Q5. A possible ion-molecule reaction mechanism for the synthesis of ammonia in interstellar gas clouds is shown below. N+     + H2     ® NH+   +   H                k1 NH+ + H2 ® NH2+ +   H                 k2 NH2+ + H2 ® NH3+   +   H                 k3 NH3+ + H2 ® NH4+ +   H                 k4 NH4+ + e-   ® NH3    +   H                 k5 NH4+ + e- ® NH2    + 2H                 k6 Use the steady-state approximation to derive equations for the concentrations of the intermediates NH+, NH2+, NH3+ and NH4+ in terms of the reactant concentrations [N+], [H2] and [e-]. Treat the electrons as you would any other reactant. b) Show that the overall rate of productionmjngbh of NH3 is given by d[NH3]/dt = (k1k5/k5+k6) [N+][H2] c) What is the origin of the activation energy in a chemical reaction? d) The rates of many ion-molecule reactions show virtually no dependence on temperature. (i) What does this imply about their activation energy? (ii) What relevance does this have to reactions occurring in the interstellar medium

Q5. A possible ion-molecule reaction mechanism for the synthesis of ammonia in interstellar gas clouds is shown below.

N⁺     + H₂     ® NH⁺   +   H                k₁

NH⁺ + H₂ ® NH₂⁺ +   H                 k₂

NH₂⁺ + H₂ ® NH₃⁺   +   H                 k₃

NH₃⁺ + H₂ ® NH₄⁺ +   H                 k₄

NH₄⁺ + e^-   ® NH₃    +   H                 k₅

NH₄⁺ + e^- ® NH₂    + 2H                 k₆

1. Use the steady-state approximation to derive equations for the concentrations of the intermediates NH⁺, NH₂⁺, NH₃⁺ and NH₄⁺ in terms of the reactant concentrations [N⁺], [H₂] and [e^-]. Treat the electrons as you would any other reactant.

b) Show that the overall rate of productionmjngbh of NH₃ is given by

d[NH₃]/dt = (k₁k₅/k₅+k₆) [N⁺][H₂]

c) What is the origin of the activation energy in a chemical reaction?

d) The rates of many ion-molecule reactions show virtually no dependence on temperature.

(i) What does this imply about their activation energy?

(ii) What relevance does this have to reactions occurring in the interstellar medium