KOH + KMnO4 + CH3COH = H2O + K2MnO4 + CH3COOK

KOH potassium hydroxide + KMnO_4 potassium permanganate + CH_3CHO acetaldehyde ⟶ H_2O water + K_2MnO_4 potassium manganate + CH_3COOK potassium acetate

Balance the chemical equation algebraically: KOH + KMnO_4 + CH_3CHO ⟶ H_2O + K_2MnO_4 + CH_3COOK Add stoichiometric coefficients, c_i, to the reactants and products: c_1 KOH + c_2 KMnO_4 + c_3 CH_3CHO ⟶ c_4 H_2O + c_5 K_2MnO_4 + c_6 CH_3COOK Set the number of atoms in the reactants equal to the number of atoms in the products for H, K, O, Mn and C: H: | c_1 + 4 c_3 = 2 c_4 + 3 c_6 K: | c_1 + c_2 = 2 c_5 + c_6 O: | c_1 + 4 c_2 + c_3 = c_4 + 4 c_5 + 2 c_6 Mn: | c_2 = c_5 C: | 2 c_3 = 2 c_6 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3 c_2 = 2 c_3 = 1 c_4 = 2 c_5 = 2 c_6 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 KOH + 2 KMnO_4 + CH_3CHO ⟶ 2 H_2O + 2 K_2MnO_4 + CH_3COOK

+ + ⟶ + +

potassium hydroxide + potassium permanganate + acetaldehyde ⟶ water + potassium manganate + potassium acetate

Construct the equilibrium constant, K, expression for: KOH + KMnO_4 + CH_3CHO ⟶ H_2O + K_2MnO_4 + CH_3COOK 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: 3 KOH + 2 KMnO_4 + CH_3CHO ⟶ 2 H_2O + 2 K_2MnO_4 + CH_3COOK 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 KOH | 3 | -3 KMnO_4 | 2 | -2 CH_3CHO | 1 | -1 H_2O | 2 | 2 K_2MnO_4 | 2 | 2 CH_3COOK | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression KOH | 3 | -3 | ([KOH])^(-3) KMnO_4 | 2 | -2 | ([KMnO4])^(-2) CH_3CHO | 1 | -1 | ([CH3CHO])^(-1) H_2O | 2 | 2 | ([H2O])^2 K_2MnO_4 | 2 | 2 | ([K2MnO4])^2 CH_3COOK | 1 | 1 | [CH3COOK] 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 = ([KOH])^(-3) ([KMnO4])^(-2) ([CH3CHO])^(-1) ([H2O])^2 ([K2MnO4])^2 [CH3COOK] = (([H2O])^2 ([K2MnO4])^2 [CH3COOK])/(([KOH])^3 ([KMnO4])^2 [CH3CHO])

Construct the rate of reaction expression for: KOH + KMnO_4 + CH_3CHO ⟶ H_2O + K_2MnO_4 + CH_3COOK 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: 3 KOH + 2 KMnO_4 + CH_3CHO ⟶ 2 H_2O + 2 K_2MnO_4 + CH_3COOK 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 KOH | 3 | -3 KMnO_4 | 2 | -2 CH_3CHO | 1 | -1 H_2O | 2 | 2 K_2MnO_4 | 2 | 2 CH_3COOK | 1 | 1 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 KOH | 3 | -3 | -1/3 (Δ[KOH])/(Δt) KMnO_4 | 2 | -2 | -1/2 (Δ[KMnO4])/(Δt) CH_3CHO | 1 | -1 | -(Δ[CH3CHO])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(Δt) K_2MnO_4 | 2 | 2 | 1/2 (Δ[K2MnO4])/(Δt) CH_3COOK | 1 | 1 | (Δ[CH3COOK])/(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 = -1/3 (Δ[KOH])/(Δt) = -1/2 (Δ[KMnO4])/(Δt) = -(Δ[CH3CHO])/(Δt) = 1/2 (Δ[H2O])/(Δt) = 1/2 (Δ[K2MnO4])/(Δt) = (Δ[CH3COOK])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| potassium hydroxide | potassium permanganate | acetaldehyde | water | potassium manganate | potassium acetate formula | KOH | KMnO_4 | CH_3CHO | H_2O | K_2MnO_4 | CH_3COOK Hill formula | HKO | KMnO_4 | C_2H_4O | H_2O | K_2MnO_4 | C_2H_3KO_2 name | potassium hydroxide | potassium permanganate | acetaldehyde | water | potassium manganate | potassium acetate IUPAC name | potassium hydroxide | potassium permanganate | acetaldehyde | water | dipotassium dioxido-dioxomanganese | potassium acetate

| potassium hydroxide | potassium permanganate | acetaldehyde | water | potassium manganate | potassium acetate molar mass | 56.105 g/mol | 158.03 g/mol | 44.053 g/mol | 18.015 g/mol | 197.13 g/mol | 98.142 g/mol phase | solid (at STP) | solid (at STP) | gas (at STP) | liquid (at STP) | solid (at STP) | solid (at STP) melting point | 406 °C | 240 °C | -123 °C | 0 °C | 190 °C | 304 °C boiling point | 1327 °C | | 20.1 °C | 99.9839 °C | | density | 2.044 g/cm^3 | 1 g/cm^3 | 0.784 g/cm^3 (at 20 °C) | 1 g/cm^3 | | 1.57 g/cm^3 solubility in water | soluble | | miscible | | decomposes | surface tension | | | 0.0212 N/m | 0.0728 N/m | | 0.0256 N/m dynamic viscosity | 0.001 Pa s (at 550 °C) | | 2.456×10^-4 Pa s (at 15 °C) | 8.9×10^-4 Pa s (at 25 °C) | | odor | | odorless | | odorless | |