Nitrous oxide decomposes on a silver surface at by the overall reaction

CHEMISTRY · Multi-part · A Level · Chemistry · Kinetics · Kinetics

Problem

Nitrous oxide decomposes on a silver surface at

600\,\text{K}

by the overall reaction

2\,\text{N}_2\text{O}(g) \rightarrow 2\,\text{N}_2(g) + \text{O}_2(g)

. Assume that the initial rate is proportional to the fraction

\theta

of surface sites occupied by N2O and that Langmuir adsorption behavior applies. The adsorption equilibrium constant for N2O on silver at

600\,\text{K}

K_{\text{ads}} = 2.5 \times 10^{-3}\,\text{mbar}^{-1}

. A reactor is fed with N2O at

P_{\text{N}_2\text{O}} = 40\,\text{mbar}

, and the surface site density is

1.5 \times 10^{-9}\,\text{mol}\,\text{sites}\,\text{cm}^{-2}

. The intrinsic surface rate constant for the rate-determining step is

k_s = 3.0 \times 10^{2}\,\text{s}^{-1}

. (a) Calculate the fraction

\theta

of surface sites initially occupied by N2O under the stated conditions. (b) Using

\theta

from part (a), determine the initial rate per unit surface area (

\text{mol}\,\text{cm}^{-2}\,\text{s}^{-1}

). (c) If the partial pressure of N2O is reduced to

20\,\text{mbar}

while temperature and all other parameters remain constant, by what factor will the initial rate change? Show your reasoning.