H2S + H2MnO4 = H2O + H2SO4 + MnO2

H_2S hydrogen sulfide + H2MnO4 ⟶ H_2O water + H_2SO_4 sulfuric acid + MnO_2 manganese dioxide

Balance the chemical equation algebraically: H_2S + H2MnO4 ⟶ H_2O + H_2SO_4 + MnO_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2S + c_2 H2MnO4 ⟶ c_3 H_2O + c_4 H_2SO_4 + c_5 MnO_2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, S, Mn and O: H: | 2 c_1 + 2 c_2 = 2 c_3 + 2 c_4 S: | c_1 = c_4 Mn: | c_2 = c_5 O: | 4 c_2 = c_3 + 4 c_4 + 2 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 4 c_3 = 4 c_4 = 1 c_5 = 4 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | H_2S + 4 H2MnO4 ⟶ 4 H_2O + H_2SO_4 + 4 MnO_2

+ H2MnO4 ⟶ + +

hydrogen sulfide + H2MnO4 ⟶ water + sulfuric acid + manganese dioxide

Construct the equilibrium constant, K, expression for: H_2S + H2MnO4 ⟶ H_2O + H_2SO_4 + MnO_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: H_2S + 4 H2MnO4 ⟶ 4 H_2O + H_2SO_4 + 4 MnO_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_2S | 1 | -1 H2MnO4 | 4 | -4 H_2O | 4 | 4 H_2SO_4 | 1 | 1 MnO_2 | 4 | 4 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2S | 1 | -1 | ([H2S])^(-1) H2MnO4 | 4 | -4 | ([H2MnO4])^(-4) H_2O | 4 | 4 | ([H2O])^4 H_2SO_4 | 1 | 1 | [H2SO4] MnO_2 | 4 | 4 | ([MnO2])^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 = ([H2S])^(-1) ([H2MnO4])^(-4) ([H2O])^4 [H2SO4] ([MnO2])^4 = (([H2O])^4 [H2SO4] ([MnO2])^4)/([H2S] ([H2MnO4])^4)

Construct the rate of reaction expression for: H_2S + H2MnO4 ⟶ H_2O + H_2SO_4 + MnO_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: H_2S + 4 H2MnO4 ⟶ 4 H_2O + H_2SO_4 + 4 MnO_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_2S | 1 | -1 H2MnO4 | 4 | -4 H_2O | 4 | 4 H_2SO_4 | 1 | 1 MnO_2 | 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 H_2S | 1 | -1 | -(Δ[H2S])/(Δt) H2MnO4 | 4 | -4 | -1/4 (Δ[H2MnO4])/(Δt) H_2O | 4 | 4 | 1/4 (Δ[H2O])/(Δt) H_2SO_4 | 1 | 1 | (Δ[H2SO4])/(Δt) MnO_2 | 4 | 4 | 1/4 (Δ[MnO2])/(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 = -(Δ[H2S])/(Δt) = -1/4 (Δ[H2MnO4])/(Δt) = 1/4 (Δ[H2O])/(Δt) = (Δ[H2SO4])/(Δt) = 1/4 (Δ[MnO2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| hydrogen sulfide | H2MnO4 | water | sulfuric acid | manganese dioxide formula | H_2S | H2MnO4 | H_2O | H_2SO_4 | MnO_2 Hill formula | H_2S | H2MnO4 | H_2O | H_2O_4S | MnO_2 name | hydrogen sulfide | | water | sulfuric acid | manganese dioxide IUPAC name | hydrogen sulfide | | water | sulfuric acid | dioxomanganese

| hydrogen sulfide | H2MnO4 | water | sulfuric acid | manganese dioxide molar mass | 34.08 g/mol | 120.95 g/mol | 18.015 g/mol | 98.07 g/mol | 86.936 g/mol phase | gas (at STP) | | liquid (at STP) | liquid (at STP) | solid (at STP) melting point | -85 °C | | 0 °C | 10.371 °C | 535 °C boiling point | -60 °C | | 99.9839 °C | 279.6 °C | density | 0.001393 g/cm^3 (at 25 °C) | | 1 g/cm^3 | 1.8305 g/cm^3 | 5.03 g/cm^3 solubility in water | | | | very soluble | insoluble surface tension | | | 0.0728 N/m | 0.0735 N/m | dynamic viscosity | 1.239×10^-5 Pa s (at 25 °C) | | 8.9×10^-4 Pa s (at 25 °C) | 0.021 Pa s (at 25 °C) | odor | | | odorless | odorless |