5 tonnes of citric acid (C6H8O7) were dissolved in 20L of water. What is the expected vapour pressure of the solution or mixture at 25°C? Note that vapour pressure of H2O at 25°C is 0.0317bars

1 answer

To calculate the expected vapor pressure of the solution of citric acid (C₆H₈O₇) in water at 25°C, we can use Raoult's Law. Raoult's Law states that the vapor pressure of a solvent in a solution is equal to the vapor pressure of the pure solvent multiplied by the mole fraction of the solvent in the solution.

  1. Determine the moles of citric acid and water:

    • Molar mass of citric acid (C₆H₈O₇): \[ \text{Molar mass} = 6 \times 12.01 , (\text{C}) + 8 \times 1.01 , (\text{H}) + 7 \times 16.00 , (\text{O}) = 192.13 , \text{g/mol} \]

    • Mass of citric acid: \[ 5 , \text{tonnes} = 5,000 , \text{kg} = 5,000,000 , \text{g} \]

    • Moles of citric acid: \[ \text{Moles of citric acid} = \frac{5,000,000 , \text{g}}{192.13 , \text{g/mol}} \approx 26040.6 , \text{mol} \]

    • Assuming the density of water is approximately 1 g/mL: \[ \text{Mass of water} = 20 , \text{L} \times 1000 , \text{g/L} = 20,000 , \text{g} \]

    • Moles of water: \[ \text{Moles of water} = \frac{20,000 , \text{g}}{18.02 , \text{g/mol}} \approx 1105.56 , \text{mol} \]

  2. Calculate the total moles in the solution: \[ \text{Total moles} = \text{Moles of citric acid} + \text{Moles of water} \approx 26040.6 , \text{mol} + 1105.56 , \text{mol} \approx 27146.16 , \text{mol} \]

  3. Calculate the mole fraction of water (\(X_{\text{water}}\)): \[ X_{\text{water}} = \frac{\text{Moles of water}}{\text{Total moles}} = \frac{1105.56 , \text{mol}}{27146.16 , \text{mol}} \approx 0.0407 \]

  4. Use Raoult's Law to calculate the vapor pressure of the solution: \[ P_{\text{solution}} = X_{\text{water}} \times P^0_{\text{water}} \] Given \(P^0_{\text{water}} = 0.0317 , \text{bars}\), we can calculate: \[ P_{\text{solution}} = 0.0407 \times 0.0317 \approx 0.00129 , \text{bars} \]

Thus, the expected vapor pressure of the solution at 25°C is approximately 0.00129 bars.