KOH + Br2 + MnCl2 = H2O + KCl + K2MnO4 + KBr

KOH (potassium hydroxide) + Br_2 (bromine) + MnCl_2 (manganese(II) chloride) ⟶ H_2O (water) + KCl (potassium chloride) + K_2MnO_4 (potassium manganate) + KBr (potassium bromide)

Balance the chemical equation algebraically: KOH + Br_2 + MnCl_2 ⟶ H_2O + KCl + K_2MnO_4 + KBr Add stoichiometric coefficients, c_i, to the reactants and products: c_1 KOH + c_2 Br_2 + c_3 MnCl_2 ⟶ c_4 H_2O + c_5 KCl + c_6 K_2MnO_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, Br, Cl and Mn: H: | c_1 = 2 c_4 K: | c_1 = c_5 + 2 c_6 + c_7 O: | c_1 = c_4 + 4 c_6 Br: | 2 c_2 = c_7 Cl: | 2 c_3 = c_5 Mn: | c_3 = c_6 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 8 c_2 = 2 c_3 = 1 c_4 = 4 c_5 = 2 c_6 = 1 c_7 = 4 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 8 KOH + 2 Br_2 + MnCl_2 ⟶ 4 H_2O + 2 KCl + K_2MnO_4 + 4 KBr

+ + ⟶ + + +

potassium hydroxide + bromine + manganese(II) chloride ⟶ water + potassium chloride + potassium manganate + potassium bromide

Construct the equilibrium constant, K, expression for: KOH + Br_2 + MnCl_2 ⟶ H_2O + KCl + K_2MnO_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: 8 KOH + 2 Br_2 + MnCl_2 ⟶ 4 H_2O + 2 KCl + K_2MnO_4 + 4 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 | 8 | -8 Br_2 | 2 | -2 MnCl_2 | 1 | -1 H_2O | 4 | 4 KCl | 2 | 2 K_2MnO_4 | 1 | 1 KBr | 4 | 4 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression KOH | 8 | -8 | ([KOH])^(-8) Br_2 | 2 | -2 | ([Br2])^(-2) MnCl_2 | 1 | -1 | ([MnCl2])^(-1) H_2O | 4 | 4 | ([H2O])^4 KCl | 2 | 2 | ([KCl])^2 K_2MnO_4 | 1 | 1 | [K2MnO4] KBr | 4 | 4 | ([KBr])^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 = ([KOH])^(-8) ([Br2])^(-2) ([MnCl2])^(-1) ([H2O])^4 ([KCl])^2 [K2MnO4] ([KBr])^4 = (([H2O])^4 ([KCl])^2 [K2MnO4] ([KBr])^4)/(([KOH])^8 ([Br2])^2 [MnCl2])

Construct the rate of reaction expression for: KOH + Br_2 + MnCl_2 ⟶ H_2O + KCl + K_2MnO_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: 8 KOH + 2 Br_2 + MnCl_2 ⟶ 4 H_2O + 2 KCl + K_2MnO_4 + 4 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 | 8 | -8 Br_2 | 2 | -2 MnCl_2 | 1 | -1 H_2O | 4 | 4 KCl | 2 | 2 K_2MnO_4 | 1 | 1 KBr | 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 KOH | 8 | -8 | -1/8 (Δ[KOH])/(Δt) Br_2 | 2 | -2 | -1/2 (Δ[Br2])/(Δt) MnCl_2 | 1 | -1 | -(Δ[MnCl2])/(Δt) H_2O | 4 | 4 | 1/4 (Δ[H2O])/(Δt) KCl | 2 | 2 | 1/2 (Δ[KCl])/(Δt) K_2MnO_4 | 1 | 1 | (Δ[K2MnO4])/(Δt) KBr | 4 | 4 | 1/4 (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 = -1/8 (Δ[KOH])/(Δt) = -1/2 (Δ[Br2])/(Δt) = -(Δ[MnCl2])/(Δt) = 1/4 (Δ[H2O])/(Δt) = 1/2 (Δ[KCl])/(Δt) = (Δ[K2MnO4])/(Δt) = 1/4 (Δ[KBr])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| potassium hydroxide | bromine | manganese(II) chloride | water | potassium chloride | potassium manganate | potassium bromide formula | KOH | Br_2 | MnCl_2 | H_2O | KCl | K_2MnO_4 | KBr Hill formula | HKO | Br_2 | Cl_2Mn | H_2O | ClK | K_2MnO_4 | BrK name | potassium hydroxide | bromine | manganese(II) chloride | water | potassium chloride | potassium manganate | potassium bromide IUPAC name | potassium hydroxide | molecular bromine | dichloromanganese | water | potassium chloride | dipotassium dioxido-dioxomanganese | potassium bromide

| potassium hydroxide | bromine | manganese(II) chloride | water | potassium chloride | potassium manganate | potassium bromide molar mass | 56.105 g/mol | 159.81 g/mol | 125.8 g/mol | 18.015 g/mol | 74.55 g/mol | 197.13 g/mol | 119 g/mol phase | solid (at STP) | liquid (at STP) | solid (at STP) | liquid (at STP) | solid (at STP) | solid (at STP) | solid (at STP) melting point | 406 °C | -7.2 °C | 652 °C | 0 °C | 770 °C | 190 °C | 734 °C boiling point | 1327 °C | 58.8 °C | | 99.9839 °C | 1420 °C | | 1435 °C density | 2.044 g/cm^3 | 3.119 g/cm^3 | 2.98 g/cm^3 | 1 g/cm^3 | 1.98 g/cm^3 | | 2.75 g/cm^3 solubility in water | soluble | insoluble | | | soluble | decomposes | soluble surface tension | | 0.0409 N/m | | 0.0728 N/m | | | dynamic viscosity | 0.001 Pa s (at 550 °C) | 9.44×10^-4 Pa s (at 25 °C) | | 8.9×10^-4 Pa s (at 25 °C) | | | odor | | | | odorless | odorless | |