Hot Tungsten
Could someone please explain this chemistry question to me?
Ammonia decomposes on the surface of a hot tungsten wire. Following are the half-lives that were obtained at 1100 ⁰C for different initial concentrations of NH3: [NH3]0 = 0.0031 N, t1/2 = 7.6 min, 0.0015 M, 3.7 min; 0.0068 M, 1.7 min. For this decomposition, what is….
a.) The order of the reaction?
b.) The rate constant k?
(a) Let’s pretend instead that
[NH3] = 0.0015 M, t1/2 = 7.6 min
[NH3] = 0.0031 M, t1/2 = 3.7 min
[NH3] = 0.0068 M, t1/2 = 1.7 min
(I can’t function without monotonic data trends.) You can either approach this tactically (“Oh, the half-life changes with concentration. Weird! Well, it’s definitely not first order in NH3, because then the half-life would always be the same, so it must be second-order in NH3 because if it’s not, then everyone will fail this question.”), or analytically by again eliminating first order (because t1/2 is not independent of concentration) and then fitting a line to ln( t1/2 ) vs ln( [NH3]initial ) to find the slope 1-n, where n is the rxn order. (Ouch!) Probably though you know that t1/2 is inversely proportional to initial reactant concentration in a 2nd order rxn, and you noticed that doubling [NH3] from .0015 M to .0031 M cut t1/2 in two, so you’re persuaded that this rxn is 2nd order in [NH3] without betting on the success of your classmates or making any log-log plots.
(b) This rxn is 2nd order in [NH3], so t1/2 = 1 / (k [NH3]init). Choose any data point:
k = 1 / (t1/2 [NH3]init) = 1 / [ (7.6 min)(60 s / 1 min) (0.0015 M) ]
(OK, or do you need to derive that from the rate equation?)
w
Willy’s Tungsten Gray 1990 Mustang Notchback
