NaOH + MnO2 + NaClO3 = H2O + NaCl + NaMnO4

NaOH sodium hydroxide + MnO_2 manganese dioxide + NaClO_3 sodium chlorate ⟶ H_2O water + NaCl sodium chloride + NaMnO_4 sodium permanganate

Balance the chemical equation algebraically: NaOH + MnO_2 + NaClO_3 ⟶ H_2O + NaCl + NaMnO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 NaOH + c_2 MnO_2 + c_3 NaClO_3 ⟶ c_4 H_2O + c_5 NaCl + c_6 NaMnO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, Na, O, Mn and Cl: H: | c_1 = 2 c_4 Na: | c_1 + c_3 = c_5 + c_6 O: | c_1 + 2 c_2 + 3 c_3 = c_4 + 4 c_6 Mn: | c_2 = c_6 Cl: | c_3 = c_5 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 = 2 c_2 = 2 c_3 = 1 c_4 = 1 c_5 = 1 c_6 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 NaOH + 2 MnO_2 + NaClO_3 ⟶ H_2O + NaCl + 2 NaMnO_4

+ + ⟶ + +

sodium hydroxide + manganese dioxide + sodium chlorate ⟶ water + sodium chloride + sodium permanganate

Construct the equilibrium constant, K, expression for: NaOH + MnO_2 + NaClO_3 ⟶ H_2O + NaCl + 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: 2 NaOH + 2 MnO_2 + NaClO_3 ⟶ H_2O + NaCl + 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 | 2 | -2 MnO_2 | 2 | -2 NaClO_3 | 1 | -1 H_2O | 1 | 1 NaCl | 1 | 1 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 | 2 | -2 | ([NaOH])^(-2) MnO_2 | 2 | -2 | ([MnO2])^(-2) NaClO_3 | 1 | -1 | ([NaClO3])^(-1) H_2O | 1 | 1 | [H2O] NaCl | 1 | 1 | [NaCl] 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])^(-2) ([MnO2])^(-2) ([NaClO3])^(-1) [H2O] [NaCl] ([NaMnO4])^2 = ([H2O] [NaCl] ([NaMnO4])^2)/(([NaOH])^2 ([MnO2])^2 [NaClO3])

Construct the rate of reaction expression for: NaOH + MnO_2 + NaClO_3 ⟶ H_2O + NaCl + 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: 2 NaOH + 2 MnO_2 + NaClO_3 ⟶ H_2O + NaCl + 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 | 2 | -2 MnO_2 | 2 | -2 NaClO_3 | 1 | -1 H_2O | 1 | 1 NaCl | 1 | 1 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 | 2 | -2 | -1/2 (Δ[NaOH])/(Δt) MnO_2 | 2 | -2 | -1/2 (Δ[MnO2])/(Δt) NaClO_3 | 1 | -1 | -(Δ[NaClO3])/(Δt) H_2O | 1 | 1 | (Δ[H2O])/(Δt) NaCl | 1 | 1 | (Δ[NaCl])/(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 = -1/2 (Δ[NaOH])/(Δt) = -1/2 (Δ[MnO2])/(Δt) = -(Δ[NaClO3])/(Δt) = (Δ[H2O])/(Δt) = (Δ[NaCl])/(Δt) = 1/2 (Δ[NaMnO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sodium hydroxide | manganese dioxide | sodium chlorate | water | sodium chloride | sodium permanganate formula | NaOH | MnO_2 | NaClO_3 | H_2O | NaCl | NaMnO_4 Hill formula | HNaO | MnO_2 | ClNaO_3 | H_2O | ClNa | MnNaO_4 name | sodium hydroxide | manganese dioxide | sodium chlorate | water | sodium chloride | sodium permanganate IUPAC name | sodium hydroxide | dioxomanganese | sodium chlorate | water | sodium chloride | sodium permanganate

| sodium hydroxide | manganese dioxide | sodium chlorate | water | sodium chloride | sodium permanganate molar mass | 39.997 g/mol | 86.936 g/mol | 106.4 g/mol | 18.015 g/mol | 58.44 g/mol | 141.92 g/mol phase | solid (at STP) | solid (at STP) | liquid (at STP) | liquid (at STP) | solid (at STP) | liquid (at STP) melting point | 323 °C | 535 °C | | 0 °C | 801 °C | boiling point | 1390 °C | | 106 °C | 99.9839 °C | 1413 °C | 100 °C density | 2.13 g/cm^3 | 5.03 g/cm^3 | 1.3 g/cm^3 | 1 g/cm^3 | 2.16 g/cm^3 | 1.391 g/cm^3 solubility in water | soluble | insoluble | very soluble | | soluble | surface tension | 0.07435 N/m | | | 0.0728 N/m | | dynamic viscosity | 0.004 Pa s (at 350 °C) | | 0.00542 Pa s (at 286 °C) | 8.9×10^-4 Pa s (at 25 °C) | | odor | | | odorless | odorless | odorless |