$$25.0 \mathrm{~mL}$$ of $$0.050 ~\mathrm{M} ~\mathrm{Ba}\left(\mathrm{NO}_{3}\right)_{2}$$ is mixed with $$25.0 \mathrm{~mL}$$ of $$0.020 ~\mathrm{M} ~\mathrm{NaF} . \mathrm{K}_{\mathrm{Sp}}$$ of $$\mathrm{BaF}_{2}$$ is $$0.5 \times 10^{-6}$$ at $$298 \mathrm{~K}$$. The ratio of $$\left[\mathrm{Ba}^{2+}\right]\left[\mathrm{F}^{-}\right]^{2}$$ and $$\mathrm{K}_{\mathrm{sp}}$$ is ___________.

(Nearest integer)

An analyst wants to convert $$1 \mathrm{~L} \mathrm{~HCl}$$ of $$\mathrm{pH}=1$$ to a solution of $$\mathrm{HCl}$$ of $$\mathrm{pH} ~2$$. The volume of water needed to do this dilution is __________ $$\mathrm{mL}$$. (Nearest integer)

The solubility product of $$\mathrm{BaSO}_{4}$$ is $$1 \times 10^{-10}$$ at $$298 \mathrm{~K}$$. The solubility of $$\mathrm{BaSO}_{4}$$ in $$0.1 ~\mathrm{M} ~\mathrm{K}_{2} \mathrm{SO}_{4}(\mathrm{aq})$$ solution is ___________ $$\times 10^{-9} \mathrm{~g} \mathrm{~L}^{-1}$$ (nearest integer).

Given: Molar mass of $$\mathrm{BaSO}_{4}$$ is $$233 \mathrm{~g} \mathrm{~mol}^{-1}$$

The titration curve of weak acid vs. strong base with phenolphthalein as indictor) is shown below. The $$\mathrm{K}_{\text {phenolphthalein }}=4 \times 10^{-10}$$.

Given: $$\log 2=0.3$$

The number of following statement/s which is/are correct about phenolphthalein is ___________

A. It can be used as an indicator for the titration of weak acid with weak base.

B. It begins to change colour at $$\mathrm{pH}=8.4$$

C. It is a weak organic base

D. It is colourless in acidic medium