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Suppose a solution contains ethanol and water. The mole fraction of ethanol is 0.3. The vapor pressure of pure ethanol at 25 °C is 59.3 mmHg, and water is 23.8 mmHg. Find the total vapor pressure of the solution.
Step 1: Determine the mole fraction of water:
Xwater = 1.000 − 0.3 = 0.7
Step 2: Use Raoult’s Law to calculate the vapor pressure of each component:
Pethanol = Xethanol × Pethanol,pure = 0.3 × 59.3 = 17.79 mmHg
Pwater = Xwater × Pwater,pure = 0.7 × 23.8 = 16.66 mmHg
Step 3: Calculate the total vapor pressure of the solution:
Ptotal = Pethanol + Pwater = 17.79 + 16.66 = 34.45 mmHg
Therefore, the total vapor pressure of the ethanol-water solution is 34.45 mmHg at 25 °C.
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