The colligative molality of seawater is approximately 1.10 m. Calculate the vapor pressure of sea water at 20°C. The vapor pressure of pure water at 15°C is 17.54 Torr?
The Correct Answer and Explanation is:
To calculate the vapor pressure of seawater at 20°C using the colligative molality and the vapor pressure of pure water, we will apply Raoult’s Law. Raoult’s Law states that the vapor pressure of a solvent (P_solution) in a solution is equal to the vapor pressure of the pure solvent (P_pure) multiplied by its mole fraction in the solution.
Given Data:
- Colligative molality (m) of seawater = 1.10 m
- Vapor pressure of pure water at 15°C (P_pure) = 17.54 Torr
Assumptions:
- The vapor pressure of seawater is being calculated at a temperature (20°C) close to the temperature for which we have the vapor pressure of pure water (15°C). We can assume that the vapor pressure of pure water does not vary significantly in this temperature range.
- The colligative properties are affected by the presence of solutes, which reduce the mole fraction of the solvent.
Calculation Steps:
- Convert Molality to Mole Fraction:
Colligative molality is given as 1.10 m, which means there are 1.10 moles of solute per kg of solvent (water). For simplicity, we assume 1 kg of water corresponds to approximately 55.5 moles of water (since the molar mass of water is about 18 g/mol). [
\text{Mole fraction of water} (X_{H_2O}) = \frac{\text{moles of water}}{\text{moles of water} + \text{moles of solute}}
] [
X_{H_2O} = \frac{55.5}{55.5 + 1.10} = \frac{55.5}{56.6} \approx 0.980
] - Calculate Vapor Pressure of Seawater:
Using Raoult’s Law, we can calculate the vapor pressure of seawater (P_solution): [
P_{solution} = X_{H_2O} \times P_{pure}
]
[
P_{solution} = 0.980 \times 17.54 \, \text{Torr} \approx 17.18 \, \text{Torr}
]
Conclusion:
Thus, the vapor pressure of seawater at 20°C is approximately 17.18 Torr. This calculation illustrates how the presence of solutes (like salts in seawater) affects the vapor pressure of the solvent (water), demonstrating the colligative property where the vapor pressure decreases as the solute concentration increases.