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H2O + K2MnO4 + K2S = S + KOH + MnO(OH)2

Input interpretation

H_2O water + K_2MnO_4 potassium manganate + K2S ⟶ S mixed sulfur + KOH potassium hydroxide + MnO(OH)2
H_2O water + K_2MnO_4 potassium manganate + K2S ⟶ S mixed sulfur + KOH potassium hydroxide + MnO(OH)2

Balanced equation

Balance the chemical equation algebraically: H_2O + K_2MnO_4 + K2S ⟶ S + KOH + MnO(OH)2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 K_2MnO_4 + c_3 K2S ⟶ c_4 S + c_5 KOH + c_6 MnO(OH)2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, K, Mn and S: H: | 2 c_1 = c_5 + 2 c_6 O: | c_1 + 4 c_2 = c_5 + 3 c_6 K: | 2 c_2 + 2 c_3 = c_5 Mn: | c_2 = c_6 S: | c_3 = c_4 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3 c_2 = 1 c_3 = 1 c_4 = 1 c_5 = 4 c_6 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 H_2O + K_2MnO_4 + K2S ⟶ S + 4 KOH + MnO(OH)2
Balance the chemical equation algebraically: H_2O + K_2MnO_4 + K2S ⟶ S + KOH + MnO(OH)2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 K_2MnO_4 + c_3 K2S ⟶ c_4 S + c_5 KOH + c_6 MnO(OH)2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, K, Mn and S: H: | 2 c_1 = c_5 + 2 c_6 O: | c_1 + 4 c_2 = c_5 + 3 c_6 K: | 2 c_2 + 2 c_3 = c_5 Mn: | c_2 = c_6 S: | c_3 = c_4 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3 c_2 = 1 c_3 = 1 c_4 = 1 c_5 = 4 c_6 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 H_2O + K_2MnO_4 + K2S ⟶ S + 4 KOH + MnO(OH)2

Structures

+ + K2S ⟶ + + MnO(OH)2
+ + K2S ⟶ + + MnO(OH)2

Names

water + potassium manganate + K2S ⟶ mixed sulfur + potassium hydroxide + MnO(OH)2
water + potassium manganate + K2S ⟶ mixed sulfur + potassium hydroxide + MnO(OH)2

Equilibrium constant

Construct the equilibrium constant, K, expression for: H_2O + K_2MnO_4 + K2S ⟶ S + KOH + MnO(OH)2 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 H_2O + K_2MnO_4 + K2S ⟶ S + 4 KOH + MnO(OH)2 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 H_2O | 3 | -3 K_2MnO_4 | 1 | -1 K2S | 1 | -1 S | 1 | 1 KOH | 4 | 4 MnO(OH)2 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 3 | -3 | ([H2O])^(-3) K_2MnO_4 | 1 | -1 | ([K2MnO4])^(-1) K2S | 1 | -1 | ([K2S])^(-1) S | 1 | 1 | [S] KOH | 4 | 4 | ([KOH])^4 MnO(OH)2 | 1 | 1 | [MnO(OH)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 = ([H2O])^(-3) ([K2MnO4])^(-1) ([K2S])^(-1) [S] ([KOH])^4 [MnO(OH)2] = ([S] ([KOH])^4 [MnO(OH)2])/(([H2O])^3 [K2MnO4] [K2S])
Construct the equilibrium constant, K, expression for: H_2O + K_2MnO_4 + K2S ⟶ S + KOH + MnO(OH)2 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 H_2O + K_2MnO_4 + K2S ⟶ S + 4 KOH + MnO(OH)2 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 H_2O | 3 | -3 K_2MnO_4 | 1 | -1 K2S | 1 | -1 S | 1 | 1 KOH | 4 | 4 MnO(OH)2 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 3 | -3 | ([H2O])^(-3) K_2MnO_4 | 1 | -1 | ([K2MnO4])^(-1) K2S | 1 | -1 | ([K2S])^(-1) S | 1 | 1 | [S] KOH | 4 | 4 | ([KOH])^4 MnO(OH)2 | 1 | 1 | [MnO(OH)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 = ([H2O])^(-3) ([K2MnO4])^(-1) ([K2S])^(-1) [S] ([KOH])^4 [MnO(OH)2] = ([S] ([KOH])^4 [MnO(OH)2])/(([H2O])^3 [K2MnO4] [K2S])

Rate of reaction

Construct the rate of reaction expression for: H_2O + K_2MnO_4 + K2S ⟶ S + KOH + MnO(OH)2 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 H_2O + K_2MnO_4 + K2S ⟶ S + 4 KOH + MnO(OH)2 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 H_2O | 3 | -3 K_2MnO_4 | 1 | -1 K2S | 1 | -1 S | 1 | 1 KOH | 4 | 4 MnO(OH)2 | 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 H_2O | 3 | -3 | -1/3 (Δ[H2O])/(Δt) K_2MnO_4 | 1 | -1 | -(Δ[K2MnO4])/(Δt) K2S | 1 | -1 | -(Δ[K2S])/(Δt) S | 1 | 1 | (Δ[S])/(Δt) KOH | 4 | 4 | 1/4 (Δ[KOH])/(Δt) MnO(OH)2 | 1 | 1 | (Δ[MnO(OH)2])/(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[H2O])/(Δt) = -(Δ[K2MnO4])/(Δt) = -(Δ[K2S])/(Δt) = (Δ[S])/(Δt) = 1/4 (Δ[KOH])/(Δt) = (Δ[MnO(OH)2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: H_2O + K_2MnO_4 + K2S ⟶ S + KOH + MnO(OH)2 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 H_2O + K_2MnO_4 + K2S ⟶ S + 4 KOH + MnO(OH)2 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 H_2O | 3 | -3 K_2MnO_4 | 1 | -1 K2S | 1 | -1 S | 1 | 1 KOH | 4 | 4 MnO(OH)2 | 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 H_2O | 3 | -3 | -1/3 (Δ[H2O])/(Δt) K_2MnO_4 | 1 | -1 | -(Δ[K2MnO4])/(Δt) K2S | 1 | -1 | -(Δ[K2S])/(Δt) S | 1 | 1 | (Δ[S])/(Δt) KOH | 4 | 4 | 1/4 (Δ[KOH])/(Δt) MnO(OH)2 | 1 | 1 | (Δ[MnO(OH)2])/(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[H2O])/(Δt) = -(Δ[K2MnO4])/(Δt) = -(Δ[K2S])/(Δt) = (Δ[S])/(Δt) = 1/4 (Δ[KOH])/(Δt) = (Δ[MnO(OH)2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| water | potassium manganate | K2S | mixed sulfur | potassium hydroxide | MnO(OH)2 formula | H_2O | K_2MnO_4 | K2S | S | KOH | MnO(OH)2 Hill formula | H_2O | K_2MnO_4 | K2S | S | HKO | H2MnO3 name | water | potassium manganate | | mixed sulfur | potassium hydroxide | IUPAC name | water | dipotassium dioxido-dioxomanganese | | sulfur | potassium hydroxide |
| water | potassium manganate | K2S | mixed sulfur | potassium hydroxide | MnO(OH)2 formula | H_2O | K_2MnO_4 | K2S | S | KOH | MnO(OH)2 Hill formula | H_2O | K_2MnO_4 | K2S | S | HKO | H2MnO3 name | water | potassium manganate | | mixed sulfur | potassium hydroxide | IUPAC name | water | dipotassium dioxido-dioxomanganese | | sulfur | potassium hydroxide |

Substance properties

| water | potassium manganate | K2S | mixed sulfur | potassium hydroxide | MnO(OH)2 molar mass | 18.015 g/mol | 197.13 g/mol | 110.26 g/mol | 32.06 g/mol | 56.105 g/mol | 104.95 g/mol phase | liquid (at STP) | solid (at STP) | | solid (at STP) | solid (at STP) | melting point | 0 °C | 190 °C | | 112.8 °C | 406 °C | boiling point | 99.9839 °C | | | 444.7 °C | 1327 °C | density | 1 g/cm^3 | | | 2.07 g/cm^3 | 2.044 g/cm^3 | solubility in water | | decomposes | | | soluble | surface tension | 0.0728 N/m | | | | | dynamic viscosity | 8.9×10^-4 Pa s (at 25 °C) | | | | 0.001 Pa s (at 550 °C) | odor | odorless | | | | |
| water | potassium manganate | K2S | mixed sulfur | potassium hydroxide | MnO(OH)2 molar mass | 18.015 g/mol | 197.13 g/mol | 110.26 g/mol | 32.06 g/mol | 56.105 g/mol | 104.95 g/mol phase | liquid (at STP) | solid (at STP) | | solid (at STP) | solid (at STP) | melting point | 0 °C | 190 °C | | 112.8 °C | 406 °C | boiling point | 99.9839 °C | | | 444.7 °C | 1327 °C | density | 1 g/cm^3 | | | 2.07 g/cm^3 | 2.044 g/cm^3 | solubility in water | | decomposes | | | soluble | surface tension | 0.0728 N/m | | | | | dynamic viscosity | 8.9×10^-4 Pa s (at 25 °C) | | | | 0.001 Pa s (at 550 °C) | odor | odorless | | | | |

Units

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