(Solved): Some useful conversion factors: \( 1 \mathrm{~atm}=760 \mathrm{mmHg}, 1 \mathrm{~atm}=760 \) torr, ...

Some useful conversion factors: \( 1 \mathrm{~atm}=760 \mathrm{mmHg}, 1 \mathrm{~atm}=760 \) torr, \( 1 \mathrm{~atm}=14.7 \mathrm{psi}, \mathrm{T}(\mathrm{K})=273+\mathrm{T}\left({ }^{\circ} \mathrm{C}\right), \mathrm{R}=0.08206 \frac{\mathrm{L} \cdot \cdot \mathrm{tm}}{\text { mol.K }} \) \( \mathrm{N}_{\mathrm{A}}=6.022 \times 10^{23}, 1 \mathrm{ft}^{3}=28.32 \mathrm{~L}, 1 \mathrm{ft}=0.3048 \mathrm{~m}, 1 \mathrm{~L}=1 \mathrm{dm}^{3} \) 1. You place a piece of aluminum in \( 500.0 \mathrm{~mL} \) of \( 2.500 \mathrm{M} \) solution of \( \mathrm{HCl} \). You collect the \( \mathrm{H}_{2} \) gas that is formed over water. At the end of the reaction, all of the aluminum has been used up, and you have collected the \( \mathrm{H}_{2} \) gas in a \( 2.50 \mathrm{~L} \) flask with a total pressure of \( 1.856 \mathrm{~atm} \) at a temperature of \( 80.0^{\circ} \mathrm{C} \). Determine the mass of the piece of aluminum that was used in this experiment. The vapor pressure of water is \( 355.1 \mathrm{mmHg} \) at \( 80^{\circ} \mathrm{C} \). The balanced chemical reaction is the following: \[ 2 \mathrm{Al}(\mathrm{s})+6 \mathrm{HCl}(\mathrm{aq}) \rightarrow 2 \mathrm{AlCl}_{3}(\mathrm{aq})+3 \mathrm{H}_{2}(\mathrm{~g}) \]