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The smog constituent peroxyacetyl nitrate (PAN) dissociates into peroxyacetyl
radicals and NO2(g) in a first order reaction with a
half-life of 32 min.
If the initial concentration of PAN in an air sample is 2.7 ×1015 molecules/L, what will be the concentration 2.24 h later?
For a first order reaction, the integrated rate law is
and the rate constant can be found from the half-life: .
Thus, k = 0.693/t½ = 0.693/32 = 0.022 min1.
For an initial concentration [PAN]0 = 2.7 ×1015
molecules/L and at t = 2.24 h = 134 min:
[PAN] = [PAN]oekt = (2.7×1015)e(0.022)(134) = 1.4×1014 molecules/L.