A vacuum reactor is used to synthesize WO$3$ nanoparticles for use in

an electrochromic window device. To create the WO$3$ nanoparticles, a tungsten $($W$)$

metal filament $1\mathrm{.}0$ mm in diameter and $10$ cm long is heated to $2200$C in a vacuum

with a trace pressure of oxygen gas. Assuming all of the W evaporating from the

surface of the filament is rapidly and completely oxidized to WO$3,$ determine the

maximum rate of production of WO$3$ from this reactor $($g$/$s$).$ The equilibrium vapor

pressure of W at $2200$C is approximately $1010$ atm