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Molarity and molality of a solution of a liquid (mol wt=50) in aqueous solution is 9 and 10 respectively. What is the density of solution?

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Answer 1

Solving:

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Molarity

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$\large \mathtt{ = \dfrac{mass \: of \: solute}{molar \: mass \: of \: solute} \times \dfrac{100}{volume\: of \: solution} }$

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$\large \: \: \: \: \: \: \: \: \: \: : ⇒ \: \mathtt{m = \dfrac{w}{ {m} '} \times \dfrac{1000}{v} }$

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$\large \: : ⇒ \: \mathtt{w = \dfrac{m \times m' \times v}{1000} } \: \rm \longrightarrow(1)$

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Molarity

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$\large \mathtt{ = \dfrac{mass \: of \: solute}{molar \: mass \: of \: solute} \times \dfrac{100}{mass\: of \: solvent} }$

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$\large \: \: \: \: \: \: \: \: \: \: : ⇒ \: \mathtt{m = \dfrac{w}{ {m} '} \times \dfrac{1000}{w'} }$

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$\large \: : ⇒ \: \mathtt{w = \dfrac{m \times m' \times w'}{1000} } \: \rm \longrightarrow(2)$

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Mass of Solution = Mass of Solvent + Mass of Solute

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⇒ w" = w + w'

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⇒ vd = w + w'

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⇒ w' = vd - w ________ (3)

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Putting Values in equation

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$\large : ⇒ \: \mathtt{ \dfrac{m \times m' \times v}{1000} = \mathtt{ \dfrac{m \times m' \times (vd - w)}{1000} } }$

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⇒ M × v = mvd - mw

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$\large⇒ \mathtt{ M × v = mvd -m \left( \dfrac{mm'v}{1000} \right)}$

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$\large⇒ \mathtt{ M = m \left( d - \dfrac{m'M}{100} \right)}$

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$\large⇒ \mathtt{ d = M \left( \dfrac{1}{m} + \dfrac{m'}{1000} \right)}$

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Density

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$\large \mathtt{ = molarity\left( \dfrac{1}{molality} + \dfrac{molecular \: weight}{1000} \right)}$

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$\large \: \: \: \: \: \: \: : ⇒ \mathtt{ d = 9 \left( \dfrac{1}{10} + \dfrac{50}{1000} \right)}$

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D = 1.35g/cc

Answer 2

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