Answer:
the total gas pressure after one half-life is 4.38 atm
Explanation:
The balanced equation for the decomposition of N2O to N2 and O2 is given as:
2N₂O(gas) ⇒ 2N₂(gas) + O₂(gas)
2 moles of N₂O produce 2 moles of N₂ and 1 mole of O₂
The change in pressure depends on the coefficient (number of moles) of the reactant and product.
N₂O N₂ O₂
number of moles 2 2 1
Initial pressure (atm) 3.50 0 0
change in pressure -2x +2x x
Final pressure (atm) 3.50 - 2x 2x x
The total final pressure is the sum of the individual total pressure. i.e.:
Total final pressure = final pressure of N₂O + final pressure of N₂ + final pressure of O₂
Total final pressure = (3.5 - 2x) + (2x) + x
Total final pressure = 3.5 + x
After one half life, the initial pressure of N₂O would be half its value.
Final pressure of N₂O = half of the initial pressure of N₂O
3.5 - 2x = 0.5(3.5)
3.5 - 2x = 1.75
2x = 1.75
x = 0.875 atm
Therefore, Total final pressure = 3.5 + x = 3.5 + 0.875
Total final pressure = 4.38 atm to 3 significant figures
