KBrO3 + Mn(OH)2 = H2O + MnO2 + KBr

KBrO_3 potassium bromate + Mn(OH)_2 manganese hydroxide ⟶ H_2O water + MnO_2 manganese dioxide + KBr potassium bromide

Balance the chemical equation algebraically: KBrO_3 + Mn(OH)_2 ⟶ H_2O + MnO_2 + KBr Add stoichiometric coefficients, c_i, to the reactants and products: c_1 KBrO_3 + c_2 Mn(OH)_2 ⟶ c_3 H_2O + c_4 MnO_2 + c_5 KBr Set the number of atoms in the reactants equal to the number of atoms in the products for Br, K, O, H and Mn: Br: | c_1 = c_5 K: | c_1 = c_5 O: | 3 c_1 + 2 c_2 = c_3 + 2 c_4 H: | 2 c_2 = 2 c_3 Mn: | c_2 = 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 3 c_3 = 3 c_4 = 3 c_5 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | KBrO_3 + 3 Mn(OH)_2 ⟶ 3 H_2O + 3 MnO_2 + KBr

+ ⟶ + +

potassium bromate + manganese hydroxide ⟶ water + manganese dioxide + potassium bromide

Construct the equilibrium constant, K, expression for: KBrO_3 + Mn(OH)_2 ⟶ H_2O + MnO_2 + KBr 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: KBrO_3 + 3 Mn(OH)_2 ⟶ 3 H_2O + 3 MnO_2 + KBr 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 KBrO_3 | 1 | -1 Mn(OH)_2 | 3 | -3 H_2O | 3 | 3 MnO_2 | 3 | 3 KBr | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression KBrO_3 | 1 | -1 | ([KBrO3])^(-1) Mn(OH)_2 | 3 | -3 | ([Mn(OH)2])^(-3) H_2O | 3 | 3 | ([H2O])^3 MnO_2 | 3 | 3 | ([MnO2])^3 KBr | 1 | 1 | [KBr] 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 = ([KBrO3])^(-1) ([Mn(OH)2])^(-3) ([H2O])^3 ([MnO2])^3 [KBr] = (([H2O])^3 ([MnO2])^3 [KBr])/([KBrO3] ([Mn(OH)2])^3)

Construct the rate of reaction expression for: KBrO_3 + Mn(OH)_2 ⟶ H_2O + MnO_2 + KBr 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: KBrO_3 + 3 Mn(OH)_2 ⟶ 3 H_2O + 3 MnO_2 + KBr 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 KBrO_3 | 1 | -1 Mn(OH)_2 | 3 | -3 H_2O | 3 | 3 MnO_2 | 3 | 3 KBr | 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 KBrO_3 | 1 | -1 | -(Δ[KBrO3])/(Δt) Mn(OH)_2 | 3 | -3 | -1/3 (Δ[Mn(OH)2])/(Δt) H_2O | 3 | 3 | 1/3 (Δ[H2O])/(Δt) MnO_2 | 3 | 3 | 1/3 (Δ[MnO2])/(Δt) KBr | 1 | 1 | (Δ[KBr])/(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[KBrO3])/(Δt) = -1/3 (Δ[Mn(OH)2])/(Δt) = 1/3 (Δ[H2O])/(Δt) = 1/3 (Δ[MnO2])/(Δt) = (Δ[KBr])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| potassium bromate | manganese hydroxide | water | manganese dioxide | potassium bromide formula | KBrO_3 | Mn(OH)_2 | H_2O | MnO_2 | KBr Hill formula | BrKO_3 | H_2MnO_2 | H_2O | MnO_2 | BrK name | potassium bromate | manganese hydroxide | water | manganese dioxide | potassium bromide IUPAC name | potassium bromate | manganous dihydroxide | water | dioxomanganese | potassium bromide

| potassium bromate | manganese hydroxide | water | manganese dioxide | potassium bromide molar mass | 167 g/mol | 88.952 g/mol | 18.015 g/mol | 86.936 g/mol | 119 g/mol phase | solid (at STP) | | liquid (at STP) | solid (at STP) | solid (at STP) melting point | 350 °C | | 0 °C | 535 °C | 734 °C boiling point | | | 99.9839 °C | | 1435 °C density | 3.218 g/cm^3 | | 1 g/cm^3 | 5.03 g/cm^3 | 2.75 g/cm^3 solubility in water | | | | insoluble | soluble surface tension | | | 0.0728 N/m | | dynamic viscosity | | | 8.9×10^-4 Pa s (at 25 °C) | | odor | | | odorless | |