MnSO4 + K2MnO4 = K2SO4 + MnO2

MnSO_4 manganese(II) sulfate + K_2MnO_4 potassium manganate ⟶ K_2SO_4 potassium sulfate + MnO_2 manganese dioxide

Balance the chemical equation algebraically: MnSO_4 + K_2MnO_4 ⟶ K_2SO_4 + MnO_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 MnSO_4 + c_2 K_2MnO_4 ⟶ c_3 K_2SO_4 + c_4 MnO_2 Set the number of atoms in the reactants equal to the number of atoms in the products for Mn, O, S and K: Mn: | c_1 + c_2 = c_4 O: | 4 c_1 + 4 c_2 = 4 c_3 + 2 c_4 S: | c_1 = c_3 K: | 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 1 c_3 = 1 c_4 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | MnSO_4 + K_2MnO_4 ⟶ K_2SO_4 + 2 MnO_2

+ ⟶ +

manganese(II) sulfate + potassium manganate ⟶ potassium sulfate + manganese dioxide

Construct the equilibrium constant, K, expression for: MnSO_4 + K_2MnO_4 ⟶ K_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: MnSO_4 + K_2MnO_4 ⟶ K_2SO_4 + 2 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 MnSO_4 | 1 | -1 K_2MnO_4 | 1 | -1 K_2SO_4 | 1 | 1 MnO_2 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression MnSO_4 | 1 | -1 | ([MnSO4])^(-1) K_2MnO_4 | 1 | -1 | ([K2MnO4])^(-1) K_2SO_4 | 1 | 1 | [K2SO4] MnO_2 | 2 | 2 | ([MnO2])^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 = ([MnSO4])^(-1) ([K2MnO4])^(-1) [K2SO4] ([MnO2])^2 = ([K2SO4] ([MnO2])^2)/([MnSO4] [K2MnO4])

Construct the rate of reaction expression for: MnSO_4 + K_2MnO_4 ⟶ K_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: MnSO_4 + K_2MnO_4 ⟶ K_2SO_4 + 2 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 MnSO_4 | 1 | -1 K_2MnO_4 | 1 | -1 K_2SO_4 | 1 | 1 MnO_2 | 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 MnSO_4 | 1 | -1 | -(Δ[MnSO4])/(Δt) K_2MnO_4 | 1 | -1 | -(Δ[K2MnO4])/(Δt) K_2SO_4 | 1 | 1 | (Δ[K2SO4])/(Δt) MnO_2 | 2 | 2 | 1/2 (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[MnSO4])/(Δt) = -(Δ[K2MnO4])/(Δt) = (Δ[K2SO4])/(Δt) = 1/2 (Δ[MnO2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| manganese(II) sulfate | potassium manganate | potassium sulfate | manganese dioxide formula | MnSO_4 | K_2MnO_4 | K_2SO_4 | MnO_2 Hill formula | MnSO_4 | K_2MnO_4 | K_2O_4S | MnO_2 name | manganese(II) sulfate | potassium manganate | potassium sulfate | manganese dioxide IUPAC name | manganese(+2) cation sulfate | dipotassium dioxido-dioxomanganese | dipotassium sulfate | dioxomanganese

| manganese(II) sulfate | potassium manganate | potassium sulfate | manganese dioxide molar mass | 150.99 g/mol | 197.13 g/mol | 174.25 g/mol | 86.936 g/mol phase | solid (at STP) | solid (at STP) | | solid (at STP) melting point | 710 °C | 190 °C | | 535 °C density | 3.25 g/cm^3 | | | 5.03 g/cm^3 solubility in water | soluble | decomposes | soluble | insoluble