In a qualitative analysis, $\mathrm{Bi}^{3+}$ is detected by appearance of precipitate of $\mathrm{BiO}(\mathrm{OH})(\mathrm{s})$. Calculate pH when the following equilibrium exists at 298 K .

$$ \mathrm{BiO}(\mathrm{OH})(\mathrm{s}) \rightleftharpoons \mathrm{BiO}^{+}(\mathrm{aq})+\mathrm{OH}^{-}(\mathrm{aq}), \mathrm{K}=4 \times 10^{-10} $$

(Given : $\log 2=0.3010$ )

At 298 K , a certain buffer solution contains equal concentrations of $\mathrm{X}^{-}$and $\mathrm{HX}, \mathrm{K}_{\mathrm{b}}$ for $\mathrm{X}^{-}$is $10^{-10}$. What is the pH of this buffer solution?

Phenolphthalein is used as an indicator for the titration of sodium hydroxide solution against a standard solution of oxalic acid. The colour change that is observed at an alkaline pH close to the equivalence point during this titration is:

If the molar conductivity $\left(\Lambda_{\mathrm{m}}\right)$ of a $0.050 \mathrm{~mol} \mathrm{~L}^{-1}$ solution of a monobasic weak acid is $90 \mathrm{~S} \mathrm{~cm}^2 \mathrm{~mol}^{-1}$, its extent (degree) of dissociation will be

[Assume $\Lambda_{+}^{\circ}=349.6 \mathrm{~S} \mathrm{~cm}^2 \mathrm{~mol}^{-1}$ and $\Lambda_{-}^{\circ}=50.4 \mathrm{~S} \mathrm{~cm}^2 \mathrm{~mol}^{-1}$.]