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KMnO4 + CH2O = H2O + CO2 + K2CO3 + Mn

Input interpretation

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

Balanced equation

Balance the chemical equation algebraically: KMnO_4 + HCHO ⟶ H_2O + CO_2 + K_2CO_3 + Mn 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 K_2CO_3 + c_6 Mn 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_5 Mn: | c_1 = c_6 O: | 4 c_1 + c_2 = c_3 + 2 c_4 + 3 c_5 C: | c_2 = c_4 + c_5 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_5 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 7/2 c_3 = 7/2 c_4 = 5/2 c_5 = 1 c_6 = 2 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 4 c_2 = 7 c_3 = 7 c_4 = 5 c_5 = 2 c_6 = 4 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 KMnO_4 + 7 HCHO ⟶ 7 H_2O + 5 CO_2 + 2 K_2CO_3 + 4 Mn
Balance the chemical equation algebraically: KMnO_4 + HCHO ⟶ H_2O + CO_2 + K_2CO_3 + Mn 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 K_2CO_3 + c_6 Mn 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_5 Mn: | c_1 = c_6 O: | 4 c_1 + c_2 = c_3 + 2 c_4 + 3 c_5 C: | c_2 = c_4 + c_5 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_5 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 7/2 c_3 = 7/2 c_4 = 5/2 c_5 = 1 c_6 = 2 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 4 c_2 = 7 c_3 = 7 c_4 = 5 c_5 = 2 c_6 = 4 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 KMnO_4 + 7 HCHO ⟶ 7 H_2O + 5 CO_2 + 2 K_2CO_3 + 4 Mn

Structures

+ ⟶ + + +
+ ⟶ + + +

Names

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

Equilibrium constant

Construct the equilibrium constant, K, expression for: KMnO_4 + HCHO ⟶ H_2O + CO_2 + K_2CO_3 + Mn 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 + 7 HCHO ⟶ 7 H_2O + 5 CO_2 + 2 K_2CO_3 + 4 Mn 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 | 7 | -7 H_2O | 7 | 7 CO_2 | 5 | 5 K_2CO_3 | 2 | 2 Mn | 4 | 4 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 | 7 | -7 | ([HCHO])^(-7) H_2O | 7 | 7 | ([H2O])^7 CO_2 | 5 | 5 | ([CO2])^5 K_2CO_3 | 2 | 2 | ([K2CO3])^2 Mn | 4 | 4 | ([Mn])^4 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])^(-7) ([H2O])^7 ([CO2])^5 ([K2CO3])^2 ([Mn])^4 = (([H2O])^7 ([CO2])^5 ([K2CO3])^2 ([Mn])^4)/(([KMnO4])^4 ([HCHO])^7)
Construct the equilibrium constant, K, expression for: KMnO_4 + HCHO ⟶ H_2O + CO_2 + K_2CO_3 + Mn 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 + 7 HCHO ⟶ 7 H_2O + 5 CO_2 + 2 K_2CO_3 + 4 Mn 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 | 7 | -7 H_2O | 7 | 7 CO_2 | 5 | 5 K_2CO_3 | 2 | 2 Mn | 4 | 4 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 | 7 | -7 | ([HCHO])^(-7) H_2O | 7 | 7 | ([H2O])^7 CO_2 | 5 | 5 | ([CO2])^5 K_2CO_3 | 2 | 2 | ([K2CO3])^2 Mn | 4 | 4 | ([Mn])^4 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])^(-7) ([H2O])^7 ([CO2])^5 ([K2CO3])^2 ([Mn])^4 = (([H2O])^7 ([CO2])^5 ([K2CO3])^2 ([Mn])^4)/(([KMnO4])^4 ([HCHO])^7)

Rate of reaction

Construct the rate of reaction expression for: KMnO_4 + HCHO ⟶ H_2O + CO_2 + K_2CO_3 + Mn 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 + 7 HCHO ⟶ 7 H_2O + 5 CO_2 + 2 K_2CO_3 + 4 Mn 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 | 7 | -7 H_2O | 7 | 7 CO_2 | 5 | 5 K_2CO_3 | 2 | 2 Mn | 4 | 4 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 | 7 | -7 | -1/7 (Δ[HCHO])/(Δt) H_2O | 7 | 7 | 1/7 (Δ[H2O])/(Δt) CO_2 | 5 | 5 | 1/5 (Δ[CO2])/(Δt) K_2CO_3 | 2 | 2 | 1/2 (Δ[K2CO3])/(Δt) Mn | 4 | 4 | 1/4 (Δ[Mn])/(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) = -1/7 (Δ[HCHO])/(Δt) = 1/7 (Δ[H2O])/(Δt) = 1/5 (Δ[CO2])/(Δt) = 1/2 (Δ[K2CO3])/(Δt) = 1/4 (Δ[Mn])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: KMnO_4 + HCHO ⟶ H_2O + CO_2 + K_2CO_3 + Mn 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 + 7 HCHO ⟶ 7 H_2O + 5 CO_2 + 2 K_2CO_3 + 4 Mn 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 | 7 | -7 H_2O | 7 | 7 CO_2 | 5 | 5 K_2CO_3 | 2 | 2 Mn | 4 | 4 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 | 7 | -7 | -1/7 (Δ[HCHO])/(Δt) H_2O | 7 | 7 | 1/7 (Δ[H2O])/(Δt) CO_2 | 5 | 5 | 1/5 (Δ[CO2])/(Δt) K_2CO_3 | 2 | 2 | 1/2 (Δ[K2CO3])/(Δt) Mn | 4 | 4 | 1/4 (Δ[Mn])/(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) = -1/7 (Δ[HCHO])/(Δt) = 1/7 (Δ[H2O])/(Δt) = 1/5 (Δ[CO2])/(Δt) = 1/2 (Δ[K2CO3])/(Δt) = 1/4 (Δ[Mn])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

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

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