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K2MnO4 + H2C2O4 = H2O + CO2 + K2O + Mn2O3

Input interpretation

K_2MnO_4 potassium manganate + HO_2CCO_2H oxalic acid ⟶ H_2O water + CO_2 carbon dioxide + K_2O potassium oxide + Mn_2O_3 manganese(III) oxide
K_2MnO_4 potassium manganate + HO_2CCO_2H oxalic acid ⟶ H_2O water + CO_2 carbon dioxide + K_2O potassium oxide + Mn_2O_3 manganese(III) oxide

Balanced equation

Balance the chemical equation algebraically: K_2MnO_4 + HO_2CCO_2H ⟶ H_2O + CO_2 + K_2O + Mn_2O_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 K_2MnO_4 + c_2 HO_2CCO_2H ⟶ c_3 H_2O + c_4 CO_2 + c_5 K_2O + c_6 Mn_2O_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: | 2 c_1 = 2 c_5 Mn: | c_1 = 2 c_6 O: | 4 c_1 + 4 c_2 = c_3 + 2 c_4 + c_5 + 3 c_6 C: | 2 c_2 = c_4 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_6 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 3 c_3 = 3 c_4 = 6 c_5 = 2 c_6 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 K_2MnO_4 + 3 HO_2CCO_2H ⟶ 3 H_2O + 6 CO_2 + 2 K_2O + Mn_2O_3
Balance the chemical equation algebraically: K_2MnO_4 + HO_2CCO_2H ⟶ H_2O + CO_2 + K_2O + Mn_2O_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 K_2MnO_4 + c_2 HO_2CCO_2H ⟶ c_3 H_2O + c_4 CO_2 + c_5 K_2O + c_6 Mn_2O_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: | 2 c_1 = 2 c_5 Mn: | c_1 = 2 c_6 O: | 4 c_1 + 4 c_2 = c_3 + 2 c_4 + c_5 + 3 c_6 C: | 2 c_2 = c_4 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_6 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 3 c_3 = 3 c_4 = 6 c_5 = 2 c_6 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 K_2MnO_4 + 3 HO_2CCO_2H ⟶ 3 H_2O + 6 CO_2 + 2 K_2O + Mn_2O_3

Structures

+ ⟶ + + +
+ ⟶ + + +

Names

potassium manganate + oxalic acid ⟶ water + carbon dioxide + potassium oxide + manganese(III) oxide
potassium manganate + oxalic acid ⟶ water + carbon dioxide + potassium oxide + manganese(III) oxide

Equilibrium constant

Construct the equilibrium constant, K, expression for: K_2MnO_4 + HO_2CCO_2H ⟶ H_2O + CO_2 + K_2O + Mn_2O_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: 2 K_2MnO_4 + 3 HO_2CCO_2H ⟶ 3 H_2O + 6 CO_2 + 2 K_2O + Mn_2O_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 K_2MnO_4 | 2 | -2 HO_2CCO_2H | 3 | -3 H_2O | 3 | 3 CO_2 | 6 | 6 K_2O | 2 | 2 Mn_2O_3 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression K_2MnO_4 | 2 | -2 | ([K2MnO4])^(-2) HO_2CCO_2H | 3 | -3 | ([HO2CCO2H])^(-3) H_2O | 3 | 3 | ([H2O])^3 CO_2 | 6 | 6 | ([CO2])^6 K_2O | 2 | 2 | ([K2O])^2 Mn_2O_3 | 1 | 1 | [Mn2O3] 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 = ([K2MnO4])^(-2) ([HO2CCO2H])^(-3) ([H2O])^3 ([CO2])^6 ([K2O])^2 [Mn2O3] = (([H2O])^3 ([CO2])^6 ([K2O])^2 [Mn2O3])/(([K2MnO4])^2 ([HO2CCO2H])^3)
Construct the equilibrium constant, K, expression for: K_2MnO_4 + HO_2CCO_2H ⟶ H_2O + CO_2 + K_2O + Mn_2O_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: 2 K_2MnO_4 + 3 HO_2CCO_2H ⟶ 3 H_2O + 6 CO_2 + 2 K_2O + Mn_2O_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 K_2MnO_4 | 2 | -2 HO_2CCO_2H | 3 | -3 H_2O | 3 | 3 CO_2 | 6 | 6 K_2O | 2 | 2 Mn_2O_3 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression K_2MnO_4 | 2 | -2 | ([K2MnO4])^(-2) HO_2CCO_2H | 3 | -3 | ([HO2CCO2H])^(-3) H_2O | 3 | 3 | ([H2O])^3 CO_2 | 6 | 6 | ([CO2])^6 K_2O | 2 | 2 | ([K2O])^2 Mn_2O_3 | 1 | 1 | [Mn2O3] 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 = ([K2MnO4])^(-2) ([HO2CCO2H])^(-3) ([H2O])^3 ([CO2])^6 ([K2O])^2 [Mn2O3] = (([H2O])^3 ([CO2])^6 ([K2O])^2 [Mn2O3])/(([K2MnO4])^2 ([HO2CCO2H])^3)

Rate of reaction

Construct the rate of reaction expression for: K_2MnO_4 + HO_2CCO_2H ⟶ H_2O + CO_2 + K_2O + Mn_2O_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: 2 K_2MnO_4 + 3 HO_2CCO_2H ⟶ 3 H_2O + 6 CO_2 + 2 K_2O + Mn_2O_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 K_2MnO_4 | 2 | -2 HO_2CCO_2H | 3 | -3 H_2O | 3 | 3 CO_2 | 6 | 6 K_2O | 2 | 2 Mn_2O_3 | 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 K_2MnO_4 | 2 | -2 | -1/2 (Δ[K2MnO4])/(Δt) HO_2CCO_2H | 3 | -3 | -1/3 (Δ[HO2CCO2H])/(Δt) H_2O | 3 | 3 | 1/3 (Δ[H2O])/(Δt) CO_2 | 6 | 6 | 1/6 (Δ[CO2])/(Δt) K_2O | 2 | 2 | 1/2 (Δ[K2O])/(Δt) Mn_2O_3 | 1 | 1 | (Δ[Mn2O3])/(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 = -1/2 (Δ[K2MnO4])/(Δt) = -1/3 (Δ[HO2CCO2H])/(Δt) = 1/3 (Δ[H2O])/(Δt) = 1/6 (Δ[CO2])/(Δt) = 1/2 (Δ[K2O])/(Δt) = (Δ[Mn2O3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: K_2MnO_4 + HO_2CCO_2H ⟶ H_2O + CO_2 + K_2O + Mn_2O_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: 2 K_2MnO_4 + 3 HO_2CCO_2H ⟶ 3 H_2O + 6 CO_2 + 2 K_2O + Mn_2O_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 K_2MnO_4 | 2 | -2 HO_2CCO_2H | 3 | -3 H_2O | 3 | 3 CO_2 | 6 | 6 K_2O | 2 | 2 Mn_2O_3 | 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 K_2MnO_4 | 2 | -2 | -1/2 (Δ[K2MnO4])/(Δt) HO_2CCO_2H | 3 | -3 | -1/3 (Δ[HO2CCO2H])/(Δt) H_2O | 3 | 3 | 1/3 (Δ[H2O])/(Δt) CO_2 | 6 | 6 | 1/6 (Δ[CO2])/(Δt) K_2O | 2 | 2 | 1/2 (Δ[K2O])/(Δt) Mn_2O_3 | 1 | 1 | (Δ[Mn2O3])/(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 = -1/2 (Δ[K2MnO4])/(Δt) = -1/3 (Δ[HO2CCO2H])/(Δt) = 1/3 (Δ[H2O])/(Δt) = 1/6 (Δ[CO2])/(Δt) = 1/2 (Δ[K2O])/(Δt) = (Δ[Mn2O3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| potassium manganate | oxalic acid | water | carbon dioxide | potassium oxide | manganese(III) oxide formula | K_2MnO_4 | HO_2CCO_2H | H_2O | CO_2 | K_2O | Mn_2O_3 Hill formula | K_2MnO_4 | C_2H_2O_4 | H_2O | CO_2 | K_2O | Mn_2O_3 name | potassium manganate | oxalic acid | water | carbon dioxide | potassium oxide | manganese(III) oxide IUPAC name | dipotassium dioxido-dioxomanganese | oxalic acid | water | carbon dioxide | dipotassium oxygen(2-) | oxo-(oxomanganiooxy)manganese
| potassium manganate | oxalic acid | water | carbon dioxide | potassium oxide | manganese(III) oxide formula | K_2MnO_4 | HO_2CCO_2H | H_2O | CO_2 | K_2O | Mn_2O_3 Hill formula | K_2MnO_4 | C_2H_2O_4 | H_2O | CO_2 | K_2O | Mn_2O_3 name | potassium manganate | oxalic acid | water | carbon dioxide | potassium oxide | manganese(III) oxide IUPAC name | dipotassium dioxido-dioxomanganese | oxalic acid | water | carbon dioxide | dipotassium oxygen(2-) | oxo-(oxomanganiooxy)manganese

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