A futuristic spaceship relies on the combustion of pentaboron nonahydride (B₅H₉) to produce a fuel called diboron trioxide, B₂O₃. The reaction proceeds according to the balanced equation shown below. You work in mission control and are responsible for getting this ship and its pilot, Buzz Lightyear, to an extremely important intergalactic peace mission to meet with Warmaster Zurg and prevent intergalactic war. But, prior to takeoff, someone secretly steals a tank of the B₅H₉ as well as the specs of the ship, to attempt to sabotage the conference!
With only 0.0646 light-years remaining in the flight (1 light-year = 9.46 x 10¹⁵ m), Buzz radios mission control to tell you that he only has 9.36 x 10⁹ kg of B₅H₉ left, but thankfully, there is plenty of oxygen. Buzz isn't big on math, so he asks you to run the numbers to see if he has enough fuel to get to the conference & save the galaxy.
2
You remember from the lost records that the ship uses an average of 4.20 x 10^-3 kg (.00420 kg) of B₂O₃ fuel every 100. meters and you remember that the percent yield of this reaction is only 93.6%. So how does this cliffhanger end? Will it be peace or war? Does Buzz reach the conference and save the galaxy?? (You must show work to receive credit) (14 pts)
Molar masses:
B₅H₉ — 63.14 g/mol , B₂O₃ —-- 69.62 g/mol
Reaction
2 B₅H₉ + 12 O₂ → 5 B₂O₃ + 9 H₂O
