H2O + KClO3 + Mn(NO3)2 = HNO3 + KCl + MnO2

H_2O water + KClO_3 potassium chlorate + Mn(NO_3)_2 manganese(II) nitrate ⟶ HNO_3 nitric acid + KCl potassium chloride + MnO_2 manganese dioxide

Balance the chemical equation algebraically: H_2O + KClO_3 + Mn(NO_3)_2 ⟶ HNO_3 + KCl + MnO_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 KClO_3 + c_3 Mn(NO_3)_2 ⟶ c_4 HNO_3 + c_5 KCl + c_6 MnO_2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, Cl, K, Mn and N: H: | 2 c_1 = c_4 O: | c_1 + 3 c_2 + 6 c_3 = 3 c_4 + 2 c_6 Cl: | c_2 = c_5 K: | c_2 = c_5 Mn: | c_3 = c_6 N: | 2 c_3 = 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3 c_2 = 1 c_3 = 3 c_4 = 6 c_5 = 1 c_6 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 H_2O + KClO_3 + 3 Mn(NO_3)_2 ⟶ 6 HNO_3 + KCl + 3 MnO_2

+ + ⟶ + +

water + potassium chlorate + manganese(II) nitrate ⟶ nitric acid + potassium chloride + manganese dioxide

Construct the equilibrium constant, K, expression for: H_2O + KClO_3 + Mn(NO_3)_2 ⟶ HNO_3 + KCl + MnO_2 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: 3 H_2O + KClO_3 + 3 Mn(NO_3)_2 ⟶ 6 HNO_3 + KCl + 3 MnO_2 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 H_2O | 3 | -3 KClO_3 | 1 | -1 Mn(NO_3)_2 | 3 | -3 HNO_3 | 6 | 6 KCl | 1 | 1 MnO_2 | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 3 | -3 | ([H2O])^(-3) KClO_3 | 1 | -1 | ([KClO3])^(-1) Mn(NO_3)_2 | 3 | -3 | ([Mn(NO3)2])^(-3) HNO_3 | 6 | 6 | ([HNO3])^6 KCl | 1 | 1 | [KCl] MnO_2 | 3 | 3 | ([MnO2])^3 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 = ([H2O])^(-3) ([KClO3])^(-1) ([Mn(NO3)2])^(-3) ([HNO3])^6 [KCl] ([MnO2])^3 = (([HNO3])^6 [KCl] ([MnO2])^3)/(([H2O])^3 [KClO3] ([Mn(NO3)2])^3)

Construct the rate of reaction expression for: H_2O + KClO_3 + Mn(NO_3)_2 ⟶ HNO_3 + KCl + MnO_2 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: 3 H_2O + KClO_3 + 3 Mn(NO_3)_2 ⟶ 6 HNO_3 + KCl + 3 MnO_2 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 H_2O | 3 | -3 KClO_3 | 1 | -1 Mn(NO_3)_2 | 3 | -3 HNO_3 | 6 | 6 KCl | 1 | 1 MnO_2 | 3 | 3 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 H_2O | 3 | -3 | -1/3 (Δ[H2O])/(Δt) KClO_3 | 1 | -1 | -(Δ[KClO3])/(Δt) Mn(NO_3)_2 | 3 | -3 | -1/3 (Δ[Mn(NO3)2])/(Δt) HNO_3 | 6 | 6 | 1/6 (Δ[HNO3])/(Δt) KCl | 1 | 1 | (Δ[KCl])/(Δt) MnO_2 | 3 | 3 | 1/3 (Δ[MnO2])/(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 = -1/3 (Δ[H2O])/(Δt) = -(Δ[KClO3])/(Δt) = -1/3 (Δ[Mn(NO3)2])/(Δt) = 1/6 (Δ[HNO3])/(Δt) = (Δ[KCl])/(Δt) = 1/3 (Δ[MnO2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | potassium chlorate | manganese(II) nitrate | nitric acid | potassium chloride | manganese dioxide formula | H_2O | KClO_3 | Mn(NO_3)_2 | HNO_3 | KCl | MnO_2 Hill formula | H_2O | ClKO_3 | MnN_2O_6 | HNO_3 | ClK | MnO_2 name | water | potassium chlorate | manganese(II) nitrate | nitric acid | potassium chloride | manganese dioxide IUPAC name | water | potassium chlorate | manganese(2+) dinitrate | nitric acid | potassium chloride | dioxomanganese

| water | potassium chlorate | manganese(II) nitrate | nitric acid | potassium chloride | manganese dioxide molar mass | 18.015 g/mol | 122.5 g/mol | 178.95 g/mol | 63.012 g/mol | 74.55 g/mol | 86.936 g/mol phase | liquid (at STP) | solid (at STP) | | liquid (at STP) | solid (at STP) | solid (at STP) melting point | 0 °C | 356 °C | | -41.6 °C | 770 °C | 535 °C boiling point | 99.9839 °C | | | 83 °C | 1420 °C | density | 1 g/cm^3 | 2.34 g/cm^3 | 1.536 g/cm^3 | 1.5129 g/cm^3 | 1.98 g/cm^3 | 5.03 g/cm^3 solubility in water | | soluble | | miscible | soluble | insoluble surface tension | 0.0728 N/m | | | | | dynamic viscosity | 8.9×10^-4 Pa s (at 25 °C) | | | 7.6×10^-4 Pa s (at 25 °C) | | odor | odorless | | | | odorless |