To calculate the expected vapor pressure of a solution containing 5 tonnes (5000 kg) of citric acid dissolved in 20 L of water at 25°C, we will use Raoult's Law. Raoult's Law states that the vapor pressure of a solvent in a solution is proportional to the mole fraction of the solvent.
Steps to Calculate the Vapor Pressure:
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Calculate the number of moles of water:
- The density of water is approximately 1 kg/L, so 20 L of water has a mass of 20 kg.
- Molar mass of water (H₂O) = 18.015 g/mol = 0.018015 kg/mol.
- Moles of water: \[ n_{H2O} = \frac{20 \text{ kg}}{0.018015 \text{ kg/mol}} \approx 1104.59 \text{ mol} \]
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Calculate the number of moles of citric acid:
- The molar mass of citric acid (C₆H₈O₇) = 192.13 g/mol = 0.19213 kg/mol.
- Moles of citric acid: \[ n_{\text{citric acid}} = \frac{5000 \text{ kg}}{0.19213 \text{ kg/mol}} \approx 26002.17 \text{ mol} \]
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Calculate the total moles in the solution: \[ n_{\text{total}} = n_{H2O} + n_{\text{citric acid}} \approx 1104.59 \text{ mol} + 26002.17 \text{ mol} \approx 27106.76 \text{ mol} \]
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Calculate the mole fraction of water: \[ X_{H2O} = \frac{n_{H2O}}{n_{total}} = \frac{1104.59}{27106.76} \approx 0.0407 \]
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Calculate the vapor pressure of the solution using Raoult's Law:
- Vapor pressure of pure water at 25°C, \( P_{H2O}^0 = 0.0317 \text{ bar} \). \[ P_{solution} = X_{H2O} \cdot P_{H2O}^0 = 0.0407 \cdot 0.0317 \text{ bar} \approx 0.00129 \text{ bar} \]
Conclusion:
The expected vapor pressure of the citric acid solution at 25°C is approximately 0.00129 bar.
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