Answer to Question #158421 in Physical Chemistry for Nazim Emre Yucetepe

Question

NH4NO3(k) → N2O(g) + 2H2O(g)  reaction happens and N2O gas occurs at 65 C degrees. At first 100 mg ammonium nitrate added to reaction baloon, Decomposition reaction takes place for 85 minutes.gas occuring after the reaction 4.5 cm^3 at 1 bar. find the speed constant and half life.

gas is ideal,vapor pressure of water at 65 C degrees is 187.5mmHg

Answer 1

NH₄NO₃(k) → N₂O(g) + 2H₂O(g) 

100 mg = 0.1 g

0.1 g / 80.043 g/mol = 0.001249 mol of ammonium nitrate

Decomposition reaction provides same 0.001249 moles of N₂O theoretically

Practically:

187.5 mmHg = 0.25 bar / vapor pressure of water at 65⁰C

1 – 0.25 = 0.75 bar (75000 Pa) / gas partial pressure

65 C degrees = 65 + 273.15 = 338.15 K

4.5 cm³ = 4.5 x 10^-6 m³

pV = nRT

n = pV/RT = (75000 x 4.5 x 10^-6) / (8.314 x 338.15) = 0.00012 moles of gas formed

it gives: 0.00012 moles / 85 min = 1.4 x 10⁶ mol/min speed.

Half-life: half of ammonium nitrate or 0.000625 moles decomposes.

If the relation is linear than it takes

0.000625 / 0.00012 x 85 min = 442.3 min