$1)$ A gas sample is attached to an open$-$ended mercury manometer, as shown below. The difference in heights of the mercury in the manometer is $15\mathrm{.}9$ cm when the atmospheric pressure is $691$ torr. Given that the density of mercury is $13\mathrm{.}6$ g$/$mL$,$ the pressure of the enclosed gas is $\_\_\_\_$ atm. $2)$ A $2\mathrm{.}66$ gram sample of helium gas exhibits a pressure of $2\mathrm{.}33$ atm in a $7\mathrm{.}17$ L volume. The sample is compressed to a $3\mathrm{.}77$ L volume at constant temperature. After the compression, the gas pressure is $\_\_\_\_$atm. $3)$A gas mixture contains only Ne and Ar$,$ has a total pressure of $3\mathrm{.}54$ atm, and contains $12\mathrm{.}6$ mol of gas. If the partial pressure of Ne is $2\mathrm{.}88$ atm, how many moles of Ar are in the mixture?