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$\mathrm{A}_{3} \mathrm{~B}_{2}$ is a sparingly soluble salt of molar mass $\mathrm{M}\left(\mathrm{g} \,\mathrm{mol}^{-1}\right)$ and solubility $\mathrm{x}\, \mathrm{g}\, \mathrm{L}^{-1}$. The solubility product satisfies $\mathrm{K}_{\mathrm{sp}}=a\left(\frac{\mathrm{x}}{\mathrm{M}}\right)^{5}$. The value of $a$ is ...... . (Integer answer)
$18$
$150$
$308$
$108$
Solution
$\mathrm{A}_{3} \mathrm{~B}_{2}(\mathrm{~s}) \rightleftharpoons 3 \mathrm{~A}_{(\mathrm{xa})}^{+2}+2 \mathrm{~B}_{(4)}^{-3}$
$\quad\quad\quad\quad\quad\quad3 \mathrm{~s}\quad\quad \quad 2 \mathrm{~s}$
$\mathrm{~K}_{\mathrm{sp}}=(3 \mathrm{~s})^{3}(2 \mathrm{~s})^{2}$
$\mathrm{~K}_{\mathrm{SP}}=108 \mathrm{~S}^{5} \& \mathrm{~s}=(\mathrm{X} / \mathrm{M})$
$\mathrm{K}_{\mathrm{SP}}=108\left(\frac{\mathrm{x}}{\mathrm{m}}\right)^{5}$
$\text { given } \mathrm{K}_{\mathrm{SP}}=\mathrm{a}\left(\frac{\mathrm{x}}{\mathrm{m}}\right)^{5}$
comparing a $=108$
