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Problem 13.40.

In the first-order decomposition of dinitrogen pentoxide at 335 K,

N_{2}O_{5}(*g*)
2NO_{2}(*g*) + ½O_{2}(*g*)

if we start with a 2.50-g sample of N_{2}O_{5} 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 N_{2}O_{5} 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**) [N_{2}O_{5}]_{0} = 2.50 g, [N_{2}O_{5}]_{t}
= 1.50 g, *t* = 109 s, so

so *k* = 4.69×10^{–3} s^{–1}

(**b**) t_{½} = 0.693/*k* = 0.693/4.69×10^{–3} = 148 s.

(**c**) *t* = 5.0 min = 300. s, so