HMnO4 + Sn(OH)4 = H2O + Sn(MnO4)4

HMnO4 + Sn(OH)4 ⟶ H_2O water + Sn(MnO4)4

Balance the chemical equation algebraically: HMnO4 + Sn(OH)4 ⟶ H_2O + Sn(MnO4)4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HMnO4 + c_2 Sn(OH)4 ⟶ c_3 H_2O + c_4 Sn(MnO4)4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, Mn, O and Sn: H: | c_1 + 4 c_2 = 2 c_3 Mn: | c_1 = 4 c_4 O: | 4 c_1 + 4 c_2 = c_3 + 16 c_4 Sn: | 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 HMnO4 + Sn(OH)4 ⟶ 4 H_2O + Sn(MnO4)4

HMnO4 + Sn(OH)4 ⟶ + Sn(MnO4)4

HMnO4 + Sn(OH)4 ⟶ water + Sn(MnO4)4

Construct the equilibrium constant, K, expression for: HMnO4 + Sn(OH)4 ⟶ H_2O + Sn(MnO4)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 HMnO4 + Sn(OH)4 ⟶ 4 H_2O + Sn(MnO4)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 HMnO4 | 4 | -4 Sn(OH)4 | 1 | -1 H_2O | 4 | 4 Sn(MnO4)4 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HMnO4 | 4 | -4 | ([HMnO4])^(-4) Sn(OH)4 | 1 | -1 | ([Sn(OH)4])^(-1) H_2O | 4 | 4 | ([H2O])^4 Sn(MnO4)4 | 1 | 1 | [Sn(MnO4)4] 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 = ([HMnO4])^(-4) ([Sn(OH)4])^(-1) ([H2O])^4 [Sn(MnO4)4] = (([H2O])^4 [Sn(MnO4)4])/(([HMnO4])^4 [Sn(OH)4])

Construct the rate of reaction expression for: HMnO4 + Sn(OH)4 ⟶ H_2O + Sn(MnO4)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 HMnO4 + Sn(OH)4 ⟶ 4 H_2O + Sn(MnO4)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 HMnO4 | 4 | -4 Sn(OH)4 | 1 | -1 H_2O | 4 | 4 Sn(MnO4)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 HMnO4 | 4 | -4 | -1/4 (Δ[HMnO4])/(Δt) Sn(OH)4 | 1 | -1 | -(Δ[Sn(OH)4])/(Δt) H_2O | 4 | 4 | 1/4 (Δ[H2O])/(Δt) Sn(MnO4)4 | 1 | 1 | (Δ[Sn(MnO4)4])/(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[HMnO4])/(Δt) = -(Δ[Sn(OH)4])/(Δt) = 1/4 (Δ[H2O])/(Δt) = (Δ[Sn(MnO4)4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| HMnO4 | Sn(OH)4 | water | Sn(MnO4)4 formula | HMnO4 | Sn(OH)4 | H_2O | Sn(MnO4)4 Hill formula | HMnO4 | H4O4Sn | H_2O | Mn4O16Sn name | | | water |

| HMnO4 | Sn(OH)4 | water | Sn(MnO4)4 molar mass | 119.94 g/mol | 186.74 g/mol | 18.015 g/mol | 594.45 g/mol phase | | | liquid (at STP) | melting point | | | 0 °C | boiling point | | | 99.9839 °C | density | | | 1 g/cm^3 | surface tension | | | 0.0728 N/m | dynamic viscosity | | | 8.9×10^-4 Pa s (at 25 °C) | odor | | | odorless |