(i) and (ii) are two chemical reactions carried out at TK.
\[
(i) \, X \rightarrow Y + W \, \text{with rate constant} \, k_1
\]
\[
(ii) \, X \rightarrow Z + W \, \text{with rate constant} \, k_2
\]
The activation energy for reaction (ii) is 3 times that of reaction (i). What is the expression for \( k_1 \)?