A student investigates the reaction between sulfur dioxide gas and oxygen gas to form sulfur trioxide gas inside a rigid container at a constant temperature, as represented by the balanced equation below.

\[ 2\text{SO}_2\text{(g)} + \text{O}_2\text{(g)} \rightarrow 2\text{SO}_3\text{(g)} \]

Equal masses of \(\text{SO}_2\text{(g)}\) (molar mass \(\approx 64.0\text{ g/mol}\)) and \(\text{O}_2\text{(g)}\) (molar mass \(\approx 32.0\text{ g/mol}\)) are sealed in the vessel and allowed to react completely. Assuming the temperature of the mixture remains constant and all gases exhibit ideal behavior, what is the ratio of the final total pressure to the initial total pressure in the vessel, \(\dfrac{P_{\text{final}}}{P_{\text{initial}}}\)?