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In the first-order decomposition of dinitrogen pentoxide at 335 K,
N2O5(g) 2NO2(g) + ½O2(g)
if we start with a 2.50-g sample of N2O5 at 335 K and have 1.50 g remaining after 109 s, (a) What is the value of the rate constant k? (b) What is the half-life of the reaction? (c) What mass of N2O5 will remain after 5.0 min?
For a first-order reaction, the integrated rate law can be written as
Since the concentration units cancel out, we can work directly in grams for this problem.
(a) [N2O5]0 = 2.50 g, [N2O5]t = 1.50 g, t = 109 s, so
so k = 4.69×103 s1
(b) t½ = 0.693/k = 0.693/4.69×103 = 148 s.
(c) t = 5.0 min = 300. s, so