text{L} \):
- Convert liters to grams: \( 20 , \text{L} = 20,000 , \text{g} \).
- Calculate moles of water: \[ \text{Moles of water} = \frac{20,000 , \text{g}}{18.015 , \text{g/mol}} \approx 1104.1 , \text{mol} \]
- The density of water is approximately \( 1 , \text{g/mL} \), so for \( 20 , \text{L} \):
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Calculate the Total Moles in the Solution:
- Total moles = moles of citric acid + moles of water: \[ \text{Total moles} = 26040.7 , \text{mol} + 1104.1 , \text{mol} \approx 27144.8 , \text{mol} \]
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Calculate the Mole Fraction of Water:
- The mole fraction of water (\( X_{\text{water}} \)) is calculated as: \[ X_{\text{water}} = \frac{\text{Moles of water}}{\text{Total moles}} = \frac{1104.1 , \text{mol}}{27144.8 , \text{mol}} \approx 0.0407 \]
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Calculate the Vapor Pressure of the Solution:
- According to Raoult's Law: \[ P_{\text{solution}} = X_{\text{water}} \times P^0_{\text{water}} \]
- Where \( P^0_{\text{water}} = 0.0317 , \text{bars} \): \[ P_{\text{solution}} = 0.0407 \times 0.0317 , \text{bars} \approx 0.00129 , \text{bars} (or 1.29 , \text{mbar}) \]
Thus, the expected vapor pressure of the solution at 25°C is approximately 0.00129 bars or 1.29 mbar.