The $$\mathrm{pH}$$ at which $$\mathrm{Mg}(\mathrm{OH})_2\left[\mathrm{~K}_{\mathrm{sp}}=1 \times 10^{-11}\right]$$ begins to precipitate from a solution containing $$0.10 \mathrm{~M} \mathrm{~Mg}^{2+}$$ ions is __________.

$$2 \mathrm{MnO}_4^{-}+\mathrm{bI}^{-}+\mathrm{cH}_2 \mathrm{O} \rightarrow x \mathrm{I}_2+y \mathrm{MnO}_2+z \overline{\mathrm{O}} \mathrm{H}$$

If the above equation is balanced with integer coefficients, the value of $$z$$ is ________.

An ideal gas undergoes a cyclic transformation starting from the point A and coming back to the same point by tracing the path $$\mathrm{A} \rightarrow \mathrm{B} \rightarrow \mathrm{C} \rightarrow \mathrm{A}$$ as shown in the diagram above. The total work done in the process is __________ J.

The rate of First order reaction is $$0.04 \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~s}^{-1}$$ at 10 minutes and $$0.03 \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~s}^{-1}$$ at 20 minutes after initiation. Half life of the reaction is _______ minutes.

(Given $$\log 2=0.3010, \log 3=0.4771$$)