Question #348372

1. Calculate the vapor pressure of a solution made by dissolving 65.0 g CaCl2, C6H12O6, in 655 g of water. The vapor pressure of pure water is 47.1 torr at 37°C.




2. What is the vapor pressure of an aqueous solution that has a solute mole fraction of 0.2000? The vapor pressure of water is 35.576 mmHg at 25 °C.

1
Expert's answer
2022-06-06T22:39:28-0400

1.

To use Raoult's Law , we need to calculate the mole fraction of water (the solvent) in this salt-water solution.

Psolution = Xsolvent * P0solvent


Xsolvent="molesofwater"molesofsolute+molesofsolventX_{solvent} = \frac {"molesof water"}{molesofsolute+molesofsolvent}


Xsolvent=nwaternsolute+nwaterX_{solvent}= \frac {n_{}water}{n_{solute}+n_{water}}




The molar mass of CaCl2 is 111 g/mol and of water is 18 g/mol. So,


nwater=655g18g/mol=36,39moln_{water}= \frac {655g}{18 g/mol}= 36,39mol


and


nsolutes=65g111g/mol=0,586moln_{solutes}= \frac{65g}{111g/mol}=0,586mol


but this is really:


nCa²+ = 0,586 mol

nCl- = 1,172 mol

nwater = 36,39mol


Xsolvent=36,390,586+1,172+36,39=0,954X_{solvent}= \frac {36,39}{0,586+1,172+36,39}=0,954


Note that this still relatively dilute. The pressure of the solution is then calculated via Raoult's Law


Psolution = 0.954 × 47.1= 44.93torr


2.

χsolv = 1.0000 − 0.2000 = 0.8000 <--- solv means solvent

Use Raoult's Law:

Psolution = (χsolvent) (P0solvent)

x = (0.8000) * (35.576)

x = 28.46 mmHg


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