When an acid is added to water, it increases the concentration of hydrogen ions ([tex]\( \text{H}^+ \)[/tex]) in the solution. This increase in hydrogen ions lowers the pH of the solution, making it more acidic (pH < 7).
In aqueous solutions at 25°C, the relationship between pH and pOH is given by:
[tex]\[ \text{pH} + \text{pOH} = 14 \][/tex]
Since the pH is less than 7 (due to the presence of the added acid), to satisfy the equation [tex]\(\text{pH} + \text{pOH} = 14\)[/tex], the pOH must be greater than 7. Therefore:
[tex]\[ \text{pH} < \text{pOH} \][/tex]
Another important constant in aqueous solutions is the ion-product constant for water ([tex]\( K_w \)[/tex]), which is given by:
[tex]\[ K_w = [\text{H}^+][\text{OH}^-] = 1 \times 10^{-14} \][/tex]
This constant ([tex]\( K_w \)[/tex]) remains the same at 25°C regardless of the changes in pH or pOH.
Given these observations, the correct outcome of the system after the acid is added is:
A. [tex]\( \text{pH} < \text{pOH} \)[/tex] and [tex]\( K _{ w } = 1 \times 10^{-14} \)[/tex]
Therefore, the answer is A.
