KOH + HMnO4 = H2O + KMnO4

KOH potassium hydroxide + HMnO4 ⟶ H_2O water + KMnO_4 potassium permanganate

Balance the chemical equation algebraically: KOH + HMnO4 ⟶ H_2O + KMnO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 KOH + c_2 HMnO4 ⟶ c_3 H_2O + c_4 KMnO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, K, O and Mn: H: | c_1 + c_2 = 2 c_3 K: | c_1 = c_4 O: | c_1 + 4 c_2 = c_3 + 4 c_4 Mn: | 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 1 c_3 = 1 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | KOH + HMnO4 ⟶ H_2O + KMnO_4

+ HMnO4 ⟶ +

potassium hydroxide + HMnO4 ⟶ water + potassium permanganate

Construct the equilibrium constant, K, expression for: KOH + HMnO4 ⟶ H_2O + KMnO_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: KOH + HMnO4 ⟶ H_2O + KMnO_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 KOH | 1 | -1 HMnO4 | 1 | -1 H_2O | 1 | 1 KMnO_4 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression KOH | 1 | -1 | ([KOH])^(-1) HMnO4 | 1 | -1 | ([HMnO4])^(-1) H_2O | 1 | 1 | [H2O] KMnO_4 | 1 | 1 | [KMnO4] 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 = ([KOH])^(-1) ([HMnO4])^(-1) [H2O] [KMnO4] = ([H2O] [KMnO4])/([KOH] [HMnO4])

Construct the rate of reaction expression for: KOH + HMnO4 ⟶ H_2O + KMnO_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: KOH + HMnO4 ⟶ H_2O + KMnO_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 KOH | 1 | -1 HMnO4 | 1 | -1 H_2O | 1 | 1 KMnO_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 KOH | 1 | -1 | -(Δ[KOH])/(Δt) HMnO4 | 1 | -1 | -(Δ[HMnO4])/(Δt) H_2O | 1 | 1 | (Δ[H2O])/(Δt) KMnO_4 | 1 | 1 | (Δ[KMnO4])/(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 = -(Δ[KOH])/(Δt) = -(Δ[HMnO4])/(Δt) = (Δ[H2O])/(Δt) = (Δ[KMnO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| potassium hydroxide | HMnO4 | water | potassium permanganate formula | KOH | HMnO4 | H_2O | KMnO_4 Hill formula | HKO | HMnO4 | H_2O | KMnO_4 name | potassium hydroxide | | water | potassium permanganate