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Ways of Representing the Concentration of a Solution

If excess met...

Question

If excess metallic iron is added to an $N - C u {S O}_{4}$ solution, calculate the approximate concentration of ${C u}^{2 +}$ when equilibrium is established.

2.3 \times 10^{- 4}

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3.3 \times 10^{- 4}

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2.1 \times 10^{- 3}

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4.1 \times 10^{- 5}

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Solution

The correct option is B $3.3 \times 10^{- 4}$
$F e^{2 +} + 2 e^{⊝} ⇌ F e (S)$ $E^{\circ} = - 0.44 V$
$C u^{2 +} + 2 e^{⊝} ⇌ C u (S)$ $E^{\circ} = + 0.337 V$

$F e (S) + C u^{2 +} ⇌ F e^{2 +} + C u (S)$ $E^{\circ} = - 0.44 - 0.337 = + 0.103 V$
$K_{e q} = [F e^{2 +}] / [C u^{2 +}]$
$- n F E^{\circ} = △ G = △ H - T △ S = - R T l n K_{e q}$
$\Rightarrow R T l n K_{e q} = - n F E^{\circ}$
$, l n K_{e q} = \frac{- n F E^{\circ}}{R T} = \frac{(2 \times 96 \times 485 \times 0.103)}{(298.2 \times 8.314)} = 8.02$
$K_{e q} = 3032$ so, at $[F e^{2 +}] = 1.00 [C u^{2 +}] = 3.3 \times 10^{- 4} M$

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