KMnO4 + AgNO3 = KNO3 + AgMnO4

KMnO_4 potassium permanganate + AgNO_3 silver nitrate ⟶ KNO_3 potassium nitrate + AgMnO_4 silver(I) permanganate

Balance the chemical equation algebraically: KMnO_4 + AgNO_3 ⟶ KNO_3 + AgMnO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 KMnO_4 + c_2 AgNO_3 ⟶ c_3 KNO_3 + c_4 AgMnO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for K, Mn, O, Ag and N: K: | c_1 = c_3 Mn: | c_1 = c_4 O: | 4 c_1 + 3 c_2 = 3 c_3 + 4 c_4 Ag: | c_2 = c_4 N: | 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_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: | | KMnO_4 + AgNO_3 ⟶ KNO_3 + AgMnO_4

+ ⟶ +

potassium permanganate + silver nitrate ⟶ potassium nitrate + silver(I) permanganate

Construct the equilibrium constant, K, expression for: KMnO_4 + AgNO_3 ⟶ KNO_3 + AgMnO_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: KMnO_4 + AgNO_3 ⟶ KNO_3 + AgMnO_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 | 1 | -1 AgNO_3 | 1 | -1 KNO_3 | 1 | 1 AgMnO_4 | 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 | 1 | -1 | ([KMnO4])^(-1) AgNO_3 | 1 | -1 | ([AgNO3])^(-1) KNO_3 | 1 | 1 | [KNO3] AgMnO_4 | 1 | 1 | [AgMnO4] 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])^(-1) ([AgNO3])^(-1) [KNO3] [AgMnO4] = ([KNO3] [AgMnO4])/([KMnO4] [AgNO3])

Construct the rate of reaction expression for: KMnO_4 + AgNO_3 ⟶ KNO_3 + AgMnO_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: KMnO_4 + AgNO_3 ⟶ KNO_3 + AgMnO_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 | 1 | -1 AgNO_3 | 1 | -1 KNO_3 | 1 | 1 AgMnO_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 KMnO_4 | 1 | -1 | -(Δ[KMnO4])/(Δt) AgNO_3 | 1 | -1 | -(Δ[AgNO3])/(Δt) KNO_3 | 1 | 1 | (Δ[KNO3])/(Δt) AgMnO_4 | 1 | 1 | (Δ[AgMnO4])/(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[KMnO4])/(Δt) = -(Δ[AgNO3])/(Δt) = (Δ[KNO3])/(Δt) = (Δ[AgMnO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| potassium permanganate | silver nitrate | potassium nitrate | silver(I) permanganate formula | KMnO_4 | AgNO_3 | KNO_3 | AgMnO_4 name | potassium permanganate | silver nitrate | potassium nitrate | silver(I) permanganate

| potassium permanganate | silver nitrate | potassium nitrate | silver(I) permanganate molar mass | 158.03 g/mol | 169.87 g/mol | 101.1 g/mol | 226.802 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | melting point | 240 °C | 212 °C | 334 °C | density | 1 g/cm^3 | | | solubility in water | | soluble | soluble | odor | odorless | odorless | odorless |