HClO + MnS = HCl + MnSO4

HOCl hypochlorous acid + MnS manganese sulfide ⟶ HCl hydrogen chloride + MnSO_4 manganese(II) sulfate

Balance the chemical equation algebraically: HOCl + MnS ⟶ HCl + MnSO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HOCl + c_2 MnS ⟶ c_3 HCl + c_4 MnSO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for Cl, H, O, Mn and S: Cl: | c_1 = c_3 H: | c_1 = c_3 O: | c_1 = 4 c_4 Mn: | c_2 = c_4 S: | c_2 = 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 = 4 c_2 = 1 c_3 = 4 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 HOCl + MnS ⟶ 4 HCl + MnSO_4

+ ⟶ +

hypochlorous acid + manganese sulfide ⟶ hydrogen chloride + manganese(II) sulfate

Construct the equilibrium constant, K, expression for: HOCl + MnS ⟶ HCl + MnSO_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: 4 HOCl + MnS ⟶ 4 HCl + MnSO_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 HOCl | 4 | -4 MnS | 1 | -1 HCl | 4 | 4 MnSO_4 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HOCl | 4 | -4 | ([HOCl])^(-4) MnS | 1 | -1 | ([MnS])^(-1) HCl | 4 | 4 | ([HCl])^4 MnSO_4 | 1 | 1 | [MnSO4] 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 = ([HOCl])^(-4) ([MnS])^(-1) ([HCl])^4 [MnSO4] = (([HCl])^4 [MnSO4])/(([HOCl])^4 [MnS])

Construct the rate of reaction expression for: HOCl + MnS ⟶ HCl + MnSO_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: 4 HOCl + MnS ⟶ 4 HCl + MnSO_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 HOCl | 4 | -4 MnS | 1 | -1 HCl | 4 | 4 MnSO_4 | 1 | 1 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 HOCl | 4 | -4 | -1/4 (Δ[HOCl])/(Δt) MnS | 1 | -1 | -(Δ[MnS])/(Δt) HCl | 4 | 4 | 1/4 (Δ[HCl])/(Δt) MnSO_4 | 1 | 1 | (Δ[MnSO4])/(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 = -1/4 (Δ[HOCl])/(Δt) = -(Δ[MnS])/(Δt) = 1/4 (Δ[HCl])/(Δt) = (Δ[MnSO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| hypochlorous acid | manganese sulfide | hydrogen chloride | manganese(II) sulfate formula | HOCl | MnS | HCl | MnSO_4 Hill formula | ClHO | MnS | ClH | MnSO_4 name | hypochlorous acid | manganese sulfide | hydrogen chloride | manganese(II) sulfate IUPAC name | hypochlorous acid | | hydrogen chloride | manganese(+2) cation sulfate

| hypochlorous acid | manganese sulfide | hydrogen chloride | manganese(II) sulfate molar mass | 52.46 g/mol | 87 g/mol | 36.46 g/mol | 150.99 g/mol phase | | solid (at STP) | gas (at STP) | solid (at STP) melting point | | 1141 °C | -114.17 °C | 710 °C boiling point | | | -85 °C | density | | 3.3 g/cm^3 | 0.00149 g/cm^3 (at 25 °C) | 3.25 g/cm^3 solubility in water | soluble | | miscible | soluble dynamic viscosity | | 2.64×10^-5 Pa s (at 1250 °C) | |