KMnO4 + CuSO4 = K2SO4 + Cu(MnO4)2

KMnO_4 potassium permanganate + CuSO_4 copper(II) sulfate ⟶ K_2SO_4 potassium sulfate + Cu(MnO4)2

Balance the chemical equation algebraically: KMnO_4 + CuSO_4 ⟶ K_2SO_4 + Cu(MnO4)2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 KMnO_4 + c_2 CuSO_4 ⟶ c_3 K_2SO_4 + c_4 Cu(MnO4)2 Set the number of atoms in the reactants equal to the number of atoms in the products for K, Mn, O, Cu and S: K: | c_1 = 2 c_3 Mn: | c_1 = 2 c_4 O: | 4 c_1 + 4 c_2 = 4 c_3 + 8 c_4 Cu: | c_2 = c_4 S: | c_2 = c_3 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 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 KMnO_4 + CuSO_4 ⟶ K_2SO_4 + Cu(MnO4)2

+ ⟶ + Cu(MnO4)2

potassium permanganate + copper(II) sulfate ⟶ potassium sulfate + Cu(MnO4)2

Construct the equilibrium constant, K, expression for: KMnO_4 + CuSO_4 ⟶ K_2SO_4 + Cu(MnO4)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 KMnO_4 + CuSO_4 ⟶ K_2SO_4 + Cu(MnO4)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 KMnO_4 | 2 | -2 CuSO_4 | 1 | -1 K_2SO_4 | 1 | 1 Cu(MnO4)2 | 1 | 1 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) CuSO_4 | 1 | -1 | ([CuSO4])^(-1) K_2SO_4 | 1 | 1 | [K2SO4] Cu(MnO4)2 | 1 | 1 | [Cu(MnO4)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) ([CuSO4])^(-1) [K2SO4] [Cu(MnO4)2] = ([K2SO4] [Cu(MnO4)2])/(([KMnO4])^2 [CuSO4])

Construct the rate of reaction expression for: KMnO_4 + CuSO_4 ⟶ K_2SO_4 + Cu(MnO4)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 KMnO_4 + CuSO_4 ⟶ K_2SO_4 + Cu(MnO4)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 KMnO_4 | 2 | -2 CuSO_4 | 1 | -1 K_2SO_4 | 1 | 1 Cu(MnO4)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 KMnO_4 | 2 | -2 | -1/2 (Δ[KMnO4])/(Δt) CuSO_4 | 1 | -1 | -(Δ[CuSO4])/(Δt) K_2SO_4 | 1 | 1 | (Δ[K2SO4])/(Δt) Cu(MnO4)2 | 1 | 1 | (Δ[Cu(MnO4)2])/(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) = -(Δ[CuSO4])/(Δt) = (Δ[K2SO4])/(Δt) = (Δ[Cu(MnO4)2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| potassium permanganate | copper(II) sulfate | potassium sulfate | Cu(MnO4)2 formula | KMnO_4 | CuSO_4 | K_2SO_4 | Cu(MnO4)2 Hill formula | KMnO_4 | CuO_4S | K_2O_4S | CuMn2O8 name | potassium permanganate | copper(II) sulfate | potassium sulfate | IUPAC name | potassium permanganate | copper sulfate | dipotassium sulfate |

| potassium permanganate | copper(II) sulfate | potassium sulfate | Cu(MnO4)2 molar mass | 158.03 g/mol | 159.6 g/mol | 174.25 g/mol | 301.41 g/mol phase | solid (at STP) | solid (at STP) | | melting point | 240 °C | 200 °C | | density | 1 g/cm^3 | 3.603 g/cm^3 | | solubility in water | | | soluble | odor | odorless | | |