NaOH + MnCl2 + NaOCl = H2O + NaCl + MnO2

Input interpretation

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NaOH sodium hydroxide + MnCl_2 manganese(II) chloride + NaOCl sodium hypochlorite ⟶ H_2O water + NaCl sodium chloride + MnO_2 manganese dioxide

Balanced equation

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Balance the chemical equation algebraically: NaOH + MnCl_2 + NaOCl ⟶ H_2O + NaCl + MnO_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 NaOH + c_2 MnCl_2 + c_3 NaOCl ⟶ c_4 H_2O + c_5 NaCl + c_6 MnO_2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, Na, O, Cl and Mn: H: | c_1 = 2 c_4 Na: | c_1 + c_3 = c_5 O: | c_1 + c_3 = c_4 + 2 c_6 Cl: | 2 c_2 + c_3 = c_5 Mn: | c_2 = c_6 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 = 2 c_2 = 1 c_3 = 1 c_4 = 1 c_5 = 3 c_6 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 NaOH + MnCl_2 + NaOCl ⟶ H_2O + 3 NaCl + MnO_2

+ + ⟶ + +

Names

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sodium hydroxide + manganese(II) chloride + sodium hypochlorite ⟶ water + sodium chloride + manganese dioxide

Equilibrium constant

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Construct the equilibrium constant, K, expression for: NaOH + MnCl_2 + NaOCl ⟶ H_2O + NaCl + 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: 2 NaOH + MnCl_2 + NaOCl ⟶ H_2O + 3 NaCl + 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 NaOH | 2 | -2 MnCl_2 | 1 | -1 NaOCl | 1 | -1 H_2O | 1 | 1 NaCl | 3 | 3 MnO_2 | 1 | 1 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) MnCl_2 | 1 | -1 | ([MnCl2])^(-1) NaOCl | 1 | -1 | ([NaOCl])^(-1) H_2O | 1 | 1 | [H2O] NaCl | 3 | 3 | ([NaCl])^3 MnO_2 | 1 | 1 | [MnO2] 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) ([MnCl2])^(-1) ([NaOCl])^(-1) [H2O] ([NaCl])^3 [MnO2] = ([H2O] ([NaCl])^3 [MnO2])/(([NaOH])^2 [MnCl2] [NaOCl])

Rate of reaction

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Construct the rate of reaction expression for: NaOH + MnCl_2 + NaOCl ⟶ H_2O + NaCl + 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: 2 NaOH + MnCl_2 + NaOCl ⟶ H_2O + 3 NaCl + 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 NaOH | 2 | -2 MnCl_2 | 1 | -1 NaOCl | 1 | -1 H_2O | 1 | 1 NaCl | 3 | 3 MnO_2 | 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 NaOH | 2 | -2 | -1/2 (Δ[NaOH])/(Δt) MnCl_2 | 1 | -1 | -(Δ[MnCl2])/(Δt) NaOCl | 1 | -1 | -(Δ[NaOCl])/(Δt) H_2O | 1 | 1 | (Δ[H2O])/(Δt) NaCl | 3 | 3 | 1/3 (Δ[NaCl])/(Δt) MnO_2 | 1 | 1 | (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 = -1/2 (Δ[NaOH])/(Δt) = -(Δ[MnCl2])/(Δt) = -(Δ[NaOCl])/(Δt) = (Δ[H2O])/(Δt) = 1/3 (Δ[NaCl])/(Δt) = (Δ[MnO2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)