x moles of an organic non-volatile monobasic acid were taken and dissolved in water. The change in boiling point $△ T_{b}$ . pH of the solution will be

$- l o g_{10} [x]$

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$- l o g_{10} [\frac{△ T_{b}}{K_{b}} - x]$

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$- l o g_{10} [2 x]$

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None of the above

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Solution

The correct option is B
$- l o g_{10} [\frac{△ T_{b}}{K_{b}} - x]$

$△ T_{b} = i K_{b} x \Rightarrow \frac{△ T_{b}}{K_{b} x} = i (1)$
Now consider the dissociation of HA
$H A ⇌ H^{+} + A^{-} I n i t i a l : x 00 f i n a l : x (1 - α) x α x α$
$∴ i = \frac{x (1 - α) + x α + x α}{x} = 1 + α \Rightarrow α = i - 1 (2) p H = - l o g_{10} [x α] = - l o g_{10} [x (i - 1)] = - l o g_{10} [x (\frac{△ T_{b}}{K_{b} x} - 1)] = - l o g_{10} [\frac{△ T_{b}}{K_{b}} - 1]$

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