KMnO4 + CH2O = H2O + CO2 + MnO2 + K2CO3

KMnO_4 potassium permanganate + HCHO formaldehyde ⟶ H_2O water + CO_2 carbon dioxide + MnO_2 manganese dioxide + K_2CO_3 pearl ash

Balance the chemical equation algebraically: KMnO_4 + HCHO ⟶ H_2O + CO_2 + MnO_2 + K_2CO_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 KMnO_4 + c_2 HCHO ⟶ c_3 H_2O + c_4 CO_2 + c_5 MnO_2 + c_6 K_2CO_3 Set the number of atoms in the reactants equal to the number of atoms in the products for K, Mn, O, C and H: K: | c_1 = 2 c_6 Mn: | c_1 = c_5 O: | 4 c_1 + c_2 = c_3 + 2 c_4 + 2 c_5 + 3 c_6 C: | c_2 = c_4 + c_6 H: | 2 c_2 = 2 c_3 Since the coefficients are relative quantities and underdetermined, choose a coefficient to set arbitrarily. To keep the coefficients small, the arbitrary value is ordinarily one. For instance, set c_4 = 1 and solve the system of equations for the remaining coefficients: c_1 = 4 c_2 = 3 c_3 = 3 c_4 = 1 c_5 = 4 c_6 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 KMnO_4 + 3 HCHO ⟶ 3 H_2O + CO_2 + 4 MnO_2 + 2 K_2CO_3

+ ⟶ + + +

potassium permanganate + formaldehyde ⟶ water + carbon dioxide + manganese dioxide + pearl ash

| potassium permanganate | formaldehyde | water | carbon dioxide | manganese dioxide | pearl ash molecular free energy | -737.6 kJ/mol | -102.5 kJ/mol | -237.1 kJ/mol | -394.4 kJ/mol | -465.1 kJ/mol | -1064 kJ/mol total free energy | -2950 kJ/mol | -307.5 kJ/mol | -711.3 kJ/mol | -394.4 kJ/mol | -1860 kJ/mol | -2127 kJ/mol | G_initial = -3258 kJ/mol | | G_final = -5093 kJ/mol | | | ΔG_rxn^0 | -5093 kJ/mol - -3258 kJ/mol = -1835 kJ/mol (exergonic) | | | | |

Construct the equilibrium constant, K, expression for: KMnO_4 + HCHO ⟶ H_2O + CO_2 + MnO_2 + K_2CO_3 Plan: • Balance the chemical equation. • Determine the stoichiometric numbers. • Assemble the activity expression for each chemical species. • Use the activity expressions to build the equilibrium constant expression. Write the balanced chemical equation: 4 KMnO_4 + 3 HCHO ⟶ 3 H_2O + CO_2 + 4 MnO_2 + 2 K_2CO_3 Assign stoichiometric numbers, ν_i, using the stoichiometric coefficients, c_i, from the balanced chemical equation in the following manner: ν_i = -c_i for reactants and ν_i = c_i for products: chemical species | c_i | ν_i KMnO_4 | 4 | -4 HCHO | 3 | -3 H_2O | 3 | 3 CO_2 | 1 | 1 MnO_2 | 4 | 4 K_2CO_3 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression KMnO_4 | 4 | -4 | ([KMnO4])^(-4) HCHO | 3 | -3 | ([HCHO])^(-3) H_2O | 3 | 3 | ([H2O])^3 CO_2 | 1 | 1 | [CO2] MnO_2 | 4 | 4 | ([MnO2])^4 K_2CO_3 | 2 | 2 | ([K2CO3])^2 The equilibrium constant symbol in the concentration basis is: K_c Mulitply the activity expressions to arrive at the K_c expression: Answer: | | K_c = ([KMnO4])^(-4) ([HCHO])^(-3) ([H2O])^3 [CO2] ([MnO2])^4 ([K2CO3])^2 = (([H2O])^3 [CO2] ([MnO2])^4 ([K2CO3])^2)/(([KMnO4])^4 ([HCHO])^3)

Construct the rate of reaction expression for: KMnO_4 + HCHO ⟶ H_2O + CO_2 + MnO_2 + K_2CO_3 Plan: • Balance the chemical equation. • Determine the stoichiometric numbers. • Assemble the rate term for each chemical species. • Write the rate of reaction expression. Write the balanced chemical equation: 4 KMnO_4 + 3 HCHO ⟶ 3 H_2O + CO_2 + 4 MnO_2 + 2 K_2CO_3 Assign stoichiometric numbers, ν_i, using the stoichiometric coefficients, c_i, from the balanced chemical equation in the following manner: ν_i = -c_i for reactants and ν_i = c_i for products: chemical species | c_i | ν_i KMnO_4 | 4 | -4 HCHO | 3 | -3 H_2O | 3 | 3 CO_2 | 1 | 1 MnO_2 | 4 | 4 K_2CO_3 | 2 | 2 The rate term for each chemical species, B_i, is 1/ν_i(Δ[B_i])/(Δt) where [B_i] is the amount concentration and t is time: chemical species | c_i | ν_i | rate term KMnO_4 | 4 | -4 | -1/4 (Δ[KMnO4])/(Δt) HCHO | 3 | -3 | -1/3 (Δ[HCHO])/(Δt) H_2O | 3 | 3 | 1/3 (Δ[H2O])/(Δt) CO_2 | 1 | 1 | (Δ[CO2])/(Δt) MnO_2 | 4 | 4 | 1/4 (Δ[MnO2])/(Δt) K_2CO_3 | 2 | 2 | 1/2 (Δ[K2CO3])/(Δt) (for infinitesimal rate of change, replace Δ with d) Set the rate terms equal to each other to arrive at the rate expression: Answer: | | rate = -1/4 (Δ[KMnO4])/(Δt) = -1/3 (Δ[HCHO])/(Δt) = 1/3 (Δ[H2O])/(Δt) = (Δ[CO2])/(Δt) = 1/4 (Δ[MnO2])/(Δt) = 1/2 (Δ[K2CO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| potassium permanganate | formaldehyde | water | carbon dioxide | manganese dioxide | pearl ash formula | KMnO_4 | HCHO | H_2O | CO_2 | MnO_2 | K_2CO_3 Hill formula | KMnO_4 | CH_2O | H_2O | CO_2 | MnO_2 | CK_2O_3 name | potassium permanganate | formaldehyde | water | carbon dioxide | manganese dioxide | pearl ash IUPAC name | potassium permanganate | formaldehyde | water | carbon dioxide | dioxomanganese | dipotassium carbonate