Calculate the total gas pressure after one half-life?

Question

Decomposition of N₂O to N₂ and O₂ is a first order reaction. At 730 deg. C the half life of the reaction is 3.58 x 10³ min. If the initial pressure of N₂O is 2.10 atm at 730 deg. C, 

 

a. calculate the total gas pressure after one half-life

 

b. calculate the total gas pressure after 4 days

Answer 1

For a first order reaction, fraction remaining = 0.5ⁿ where n = the number of half lives that have elapsed.

In this problem, for (a) the number of half lives elapsed (n) = 1

(a) fraction remaining = 0.5¹ = 0.5

2N₂O => 2N₂ + O₂

2.10.......0........0.....I

-2x......+2x.....+x.....C

1.05...1.05....0.525...E

Total pressure = 1.05 + 1.05 + 0.525 atm = 2.63 atm

 

For (b) the number of half lives elapsed = 4 days x 24 hr/day x 60 min/hr x 1 half live/3580 min = 1.61 half lives

fraction remaining = 0.5^1.61

fraction remaining = 0.328

2.10 atm x 0.328 = 0.689 atm of N₂O remains. This means that 1.41 atm has been converted to N₂ and 0.706 atm of O₂

Total pressure = 0.689 + 1.41 + 0.706 atm = 2.81 atm