What is the partial pressure?

Question

Dinitrogen pentoxide decomposes in the gas phase to form nitrogen dioxide and oxygen gas. The reaction is first order in dinitrogen pentoxide and has a half-life of 2.81  at 25  C. 

If a 1.6 L reaction vessel initially contains 760 torr of N₂O₅ at 25 C, what partial pressure of 

 will be present in the vessel after 230 minutes?

Answer 1

For a first order reaction, the fraction remaining equals 0.5ⁿ where n is the number of half lives that have elapsed. In equation form, this is FR = 0.5ⁿ

So, let us first find, but since you didn't supply units for the half life of 2.81, I'm assuming it is minutes. So..

230 minutes x 1 half life / 2.81 minutes = 81.9 half lives = n

FR = 0.5^81.9 = 2.2x10^-25 (this is essentially zero). SO MAYBE YOU SHOULD HAVE INCLUDED UNITS FOR THE HALF LIFE. I'M NOW GUESSING IT IS 2.81 HOURS, NOT MINUTES.

Repeating the calculation using 2.81 hours as the half life:

Converting to minutes, we have...

2.81 hours x 60 minutes/hr = 168.6 minutes = half life

half lives elapsed = 230 minutes x 1 half life / 168.6 minutes = 1.36 half lives = n

FR = 0.5^1.36 = 0.390

Pressure remaining = 0.390 x 760 torr = 296 torr