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 of $H_2PO_4^{-}$ 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,$pH = pK_a$.
Choose the correct answer from the option given below.

$pH$ of a resulting solution prepared by mixing $100 \ mL$ $0.1 \ M$ $HCl$ and $200 \ mL$ $0.05 \ M$ $NaOH$ is

The number of moles of hydroxide $(OH^{-})$ ion in $0.3 \ L$ of $0.005 \ M$ solution of $Ba(OH)_2$ is

For a weak electrolyte $A_xB_y$,the degree of dissociation $\alpha$ in terms of concentration $c$ is given by:

$A$ soft drink was bottled with a partial pressure of $CO_2$ of $3 \ bar$ over the liquid at room temperature. The partial pressure of $CO_2$ over the solution approaches a value of $30 \ bar$ when $44 \ g$ of $CO_2$ is dissolved in $1 \ kg$ of water at room temperature. The approximate $pH$ of the soft drink is............... $\times 10^{-1}$ (First dissociation constant of $H_2CO_3 = 4.0 \times 10^{-7}$; $\log 2 = 0.3$; density of the soft drink $= 1 \ g \ mL^{-1}$)

The $pH$ of the solution formed by mixing $5 \ mL$ of $M/5$ $HCl$ and $10 \ mL$ of $M/10$ $NaOH$ is: