Quick Gen. Chem Question, what do you think.....

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Speeddater

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Hope the studies is going well, as I'm sure it is. What do you guys think about question 136 in the destroyer. My solution match that provided in the solutions and answer page, however, I thought at first one had to find the amount of moles. I got choice C by accident, but I didn't think it would make sense using the mole fraction to calculate the molality. I tried looking for a way to calculate the moles, ex. mole fraction of gas = moles of gas / moles of the solution, or moles of water + moles of gas. However, since there's no way of getting the denominator, this equation is useless, so I would greatly appreciate the rationale behind using the mole fraction instead of the moles of gas. I'm guessing becuase its a fraction of its amount in moles of the solution so there's some sort of proportional relationship. Thanks again & happy studying!