2 KMnO4 (aq) + 3 KCN (aq) + H2O (ℓ) → 2 MnO2 (s) + 2 KOH (aq) + 3 KOCN (aq)

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Stoichiometry

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KMnO4          Mass: g  or Solution Volume: mL of Concentration: mol/L
KCN            Mass: g  or Solution Volume: mL of Concentration: mol/L
H2O            Mass: g
MnO2           Mass: g
KOH            Mass: g  or Solution Volume: mL of Concentration: mol/L
KOCN           Mass: g  or Solution Volume: mL of Concentration: mol/L

Enthalpy of Reaction

[2ΔHf(MnO2 (s)) + 2ΔHf(KOH (aq)) + 3ΔHf(KOCN (aq))] - [2ΔHf(KMnO4 (aq)) + 3ΔHf(KCN (aq)) + 1ΔHf(H2O (ℓ))]
[2(-520.03) + 2(-482.39) + 3(-398.42)] - [2(-793.81) + 3(-191.73) + 1(-285.83)] = -751.46 kJ
-751.46 kJ     (exothermic)

Entropy Change

[2ΔSf(MnO2 (s)) + 2ΔSf(KOH (aq)) + 3ΔSf(KOCN (aq))] - [2ΔSf(KMnO4 (aq)) + 3ΔSf(KCN (aq)) + 1ΔSf(H2O (ℓ))]
[2(53.05) + 2(91.75) + 3(209.19)] - [2(293.71) + 3(298.31) + 1(69.91)] = -635.09 J/K
-635.09 J/K     (decrease in entropy)

Free Energy of Reaction (at 298.15 K)

From ΔGf° values:
[2ΔGf(MnO2 (s)) + 2ΔGf(KOH (aq)) + 3ΔGf(KOCN (aq))] - [2ΔGf(KMnO4 (aq)) + 3ΔGf(KCN (aq)) + 1ΔGf(H2O (ℓ))]
[2(-465.18) + 2(-440.58) + 3(-380.79)] - [2(-730.57) + 3(-244.56) + 1(-237.18)] = -521.890000000001 kJ
-521.89 kJ     (spontaneous)

From ΔG = ΔH - TΔS:
-562.11 kJ     (spontaneous)

Equilibrium Constant, K (at 298.15 K)

2.73061061425267E+91
This process is favorable at 25°C.