KMnO4 + K2SO3 + KHSO4 = H2O + K2SO4 + MnSO4

KMnO_4 potassium permanganate + K_2SO_3 potassium sulfite + KHSO_4 potassium bisulfate ⟶ H_2O water + K_2SO_4 potassium sulfate + MnSO_4 manganese(II) sulfate

Balance the chemical equation algebraically: KMnO_4 + K_2SO_3 + KHSO_4 ⟶ H_2O + K_2SO_4 + MnSO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 KMnO_4 + c_2 K_2SO_3 + c_3 KHSO_4 ⟶ c_4 H_2O + c_5 K_2SO_4 + c_6 MnSO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for K, Mn, O, S and H: K: | c_1 + 2 c_2 + c_3 = 2 c_5 Mn: | c_1 = c_6 O: | 4 c_1 + 3 c_2 + 4 c_3 = c_4 + 4 c_5 + 4 c_6 S: | c_2 + c_3 = c_5 + c_6 H: | c_3 = 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 = 5/2 c_3 = 3 c_4 = 3/2 c_5 = 9/2 c_6 = 1 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 2 c_2 = 5 c_3 = 6 c_4 = 3 c_5 = 9 c_6 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 KMnO_4 + 5 K_2SO_3 + 6 KHSO_4 ⟶ 3 H_2O + 9 K_2SO_4 + 2 MnSO_4

+ + ⟶ + +

potassium permanganate + potassium sulfite + potassium bisulfate ⟶ water + potassium sulfate + manganese(II) sulfate

Construct the equilibrium constant, K, expression for: KMnO_4 + K_2SO_3 + KHSO_4 ⟶ H_2O + K_2SO_4 + 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: 2 KMnO_4 + 5 K_2SO_3 + 6 KHSO_4 ⟶ 3 H_2O + 9 K_2SO_4 + 2 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 KMnO_4 | 2 | -2 K_2SO_3 | 5 | -5 KHSO_4 | 6 | -6 H_2O | 3 | 3 K_2SO_4 | 9 | 9 MnSO_4 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression KMnO_4 | 2 | -2 | ([KMnO4])^(-2) K_2SO_3 | 5 | -5 | ([K2SO3])^(-5) KHSO_4 | 6 | -6 | ([KHSO4])^(-6) H_2O | 3 | 3 | ([H2O])^3 K_2SO_4 | 9 | 9 | ([K2SO4])^9 MnSO_4 | 2 | 2 | ([MnSO4])^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 = ([KMnO4])^(-2) ([K2SO3])^(-5) ([KHSO4])^(-6) ([H2O])^3 ([K2SO4])^9 ([MnSO4])^2 = (([H2O])^3 ([K2SO4])^9 ([MnSO4])^2)/(([KMnO4])^2 ([K2SO3])^5 ([KHSO4])^6)

Construct the rate of reaction expression for: KMnO_4 + K_2SO_3 + KHSO_4 ⟶ H_2O + K_2SO_4 + 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: 2 KMnO_4 + 5 K_2SO_3 + 6 KHSO_4 ⟶ 3 H_2O + 9 K_2SO_4 + 2 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 KMnO_4 | 2 | -2 K_2SO_3 | 5 | -5 KHSO_4 | 6 | -6 H_2O | 3 | 3 K_2SO_4 | 9 | 9 MnSO_4 | 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 KMnO_4 | 2 | -2 | -1/2 (Δ[KMnO4])/(Δt) K_2SO_3 | 5 | -5 | -1/5 (Δ[K2SO3])/(Δt) KHSO_4 | 6 | -6 | -1/6 (Δ[KHSO4])/(Δt) H_2O | 3 | 3 | 1/3 (Δ[H2O])/(Δt) K_2SO_4 | 9 | 9 | 1/9 (Δ[K2SO4])/(Δt) MnSO_4 | 2 | 2 | 1/2 (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 = -1/2 (Δ[KMnO4])/(Δt) = -1/5 (Δ[K2SO3])/(Δt) = -1/6 (Δ[KHSO4])/(Δt) = 1/3 (Δ[H2O])/(Δt) = 1/9 (Δ[K2SO4])/(Δt) = 1/2 (Δ[MnSO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| potassium permanganate | potassium sulfite | potassium bisulfate | water | potassium sulfate | manganese(II) sulfate formula | KMnO_4 | K_2SO_3 | KHSO_4 | H_2O | K_2SO_4 | MnSO_4 Hill formula | KMnO_4 | K_2O_3S | HKO_4S | H_2O | K_2O_4S | MnSO_4 name | potassium permanganate | potassium sulfite | potassium bisulfate | water | potassium sulfate | manganese(II) sulfate IUPAC name | potassium permanganate | dipotassium sulfite | potassium hydrogen sulfate | water | dipotassium sulfate | manganese(+2) cation sulfate

| potassium permanganate | potassium sulfite | potassium bisulfate | water | potassium sulfate | manganese(II) sulfate molar mass | 158.03 g/mol | 158.25 g/mol | 136.16 g/mol | 18.015 g/mol | 174.25 g/mol | 150.99 g/mol phase | solid (at STP) | | solid (at STP) | liquid (at STP) | | solid (at STP) melting point | 240 °C | | 214 °C | 0 °C | | 710 °C boiling point | | | | 99.9839 °C | | density | 1 g/cm^3 | | 2.32 g/cm^3 | 1 g/cm^3 | | 3.25 g/cm^3 solubility in water | | | | | soluble | soluble surface tension | | | | 0.0728 N/m | | dynamic viscosity | | | | 8.9×10^-4 Pa s (at 25 °C) | | odor | odorless | | | odorless | |