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J. W. Hill, R. H. Petrucci, T. W. McCreary, & S. S. Perry General Chemistry, 4th edition.

Problem 13.41.

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?




Answer:

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 min–1. 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.