Current Attempt in Progress

A gas mixture contains $20\mathrm{.}0$ mole$\%H_{2}O(v)$ and $80\mathrm{.}0$ mole$\%N_2.$

The gas temperature and absolute pressure at the start of each of the three parts of this problem are $54C$ and $500\mathrm{.}0mmHg.$ 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? $C$

b$.$ If a $30\mathrm{.}0$ liter flask is filled with some of the gas mixture and sealed, and $50\mathrm{.}0\%$ of the water vapor in the flask is condensed, what volume would be occupied by the liquid water? $c{m}^3$

What would be the system temperature? $C$

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 $760mmHg$ to $730\mathrm{.}0mm$ of $Hg,$ what would be the new gauge pressure in the cylinder? $mmHg$