Which of the following statement(s) is/are correct? \((A)\) The \(pH\) of \(1 \times 10^{-8}\,M\,HCl\) solution is \(8\). \((B)\) The conjugate base \(H _2 PO _4^{-}\)is \(HPO _4{ }^{2-}\). \((C)\) \(K _{ w }\) increases with increase in temperature. \((D)\) When a solution of weak monoprotic acid is titrated against a strong base at half neutralisation point, \(pH =\frac{1}{2} pK _{ a }\) Choose the correct answer from the option given below.

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.