KOH + KMnO4 + K2S = H2O + K2SO4 + K2MnO4

KOH potassium hydroxide + KMnO_4 potassium permanganate + K2S ⟶ H_2O water + K_2SO_4 potassium sulfate + K_2MnO_4 potassium manganate

Balance the chemical equation algebraically: KOH + KMnO_4 + K2S ⟶ H_2O + K_2SO_4 + K_2MnO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 KOH + c_2 KMnO_4 + c_3 K2S ⟶ c_4 H_2O + c_5 K_2SO_4 + c_6 K_2MnO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, K, O, Mn and S: H: | c_1 = 2 c_4 K: | c_1 + c_2 + 2 c_3 = 2 c_5 + 2 c_6 O: | c_1 + 4 c_2 = c_4 + 4 c_5 + 4 c_6 Mn: | c_2 = c_6 S: | c_3 = c_5 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 = 8 c_2 = 8 c_3 = 1 c_4 = 4 c_5 = 1 c_6 = 8 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 8 KOH + 8 KMnO_4 + K2S ⟶ 4 H_2O + K_2SO_4 + 8 K_2MnO_4

+ + K2S ⟶ + +

potassium hydroxide + potassium permanganate + K2S ⟶ water + potassium sulfate + potassium manganate

Construct the equilibrium constant, K, expression for: KOH + KMnO_4 + K2S ⟶ H_2O + K_2SO_4 + K_2MnO_4 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: 8 KOH + 8 KMnO_4 + K2S ⟶ 4 H_2O + K_2SO_4 + 8 K_2MnO_4 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 | 8 | -8 KMnO_4 | 8 | -8 K2S | 1 | -1 H_2O | 4 | 4 K_2SO_4 | 1 | 1 K_2MnO_4 | 8 | 8 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression KOH | 8 | -8 | ([KOH])^(-8) KMnO_4 | 8 | -8 | ([KMnO4])^(-8) K2S | 1 | -1 | ([K2S])^(-1) H_2O | 4 | 4 | ([H2O])^4 K_2SO_4 | 1 | 1 | [K2SO4] K_2MnO_4 | 8 | 8 | ([K2MnO4])^8 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])^(-8) ([KMnO4])^(-8) ([K2S])^(-1) ([H2O])^4 [K2SO4] ([K2MnO4])^8 = (([H2O])^4 [K2SO4] ([K2MnO4])^8)/(([KOH])^8 ([KMnO4])^8 [K2S])

Construct the rate of reaction expression for: KOH + KMnO_4 + K2S ⟶ H_2O + K_2SO_4 + K_2MnO_4 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: 8 KOH + 8 KMnO_4 + K2S ⟶ 4 H_2O + K_2SO_4 + 8 K_2MnO_4 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 | 8 | -8 KMnO_4 | 8 | -8 K2S | 1 | -1 H_2O | 4 | 4 K_2SO_4 | 1 | 1 K_2MnO_4 | 8 | 8 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 | 8 | -8 | -1/8 (Δ[KOH])/(Δt) KMnO_4 | 8 | -8 | -1/8 (Δ[KMnO4])/(Δt) K2S | 1 | -1 | -(Δ[K2S])/(Δt) H_2O | 4 | 4 | 1/4 (Δ[H2O])/(Δt) K_2SO_4 | 1 | 1 | (Δ[K2SO4])/(Δt) K_2MnO_4 | 8 | 8 | 1/8 (Δ[K2MnO4])/(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 = -1/8 (Δ[KOH])/(Δt) = -1/8 (Δ[KMnO4])/(Δt) = -(Δ[K2S])/(Δt) = 1/4 (Δ[H2O])/(Δt) = (Δ[K2SO4])/(Δt) = 1/8 (Δ[K2MnO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| potassium hydroxide | potassium permanganate | K2S | water | potassium sulfate | potassium manganate formula | KOH | KMnO_4 | K2S | H_2O | K_2SO_4 | K_2MnO_4 Hill formula | HKO | KMnO_4 | K2S | H_2O | K_2O_4S | K_2MnO_4 name | potassium hydroxide | potassium permanganate | | water | potassium sulfate | potassium manganate IUPAC name | potassium hydroxide | potassium permanganate | | water | dipotassium sulfate | dipotassium dioxido-dioxomanganese

| potassium hydroxide | potassium permanganate | K2S | water | potassium sulfate | potassium manganate molar mass | 56.105 g/mol | 158.03 g/mol | 110.26 g/mol | 18.015 g/mol | 174.25 g/mol | 197.13 g/mol phase | solid (at STP) | solid (at STP) | | liquid (at STP) | | solid (at STP) melting point | 406 °C | 240 °C | | 0 °C | | 190 °C boiling point | 1327 °C | | | 99.9839 °C | | density | 2.044 g/cm^3 | 1 g/cm^3 | | 1 g/cm^3 | | solubility in water | soluble | | | | soluble | decomposes surface tension | | | | 0.0728 N/m | | dynamic viscosity | 0.001 Pa s (at 550 °C) | | | 8.9×10^-4 Pa s (at 25 °C) | | odor | | odorless | | odorless | |