$5.$ A $7\mathrm{.}00$ L vessel contains $3\mathrm{.}50$ moles of ideal gas at a pressure of $1\mathrm{.}60$ x $106$ Pa$.$ Find $($a$)$ the temperature of the gas and $($b$)$ the average kinetic energy of a gas molecule in the vessel.

$($c$)$ What additional information would you need if you were asked to find the average speed of a gas molecule?