NaOH + Br2 + MnCl2 = H2O + NaCl + NaBr + NaMnO4

NaOH sodium hydroxide + Br_2 bromine + MnCl_2 manganese(II) chloride ⟶ H_2O water + NaCl sodium chloride + NaBr sodium bromide + NaMnO_4 sodium permanganate

Balance the chemical equation algebraically: NaOH + Br_2 + MnCl_2 ⟶ H_2O + NaCl + NaBr + NaMnO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 NaOH + c_2 Br_2 + c_3 MnCl_2 ⟶ c_4 H_2O + c_5 NaCl + c_6 NaBr + c_7 NaMnO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, Na, O, Br, Cl and Mn: H: | c_1 = 2 c_4 Na: | c_1 = c_5 + c_6 + c_7 O: | c_1 = c_4 + 4 c_7 Br: | 2 c_2 = c_6 Cl: | 2 c_3 = c_5 Mn: | 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 8 c_2 = 5/2 c_3 = 1 c_4 = 4 c_5 = 2 c_6 = 5 c_7 = 1 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 16 c_2 = 5 c_3 = 2 c_4 = 8 c_5 = 4 c_6 = 10 c_7 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 16 NaOH + 5 Br_2 + 2 MnCl_2 ⟶ 8 H_2O + 4 NaCl + 10 NaBr + 2 NaMnO_4

+ + ⟶ + + +

sodium hydroxide + bromine + manganese(II) chloride ⟶ water + sodium chloride + sodium bromide + sodium permanganate

Construct the equilibrium constant, K, expression for: NaOH + Br_2 + MnCl_2 ⟶ H_2O + NaCl + NaBr + NaMnO_4 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: 16 NaOH + 5 Br_2 + 2 MnCl_2 ⟶ 8 H_2O + 4 NaCl + 10 NaBr + 2 NaMnO_4 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 NaOH | 16 | -16 Br_2 | 5 | -5 MnCl_2 | 2 | -2 H_2O | 8 | 8 NaCl | 4 | 4 NaBr | 10 | 10 NaMnO_4 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression NaOH | 16 | -16 | ([NaOH])^(-16) Br_2 | 5 | -5 | ([Br2])^(-5) MnCl_2 | 2 | -2 | ([MnCl2])^(-2) H_2O | 8 | 8 | ([H2O])^8 NaCl | 4 | 4 | ([NaCl])^4 NaBr | 10 | 10 | ([NaBr])^10 NaMnO_4 | 2 | 2 | ([NaMnO4])^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 = ([NaOH])^(-16) ([Br2])^(-5) ([MnCl2])^(-2) ([H2O])^8 ([NaCl])^4 ([NaBr])^10 ([NaMnO4])^2 = (([H2O])^8 ([NaCl])^4 ([NaBr])^10 ([NaMnO4])^2)/(([NaOH])^16 ([Br2])^5 ([MnCl2])^2)

Construct the rate of reaction expression for: NaOH + Br_2 + MnCl_2 ⟶ H_2O + NaCl + NaBr + NaMnO_4 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: 16 NaOH + 5 Br_2 + 2 MnCl_2 ⟶ 8 H_2O + 4 NaCl + 10 NaBr + 2 NaMnO_4 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 NaOH | 16 | -16 Br_2 | 5 | -5 MnCl_2 | 2 | -2 H_2O | 8 | 8 NaCl | 4 | 4 NaBr | 10 | 10 NaMnO_4 | 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 NaOH | 16 | -16 | -1/16 (Δ[NaOH])/(Δt) Br_2 | 5 | -5 | -1/5 (Δ[Br2])/(Δt) MnCl_2 | 2 | -2 | -1/2 (Δ[MnCl2])/(Δt) H_2O | 8 | 8 | 1/8 (Δ[H2O])/(Δt) NaCl | 4 | 4 | 1/4 (Δ[NaCl])/(Δt) NaBr | 10 | 10 | 1/10 (Δ[NaBr])/(Δt) NaMnO_4 | 2 | 2 | 1/2 (Δ[NaMnO4])/(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 = -1/16 (Δ[NaOH])/(Δt) = -1/5 (Δ[Br2])/(Δt) = -1/2 (Δ[MnCl2])/(Δt) = 1/8 (Δ[H2O])/(Δt) = 1/4 (Δ[NaCl])/(Δt) = 1/10 (Δ[NaBr])/(Δt) = 1/2 (Δ[NaMnO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sodium hydroxide | bromine | manganese(II) chloride | water | sodium chloride | sodium bromide | sodium permanganate formula | NaOH | Br_2 | MnCl_2 | H_2O | NaCl | NaBr | NaMnO_4 Hill formula | HNaO | Br_2 | Cl_2Mn | H_2O | ClNa | BrNa | MnNaO_4 name | sodium hydroxide | bromine | manganese(II) chloride | water | sodium chloride | sodium bromide | sodium permanganate IUPAC name | sodium hydroxide | molecular bromine | dichloromanganese | water | sodium chloride | sodium bromide | sodium permanganate

| sodium hydroxide | bromine | manganese(II) chloride | water | sodium chloride | sodium bromide | sodium permanganate molar mass | 39.997 g/mol | 159.81 g/mol | 125.8 g/mol | 18.015 g/mol | 58.44 g/mol | 102.89 g/mol | 141.92 g/mol phase | solid (at STP) | liquid (at STP) | solid (at STP) | liquid (at STP) | solid (at STP) | solid (at STP) | liquid (at STP) melting point | 323 °C | -7.2 °C | 652 °C | 0 °C | 801 °C | 755 °C | boiling point | 1390 °C | 58.8 °C | | 99.9839 °C | 1413 °C | 1396 °C | 100 °C density | 2.13 g/cm^3 | 3.119 g/cm^3 | 2.98 g/cm^3 | 1 g/cm^3 | 2.16 g/cm^3 | 3.2 g/cm^3 | 1.391 g/cm^3 solubility in water | soluble | insoluble | | | soluble | soluble | surface tension | 0.07435 N/m | 0.0409 N/m | | 0.0728 N/m | | | dynamic viscosity | 0.004 Pa s (at 350 °C) | 9.44×10^-4 Pa s (at 25 °C) | | 8.9×10^-4 Pa s (at 25 °C) | | | odor | | | | odorless | odorless | |