KOH + MnSO4 + KBrO = H2O + K2SO4 + KMnO4 + KBr

KOH potassium hydroxide + MnSO_4 manganese(II) sulfate + KBrO ⟶ H_2O water + K_2SO_4 potassium sulfate + KMnO_4 potassium permanganate + KBr potassium bromide

Balance the chemical equation algebraically: KOH + MnSO_4 + KBrO ⟶ H_2O + K_2SO_4 + KMnO_4 + KBr Add stoichiometric coefficients, c_i, to the reactants and products: c_1 KOH + c_2 MnSO_4 + c_3 KBrO ⟶ c_4 H_2O + c_5 K_2SO_4 + c_6 KMnO_4 + c_7 KBr Set the number of atoms in the reactants equal to the number of atoms in the products for H, K, O, Mn, S and Br: H: | c_1 = 2 c_4 K: | c_1 + c_3 = 2 c_5 + c_6 + c_7 O: | c_1 + 4 c_2 + c_3 = c_4 + 4 c_5 + 4 c_6 Mn: | c_2 = c_6 S: | c_2 = c_5 Br: | c_3 = c_7 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 = 3 c_2 = 1 c_3 = 5/2 c_4 = 3/2 c_5 = 1 c_6 = 1 c_7 = 5/2 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 6 c_2 = 2 c_3 = 5 c_4 = 3 c_5 = 2 c_6 = 2 c_7 = 5 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 6 KOH + 2 MnSO_4 + 5 KBrO ⟶ 3 H_2O + 2 K_2SO_4 + 2 KMnO_4 + 5 KBr

+ + KBrO ⟶ + + +

potassium hydroxide + manganese(II) sulfate + KBrO ⟶ water + potassium sulfate + potassium permanganate + potassium bromide

Construct the equilibrium constant, K, expression for: KOH + MnSO_4 + KBrO ⟶ H_2O + K_2SO_4 + KMnO_4 + 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: 6 KOH + 2 MnSO_4 + 5 KBrO ⟶ 3 H_2O + 2 K_2SO_4 + 2 KMnO_4 + 5 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 KOH | 6 | -6 MnSO_4 | 2 | -2 KBrO | 5 | -5 H_2O | 3 | 3 K_2SO_4 | 2 | 2 KMnO_4 | 2 | 2 KBr | 5 | 5 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression KOH | 6 | -6 | ([KOH])^(-6) MnSO_4 | 2 | -2 | ([MnSO4])^(-2) KBrO | 5 | -5 | ([KBrO])^(-5) H_2O | 3 | 3 | ([H2O])^3 K_2SO_4 | 2 | 2 | ([K2SO4])^2 KMnO_4 | 2 | 2 | ([KMnO4])^2 KBr | 5 | 5 | ([KBr])^5 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])^(-6) ([MnSO4])^(-2) ([KBrO])^(-5) ([H2O])^3 ([K2SO4])^2 ([KMnO4])^2 ([KBr])^5 = (([H2O])^3 ([K2SO4])^2 ([KMnO4])^2 ([KBr])^5)/(([KOH])^6 ([MnSO4])^2 ([KBrO])^5)

Construct the rate of reaction expression for: KOH + MnSO_4 + KBrO ⟶ H_2O + K_2SO_4 + KMnO_4 + 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: 6 KOH + 2 MnSO_4 + 5 KBrO ⟶ 3 H_2O + 2 K_2SO_4 + 2 KMnO_4 + 5 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 KOH | 6 | -6 MnSO_4 | 2 | -2 KBrO | 5 | -5 H_2O | 3 | 3 K_2SO_4 | 2 | 2 KMnO_4 | 2 | 2 KBr | 5 | 5 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 | 6 | -6 | -1/6 (Δ[KOH])/(Δt) MnSO_4 | 2 | -2 | -1/2 (Δ[MnSO4])/(Δt) KBrO | 5 | -5 | -1/5 (Δ[KBrO])/(Δt) H_2O | 3 | 3 | 1/3 (Δ[H2O])/(Δt) K_2SO_4 | 2 | 2 | 1/2 (Δ[K2SO4])/(Δt) KMnO_4 | 2 | 2 | 1/2 (Δ[KMnO4])/(Δt) KBr | 5 | 5 | 1/5 (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 = -1/6 (Δ[KOH])/(Δt) = -1/2 (Δ[MnSO4])/(Δt) = -1/5 (Δ[KBrO])/(Δt) = 1/3 (Δ[H2O])/(Δt) = 1/2 (Δ[K2SO4])/(Δt) = 1/2 (Δ[KMnO4])/(Δt) = 1/5 (Δ[KBr])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| potassium hydroxide | manganese(II) sulfate | KBrO | water | potassium sulfate | potassium permanganate | potassium bromide formula | KOH | MnSO_4 | KBrO | H_2O | K_2SO_4 | KMnO_4 | KBr Hill formula | HKO | MnSO_4 | BrKO | H_2O | K_2O_4S | KMnO_4 | BrK name | potassium hydroxide | manganese(II) sulfate | | water | potassium sulfate | potassium permanganate | potassium bromide IUPAC name | potassium hydroxide | manganese(+2) cation sulfate | | water | dipotassium sulfate | potassium permanganate | potassium bromide

| potassium hydroxide | manganese(II) sulfate | KBrO | water | potassium sulfate | potassium permanganate | potassium bromide molar mass | 56.105 g/mol | 150.99 g/mol | 135 g/mol | 18.015 g/mol | 174.25 g/mol | 158.03 g/mol | 119 g/mol phase | solid (at STP) | solid (at STP) | | liquid (at STP) | | solid (at STP) | solid (at STP) melting point | 406 °C | 710 °C | | 0 °C | | 240 °C | 734 °C boiling point | 1327 °C | | | 99.9839 °C | | | 1435 °C density | 2.044 g/cm^3 | 3.25 g/cm^3 | | 1 g/cm^3 | | 1 g/cm^3 | 2.75 g/cm^3 solubility in water | soluble | soluble | | | soluble | | soluble 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 |