K + Al(MnO4)3 = KMnO4 + Al

K potassium + Al(MnO4)3 ⟶ KMnO_4 potassium permanganate + Al aluminum

Balance the chemical equation algebraically: K + Al(MnO4)3 ⟶ KMnO_4 + Al Add stoichiometric coefficients, c_i, to the reactants and products: c_1 K + c_2 Al(MnO4)3 ⟶ c_3 KMnO_4 + c_4 Al Set the number of atoms in the reactants equal to the number of atoms in the products for K, Al, Mn and O: K: | c_1 = c_3 Al: | c_2 = c_4 Mn: | 3 c_2 = c_3 O: | 12 c_2 = 4 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 = 3 c_2 = 1 c_3 = 3 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 K + Al(MnO4)3 ⟶ 3 KMnO_4 + Al

+ Al(MnO4)3 ⟶ +

potassium + Al(MnO4)3 ⟶ potassium permanganate + aluminum

Construct the equilibrium constant, K, expression for: K + Al(MnO4)3 ⟶ KMnO_4 + Al 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: 3 K + Al(MnO4)3 ⟶ 3 KMnO_4 + Al 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 K | 3 | -3 Al(MnO4)3 | 1 | -1 KMnO_4 | 3 | 3 Al | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression K | 3 | -3 | ([K])^(-3) Al(MnO4)3 | 1 | -1 | ([Al(MnO4)3])^(-1) KMnO_4 | 3 | 3 | ([KMnO4])^3 Al | 1 | 1 | [Al] 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 = ([K])^(-3) ([Al(MnO4)3])^(-1) ([KMnO4])^3 [Al] = (([KMnO4])^3 [Al])/(([K])^3 [Al(MnO4)3])

Construct the rate of reaction expression for: K + Al(MnO4)3 ⟶ KMnO_4 + Al 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: 3 K + Al(MnO4)3 ⟶ 3 KMnO_4 + Al 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 K | 3 | -3 Al(MnO4)3 | 1 | -1 KMnO_4 | 3 | 3 Al | 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 K | 3 | -3 | -1/3 (Δ[K])/(Δt) Al(MnO4)3 | 1 | -1 | -(Δ[Al(MnO4)3])/(Δt) KMnO_4 | 3 | 3 | 1/3 (Δ[KMnO4])/(Δt) Al | 1 | 1 | (Δ[Al])/(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 = -1/3 (Δ[K])/(Δt) = -(Δ[Al(MnO4)3])/(Δt) = 1/3 (Δ[KMnO4])/(Δt) = (Δ[Al])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| potassium | Al(MnO4)3 | potassium permanganate | aluminum formula | K | Al(MnO4)3 | KMnO_4 | Al Hill formula | K | AlMn3O12 | KMnO_4 | Al name | potassium | | potassium permanganate | aluminum

| potassium | Al(MnO4)3 | potassium permanganate | aluminum molar mass | 39.0983 g/mol | 383.78 g/mol | 158.03 g/mol | 26.9815385 g/mol phase | solid (at STP) | | solid (at STP) | solid (at STP) melting point | 64 °C | | 240 °C | 660.4 °C boiling point | 760 °C | | | 2460 °C density | 0.86 g/cm^3 | | 1 g/cm^3 | 2.7 g/cm^3 solubility in water | reacts | | | insoluble surface tension | | | | 0.817 N/m dynamic viscosity | | | | 1.5×10^-4 Pa s (at 760 °C) odor | | | odorless | odorless