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The following equilibria are given by ...

The following equilibria are given by
rho`N_(2)+3H_(2)hArr2NH_(3):K_(1)`
`N_(2)+O_(2)hArr2NO,K_(2)`
`H_(2)+1/2O_(2)hArrH_(2)O,K_(3)`
The equlibrium constant of the reaction
`2NH_(3)+5/2O_(2)hArr2NO+3H_(2)O`
in terms of `K_(1) and K_(3)` is

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Verified by Experts

`r = k_(1)[NO_(2)][NO_(3)]` …(i)
and form the fast equilibrium step,
`k_(eq) = ([NO_(2)][NO_(3)])/([N_(2)O_(5)]`
Thus, `[NO_(2)] [NO_(3)] = k[N_(2)O_(5)]` …(ii)
Uisng Eq. (ii) in Eq. (i), we get
`r = k_(1)k_(eq)[N_(2)O_(5)] = k[N_(2)O_(5)]` where `k = k_(1)k_(eq)`
This shows that the mechanism is conisstent with the observed rate law.
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