A student prepares a \(1.0\text{ L}\) buffer solution containing \(0.050\text{ mol}\) of a weak monoprotic acid \(\text{HA}\) (\(K_a = 1.0 \times 10^{-4}\)) and \(1.05\text{ mol}\) of \(\text{NaA}\). To this solution, the student adds \(0.050\text{ mol}\) of \(\text{HCl(g)}\), which dissolves completely without changing the volume of the solution. Assuming the temperature is \(298\text{ K}\), what is the \(\text{pH}\) of the resulting solution?