(Solved): A gas mixture contains \( 20.0 \) mole\% \( \mathrm{H}_{2} \mathrm{O}(\mathrm ...

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A gas mixture contains \( 20.0 \) mole\% \( \mathrm{H}_{2} \mathrm{O}(\mathrm{v}) \) and \( 80.0 \) mole\% \( \mathrm{N}_{2} \). The gas temperature and absolute pressure at the start of each of the three parts of this problem are \( 54^{\circ} \mathrm{C} \) and \( 500.0 \mathrm{~mm} \mathrm{Hg} \). Ideal gas behavior may be assumed in every part of this problem. a. If some of the gas mixture is put in a cylinder and slowly cooled at constant pressure, at what temperature would the first drop of liquid form? \[ { }^{\circ} \mathrm{C} \] b. If a \( 30.0 \) liter flask is filled with some of the gas mixture and sealed, and \( 30.0 \% \) of the water vapor in the flask is condensed, what volume would be occupied by the liquid water? \( \quad \mathrm{cm}^{3} \) What would be the system temperature? \[ { }^{\circ} \mathrm{C} \] c. If the gas mixture is stored in a rigid-walled cylinder and a low-pressure weather front moves in and the barometric (atmospheric) pressure drops from \( 760 \mathrm{~mm} \mathrm{Hg} \) to \( 740.0 \mathrm{~mm} \) of \( \mathrm{Hg} \), what would be the new gauge pressure in the cylinder? \[ \mathrm{Hg} \]