KMnO4 + K2S = S + K2MnO4

KMnO_4 potassium permanganate + K2S ⟶ S mixed sulfur + K_2MnO_4 potassium manganate

Balance the chemical equation algebraically: KMnO_4 + K2S ⟶ S + K_2MnO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 KMnO_4 + c_2 K2S ⟶ c_3 S + c_4 K_2MnO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for K, Mn, O and S: K: | c_1 + 2 c_2 = 2 c_4 Mn: | c_1 = c_4 O: | 4 c_1 = 4 c_4 S: | c_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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 1 c_3 = 1 c_4 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 KMnO_4 + K2S ⟶ S + 2 K_2MnO_4

+ K2S ⟶ +

potassium permanganate + K2S ⟶ mixed sulfur + potassium manganate

Construct the equilibrium constant, K, expression for: KMnO_4 + K2S ⟶ S + 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: 2 KMnO_4 + K2S ⟶ S + 2 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 KMnO_4 | 2 | -2 K2S | 1 | -1 S | 1 | 1 K_2MnO_4 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression KMnO_4 | 2 | -2 | ([KMnO4])^(-2) K2S | 1 | -1 | ([K2S])^(-1) S | 1 | 1 | [S] K_2MnO_4 | 2 | 2 | ([K2MnO4])^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 = ([KMnO4])^(-2) ([K2S])^(-1) [S] ([K2MnO4])^2 = ([S] ([K2MnO4])^2)/(([KMnO4])^2 [K2S])

Construct the rate of reaction expression for: KMnO_4 + K2S ⟶ S + 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: 2 KMnO_4 + K2S ⟶ S + 2 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 KMnO_4 | 2 | -2 K2S | 1 | -1 S | 1 | 1 K_2MnO_4 | 2 | 2 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 | 2 | -2 | -1/2 (Δ[KMnO4])/(Δt) K2S | 1 | -1 | -(Δ[K2S])/(Δt) S | 1 | 1 | (Δ[S])/(Δt) K_2MnO_4 | 2 | 2 | 1/2 (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 = -1/2 (Δ[KMnO4])/(Δt) = -(Δ[K2S])/(Δt) = (Δ[S])/(Δt) = 1/2 (Δ[K2MnO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| potassium permanganate | K2S | mixed sulfur | potassium manganate formula | KMnO_4 | K2S | S | K_2MnO_4 name | potassium permanganate | | mixed sulfur | potassium manganate IUPAC name | potassium permanganate | | sulfur | dipotassium dioxido-dioxomanganese

| potassium permanganate | K2S | mixed sulfur | potassium manganate molar mass | 158.03 g/mol | 110.26 g/mol | 32.06 g/mol | 197.13 g/mol phase | solid (at STP) | | solid (at STP) | solid (at STP) melting point | 240 °C | | 112.8 °C | 190 °C boiling point | | | 444.7 °C | density | 1 g/cm^3 | | 2.07 g/cm^3 | solubility in water | | | | decomposes odor | odorless | | |