$E_{c e l l}^{o}$ for reaction,
$4 A l (s) + 3 O_{2} (s) + 6 H_{2} O + 4 O H^{-} \to 4 [A l (O H)_{4}^{-}]$ is 2.73 V.
If $△ G_{f}^{o}$ for $O H^{-}$ and $H_{2} O$ are - 157 kJ mol $^{- 1}$ and - 237.2 kJ mol $^{- 1}$ . If $△ G_{f}^{o}$ for $[A l (O H)_{4}]^{-}$ is $x$ kJ.
$- x$ is:

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Solution

For given cell reaction,

$Δ G^{o} = - n E^{o} F$

$∴ Δ G^{o} = - 12 \times 2.73 \times 96500 J$

$= - 3.1613 \times 10^{3} k J$

$[\begin{matrix} n = 12 ∴ 4 A l^{o} \to 4 A l^{3 +} + 12 e ⇌ 3 O_{2}^{o} + 12 e \to 6 O^{2 -} \end{matrix}]$

Now for given reactions,

$Δ G^{o} = 4 \times G_{f}^{o} [A l (O H)_{4}]^{-} - 6 \times G_{f}^{o} [H_{2} O] - 4 \times G_{f}^{o} [O H^{-}]$

(Also note that $G_{f}^{o}$ for elements is zero)
$- 3.1613 \times 10^{3} = 4 \times G_{f}^{o} [A l (O H)_{4}]^{-} - 6 \times (- 237.2) - 4 \times (- 157)$

$∴ G_{f}^{o} [A l (O H)_{4}]^{-} = - 1303 k J$

$- x = 1303$

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Similar questions

4 A l (s) + 3 O_{2} (g) + 6 H_{2} O + 4 O H^{-} ⇋ 4 [A l (O H)_{4}^{-}]

E_{c e l l}^{\circ} = 2.73 V

Δ G_{f}^{\circ} (O H^{-}) = 157 k J m o l^{- 1}

Δ G_{f}^{\circ} (H_{2} O) = - 237.2 k j m o l^{- 1}

Δ G_{f}^{\circ} [A l (O H)_{4}]

4 A l (s) + 3 O_{2} (g) + 6 H_{2} O + 4 ⊖ O H \to 4 [A l (O H)_{4}]^{\oplus}

E_{c e l l}^{⊖} = 2.73 V

Δ_{f} G^{⊖} [\oplus O H] = - 157 k J m o l^{- 1}

Δ_{f} G^{⊖} (H_{2} O) = - 237.2 k J m o l^{- 1}

Δ_{f} G^{⊖} [A l (O H)_{4}]^{⊖}

(A l (O H)_{4}^{⊖}]

4 A J (s) + {3 O}_{2} (g) + 6 H_{2} O (l) + 4 O H^{-} (a q) \to 4 [A J (O H)_{4}^{-} (a q)];

E_{c e l l} = 2.73 V . I f Δ G_{f} (O H^{-}) = - 157 k J m o l^{- 1}

Δ G_{f} (H_{2} O) = - 237.2 k J m o l^{- 1},

Δ G_{f} [A J (O H)_{4}^{-}]

Δ G^{⊖}

4 A 1 + 3 O_{2} + 6 H_{2} O + 4 ⊖ O H \to 4 A 1 (O H)_{4}^{⊖}

E_{c e l l}^{⊖} = 2.73 V

Δ_{f} G_{(⊖ O H)}^{⊖} = - 157 k J m o l^{- 1}

Δ_{f} G_{(H_{2} O)}^{⊖} = - 237 k J m o l^{- 1}

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