HCl + MnO2 = H2O + Cl2 + MnCl3

HCl hydrogen chloride + MnO_2 manganese dioxide ⟶ H_2O water + Cl_2 chlorine + MnCl3

Balance the chemical equation algebraically: HCl + MnO_2 ⟶ H_2O + Cl_2 + MnCl3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HCl + c_2 MnO_2 ⟶ c_3 H_2O + c_4 Cl_2 + c_5 MnCl3 Set the number of atoms in the reactants equal to the number of atoms in the products for Cl, H, Mn and O: Cl: | c_1 = 2 c_4 + 3 c_5 H: | c_1 = 2 c_3 Mn: | c_2 = c_5 O: | 2 c_2 = c_3 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_4 = 1 and solve the system of equations for the remaining coefficients: c_1 = 8 c_2 = 2 c_3 = 4 c_4 = 1 c_5 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 8 HCl + 2 MnO_2 ⟶ 4 H_2O + Cl_2 + 2 MnCl3

+ ⟶ + + MnCl3

hydrogen chloride + manganese dioxide ⟶ water + chlorine + MnCl3

Construct the equilibrium constant, K, expression for: HCl + MnO_2 ⟶ H_2O + Cl_2 + MnCl3 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 HCl + 2 MnO_2 ⟶ 4 H_2O + Cl_2 + 2 MnCl3 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 HCl | 8 | -8 MnO_2 | 2 | -2 H_2O | 4 | 4 Cl_2 | 1 | 1 MnCl3 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HCl | 8 | -8 | ([HCl])^(-8) MnO_2 | 2 | -2 | ([MnO2])^(-2) H_2O | 4 | 4 | ([H2O])^4 Cl_2 | 1 | 1 | [Cl2] MnCl3 | 2 | 2 | ([MnCl3])^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 = ([HCl])^(-8) ([MnO2])^(-2) ([H2O])^4 [Cl2] ([MnCl3])^2 = (([H2O])^4 [Cl2] ([MnCl3])^2)/(([HCl])^8 ([MnO2])^2)

Construct the rate of reaction expression for: HCl + MnO_2 ⟶ H_2O + Cl_2 + MnCl3 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 HCl + 2 MnO_2 ⟶ 4 H_2O + Cl_2 + 2 MnCl3 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 HCl | 8 | -8 MnO_2 | 2 | -2 H_2O | 4 | 4 Cl_2 | 1 | 1 MnCl3 | 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 HCl | 8 | -8 | -1/8 (Δ[HCl])/(Δt) MnO_2 | 2 | -2 | -1/2 (Δ[MnO2])/(Δt) H_2O | 4 | 4 | 1/4 (Δ[H2O])/(Δt) Cl_2 | 1 | 1 | (Δ[Cl2])/(Δt) MnCl3 | 2 | 2 | 1/2 (Δ[MnCl3])/(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[HCl])/(Δt) = -1/2 (Δ[MnO2])/(Δt) = 1/4 (Δ[H2O])/(Δt) = (Δ[Cl2])/(Δt) = 1/2 (Δ[MnCl3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| hydrogen chloride | manganese dioxide | water | chlorine | MnCl3 formula | HCl | MnO_2 | H_2O | Cl_2 | MnCl3 Hill formula | ClH | MnO_2 | H_2O | Cl_2 | Cl3Mn name | hydrogen chloride | manganese dioxide | water | chlorine | IUPAC name | hydrogen chloride | dioxomanganese | water | molecular chlorine |

| hydrogen chloride | manganese dioxide | water | chlorine | MnCl3 molar mass | 36.46 g/mol | 86.936 g/mol | 18.015 g/mol | 70.9 g/mol | 161.3 g/mol phase | gas (at STP) | solid (at STP) | liquid (at STP) | gas (at STP) | melting point | -114.17 °C | 535 °C | 0 °C | -101 °C | boiling point | -85 °C | | 99.9839 °C | -34 °C | density | 0.00149 g/cm^3 (at 25 °C) | 5.03 g/cm^3 | 1 g/cm^3 | 0.003214 g/cm^3 (at 0 °C) | solubility in water | miscible | insoluble | | | surface tension | | | 0.0728 N/m | | dynamic viscosity | | | 8.9×10^-4 Pa s (at 25 °C) | | odor | | | odorless | |