Question

Consider the gas-phase isotopic reactions H+H2 + H2+H D+H2 + HD+H Mu + H2 → MuH+H Answer the following questions qualitatively: a) What is the order of increasing collision rates between the reactants? b) What is the order of the tunnelling contributions? c) In what way could zero-point vibration affect the reaction rate? Predict the order of rate constants based on this contribution.

Answer 1

H+H​​​​​​2​​​​​—> H​​​​​​2+ H rate constant =k​​​​​​1

D+H​​​​​​2 —> HD + H. rate constant =k​​​​​​2

Mu + H​​​​​​2 —> MuH+H. Rate constant = k​​3
As per kinetic isotopic effect (KIE), heavies isotopes leads to slower reaction rate ie. lesser no. of collisions all my < 14 C2D as per mass So, order of collision rates 2D<1¥ < 0.1 my the Schrodinge i) The probablity P, of a particle tunneling through potential energy barrier is derived from the Equation p = Sep (- 408 2m[V - E) where V → potential berries Et Energy possesed by porticle o > thickness of bavities - m - mass of particle h = 6.626 X10 kg/s from abone equation, we can easily say Probablity P of e particle temmelling decreveo with increasing them So, order of tunnelling is

in The isotopes which are heavy will have lower zero point vibrations. So, with lower enesey they will require extra energy from outside to break the bond. This means activation eneagy will be high - and S K = A e-E9/RT So, value of K will be less ice rate of reaction will be slowena of From above to Arrhenius Equation, ander rate constants of rx are # ke (k <kg

​​​​Mass order

Muonium(0.11)< Hydrogen(1)<Deuterium (2)

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