Chapter 7: Q29P (page 160)

Consider precipitation of $X^{x -}$ with role="math" localid="1655098271650" $M^{m +}$ :
${xM}^{m +} + {mX}^{x -} ⇌ M_{x} X_{m} (s) K_{sp} = [M^{m +}]^{x} [X^{x -}]^{m}$ Write mass balance equations for M and X and derive the equation
$V_{M} = V_{x}^{0} \frac{({xC}_{X}^{0} + m [M^{m +}] - x [X^{x -}]}{({mC}_{M}^{0} - m [M^{m +}] + x [X^{x -}]} where [X^{x -}] = {(K_{sp} / [M^{m +}]^{x})}^{\frac{1}{m}}$

Short Answer

Expert verified

The mass balance for M and X are.

${mC}_{M}^{o} \cdot V_{M} - m [M^{m +}] (V_{M} + V_{x}^{o}) = {xC}_{x}^{o} \cdot V_{x}^{o} - x [X^{(} x -)] (V_{M} + V_{x}^{o})$

Step by step solution

Step 1: Define the mass balance.

Mass balance is the sum of moles of ion and moles of precipitate. It is literally mole balance.

Step 2: derive the equation for mass balance M and X.

The equation of mass balance of M and X

$V_{M} = {V_{x}}^{o} (\frac{{C_{x}}^{°} + [M^{+}] - [X^{-}]}{{C_{M}}^{°} - [M^{+}] - [X^{-}]})$

The titration reaction of $M^{m +}$ with role="math" localid="1655099209443" $X^{x -}$

${xM}^{m +} + {mX}^{x -} ⇌ M_{x} X_{m (s)} {mC}_{M}^{o}, V_{M} {xC}_{x}^{°}, V_{x}^{o}$

${mC}_{M}^{0}$ is initial concentration of $M^{m +}$

$V_{M}$ is volume of added $M^{m +}$

${xC}_{x}^{0}$ is concentration of $X^{x -}$

$V_{x}^{0}$ is volume of $X^{x -}$

The mass balance of M and x .

${mC}_{M}^{o} \cdot V_{M} = m [M^{m +}] (V_{M} + . V_{x}) + mol M_{X} X_{m (s)} {mC}_{M}^{o} \cdot V_{M} = m [M^{m +}] (V_{M} + V_{x}) + {molM}_{X} X_{m (s)}$

On rearranging the above equation

we get ${mC}_{M}^{o} \cdot V_{M} - m [M^{m +}] (V_{M} + V_{x}^{o}) = {xC}_{x}^{o} \cdot V_{x}^{o} - x [X^{x -}] (V_{M} + V_{x}^{o})$

Thus the solution is $V_{M} = {V_{x}}^{o} (\frac{{C_{x}}^{°} + [M^{+}] - [X^{-}]}{{C_{M}}^{°} - [M^{+}] - [X^{-}]})$

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Short Answer

Step by step solution

Step 1: Define the mass balance.

Step 2: derive the equation for mass balance M and X.

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Consider precipitation of Xx-with role="math" localid="1655098271650" Mm+:xMm++mXx-⇌MxXm(s) Ksp=[Mm+]x[Xx-]mWrite mass balance equations for M and X and derive the equationVM=Vx0(xCX0+m[Mm+]-x[Xx-](mCM0-m[Mm+]+x[Xx-]where[Xx-]=(Ksp/[Mm+]x)1m

Short Answer

Step by step solution

Step 1: Define the mass balance.

Step 2: derive the equation for mass balance M and X.

One App. One Place for Learning.

Most popular questions from this chapter

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Study anywhere. Anytime. Across all devices.