A gaseous compound, \(\text{XY}_3\text{(g)}\), undergoes a first-order decomposition in a rigid, sealed container at constant temperature according to the balanced equation below.

\[ 2\text{XY}_3\text{(g)} \rightarrow \text{X}_2\text{(g)} + 3\text{Y}_2\text{(g)} \]

The rate constant for this reaction at the operating temperature is \(k = 2.31 \times 10^{-4}\text{ s}^{-1}\). If the reaction begins with pure \(\text{XY}_3\text{(g)}\) at an initial partial pressure of \(1.60\text{ atm}\), what is the partial pressure of \(\text{Y}_2\text{(g)}\) in the container after \(6000\text{ s}\)?