The decomposition of N2O to N2 and O2 is a first-order reaction. At 730°C, the rate constant of the reaction is 1.94 * 10-4 min-1. If the initial pressure of N2O is 5.10 atm at 730°C, calculate the total gas pressure after one half-life. Assume that the volume remains constant.

The total pressure after one half is 6.375 atm.

Explanation:

The initial pressure of product is increases while the pressure of reactant would decrease.

Balanced chemical equation:

2N₂O → 2N₂ + O₂

The pressure of N₂O is 5.10 atm. The change in pressure would be,

N₂O = - 2x

N₂ = + 2x

O₂ = + x

The total pressure will be

P (total) = P (N₂O) + P (N₂) + P (O₂)

P (total) = (5.10 - 2x) + (2x) + (x)

P (total) = 5.10 + x

After one half life:

P (N₂O) = 1/2 (5.10) = 5.10 - 2x

x = 5.10 - 1/2 (5.10) / 2

x = 5.10 - 0.5 (5.10) / 2

x = 5.10 - 2.55 / 2

x = 2.55 / 2 = 1.275 atm

Thus the total pressure will be,

P (total) = 5.10 + x

P (total) = 5.10 + 1.275

P (total) = 6.375 atm