H2SO4 + KMnO4 + C6N6FeK4 = H2O + K2SO4 + MnSO4 + C6N6FeK3

H_2SO_4 sulfuric acid + KMnO_4 potassium permanganate + C6N6FeK4 ⟶ H_2O water + K_2SO_4 potassium sulfate + MnSO_4 manganese(II) sulfate + K_3Fe(CN)_6 potassium hexacyanoferrate(III)

Balance the chemical equation algebraically: H_2SO_4 + KMnO_4 + C6N6FeK4 ⟶ H_2O + K_2SO_4 + MnSO_4 + K_3Fe(CN)_6 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 KMnO_4 + c_3 C6N6FeK4 ⟶ c_4 H_2O + c_5 K_2SO_4 + c_6 MnSO_4 + c_7 K_3Fe(CN)_6 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, K, Mn, C, N and Fe: H: | 2 c_1 = 2 c_4 O: | 4 c_1 + 4 c_2 = c_4 + 4 c_5 + 4 c_6 S: | c_1 = c_5 + c_6 K: | c_2 + 4 c_3 = 2 c_5 + 3 c_7 Mn: | c_2 = c_6 C: | 6 c_3 = 6 c_7 N: | 6 c_3 = 6 c_7 Fe: | c_3 = c_7 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 = 5 c_4 = 4 c_5 = 3 c_6 = 1 c_7 = 5 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 H_2SO_4 + KMnO_4 + 5 C6N6FeK4 ⟶ 4 H_2O + 3 K_2SO_4 + MnSO_4 + 5 K_3Fe(CN)_6

+ + C6N6FeK4 ⟶ + + +

sulfuric acid + potassium permanganate + C6N6FeK4 ⟶ water + potassium sulfate + manganese(II) sulfate + potassium hexacyanoferrate(III)

Construct the equilibrium constant, K, expression for: H_2SO_4 + KMnO_4 + C6N6FeK4 ⟶ H_2O + K_2SO_4 + MnSO_4 + K_3Fe(CN)_6 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 H_2SO_4 + KMnO_4 + 5 C6N6FeK4 ⟶ 4 H_2O + 3 K_2SO_4 + MnSO_4 + 5 K_3Fe(CN)_6 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 H_2SO_4 | 4 | -4 KMnO_4 | 1 | -1 C6N6FeK4 | 5 | -5 H_2O | 4 | 4 K_2SO_4 | 3 | 3 MnSO_4 | 1 | 1 K_3Fe(CN)_6 | 5 | 5 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 4 | -4 | ([H2SO4])^(-4) KMnO_4 | 1 | -1 | ([KMnO4])^(-1) C6N6FeK4 | 5 | -5 | ([C6N6FeK4])^(-5) H_2O | 4 | 4 | ([H2O])^4 K_2SO_4 | 3 | 3 | ([K2SO4])^3 MnSO_4 | 1 | 1 | [MnSO4] K_3Fe(CN)_6 | 5 | 5 | ([K3Fe(CN)6])^5 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 = ([H2SO4])^(-4) ([KMnO4])^(-1) ([C6N6FeK4])^(-5) ([H2O])^4 ([K2SO4])^3 [MnSO4] ([K3Fe(CN)6])^5 = (([H2O])^4 ([K2SO4])^3 [MnSO4] ([K3Fe(CN)6])^5)/(([H2SO4])^4 [KMnO4] ([C6N6FeK4])^5)

Construct the rate of reaction expression for: H_2SO_4 + KMnO_4 + C6N6FeK4 ⟶ H_2O + K_2SO_4 + MnSO_4 + K_3Fe(CN)_6 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 H_2SO_4 + KMnO_4 + 5 C6N6FeK4 ⟶ 4 H_2O + 3 K_2SO_4 + MnSO_4 + 5 K_3Fe(CN)_6 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 H_2SO_4 | 4 | -4 KMnO_4 | 1 | -1 C6N6FeK4 | 5 | -5 H_2O | 4 | 4 K_2SO_4 | 3 | 3 MnSO_4 | 1 | 1 K_3Fe(CN)_6 | 5 | 5 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 H_2SO_4 | 4 | -4 | -1/4 (Δ[H2SO4])/(Δt) KMnO_4 | 1 | -1 | -(Δ[KMnO4])/(Δt) C6N6FeK4 | 5 | -5 | -1/5 (Δ[C6N6FeK4])/(Δt) H_2O | 4 | 4 | 1/4 (Δ[H2O])/(Δt) K_2SO_4 | 3 | 3 | 1/3 (Δ[K2SO4])/(Δt) MnSO_4 | 1 | 1 | (Δ[MnSO4])/(Δt) K_3Fe(CN)_6 | 5 | 5 | 1/5 (Δ[K3Fe(CN)6])/(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[H2SO4])/(Δt) = -(Δ[KMnO4])/(Δt) = -1/5 (Δ[C6N6FeK4])/(Δt) = 1/4 (Δ[H2O])/(Δt) = 1/3 (Δ[K2SO4])/(Δt) = (Δ[MnSO4])/(Δt) = 1/5 (Δ[K3Fe(CN)6])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sulfuric acid | potassium permanganate | C6N6FeK4 | water | potassium sulfate | manganese(II) sulfate | potassium hexacyanoferrate(III) formula | H_2SO_4 | KMnO_4 | C6N6FeK4 | H_2O | K_2SO_4 | MnSO_4 | K_3Fe(CN)_6 Hill formula | H_2O_4S | KMnO_4 | C6FeK4N6 | H_2O | K_2O_4S | MnSO_4 | C_6FeK_3N_6 name | sulfuric acid | potassium permanganate | | water | potassium sulfate | manganese(II) sulfate | potassium hexacyanoferrate(III) IUPAC name | sulfuric acid | potassium permanganate | | water | dipotassium sulfate | manganese(+2) cation sulfate | ferric tripotassium hexacyanide

| sulfuric acid | potassium permanganate | C6N6FeK4 | water | potassium sulfate | manganese(II) sulfate | potassium hexacyanoferrate(III) molar mass | 98.07 g/mol | 158.03 g/mol | 368.35 g/mol | 18.015 g/mol | 174.25 g/mol | 150.99 g/mol | 329.25 g/mol phase | liquid (at STP) | solid (at STP) | | liquid (at STP) | | solid (at STP) | melting point | 10.371 °C | 240 °C | | 0 °C | | 710 °C | boiling point | 279.6 °C | | | 99.9839 °C | | | density | 1.8305 g/cm^3 | 1 g/cm^3 | | 1 g/cm^3 | | 3.25 g/cm^3 | 1.723 g/cm^3 solubility in water | very soluble | | | | soluble | soluble | surface tension | 0.0735 N/m | | | 0.0728 N/m | | | dynamic viscosity | 0.021 Pa s (at 25 °C) | | | 8.9×10^-4 Pa s (at 25 °C) | | | odor | odorless | odorless | | odorless | | |