Question #44845

A gaseous compound $A$ containing a radioactive isotope undergoes two simultaneous parallel first-order processes at $298\text{ K}$: a chemical decomposition $A(g) \rightarrow C(g)$ with a rate constant $k_c = 2.0 \times 10^{-4}\text{ s}^{-1}$, and a nuclear $\alpha$-decay transforming the isotope in $A$ to form a new species $B(g)$ with a decay constant $\lambda = 2.0 \times 10^{-4}\text{ s}^{-1}$. The chemical decomposition has a temperature coefficient $\mu = 3$ (the rate triples for every $10\text{ K}$ rise). If the system is heated to $318\text{ K}$ and allowed to react until $A$ is completely exhausted, what is the mole fraction of $B$ in the final product mixture?