KMnO4 + K2CO3 = O2 + CO2 + K2MnO4

KMnO_4 potassium permanganate + K_2CO_3 pearl ash ⟶ O_2 oxygen + CO_2 carbon dioxide + K_2MnO_4 potassium manganate

Balance the chemical equation algebraically: KMnO_4 + K_2CO_3 ⟶ O_2 + CO_2 + K_2MnO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 KMnO_4 + c_2 K_2CO_3 ⟶ c_3 O_2 + c_4 CO_2 + c_5 K_2MnO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for K, Mn, O and C: K: | c_1 + 2 c_2 = 2 c_5 Mn: | c_1 = c_5 O: | 4 c_1 + 3 c_2 = 2 c_3 + 2 c_4 + 4 c_5 C: | c_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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 4 c_2 = 2 c_3 = 1 c_4 = 2 c_5 = 4 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 KMnO_4 + 2 K_2CO_3 ⟶ O_2 + 2 CO_2 + 4 K_2MnO_4

+ ⟶ + +

potassium permanganate + pearl ash ⟶ oxygen + carbon dioxide + potassium manganate

Construct the equilibrium constant, K, expression for: KMnO_4 + K_2CO_3 ⟶ O_2 + CO_2 + K_2MnO_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: 4 KMnO_4 + 2 K_2CO_3 ⟶ O_2 + 2 CO_2 + 4 K_2MnO_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 | 4 | -4 K_2CO_3 | 2 | -2 O_2 | 1 | 1 CO_2 | 2 | 2 K_2MnO_4 | 4 | 4 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression KMnO_4 | 4 | -4 | ([KMnO4])^(-4) K_2CO_3 | 2 | -2 | ([K2CO3])^(-2) O_2 | 1 | 1 | [O2] CO_2 | 2 | 2 | ([CO2])^2 K_2MnO_4 | 4 | 4 | ([K2MnO4])^4 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])^(-4) ([K2CO3])^(-2) [O2] ([CO2])^2 ([K2MnO4])^4 = ([O2] ([CO2])^2 ([K2MnO4])^4)/(([KMnO4])^4 ([K2CO3])^2)

Construct the rate of reaction expression for: KMnO_4 + K_2CO_3 ⟶ O_2 + CO_2 + K_2MnO_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: 4 KMnO_4 + 2 K_2CO_3 ⟶ O_2 + 2 CO_2 + 4 K_2MnO_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 | 4 | -4 K_2CO_3 | 2 | -2 O_2 | 1 | 1 CO_2 | 2 | 2 K_2MnO_4 | 4 | 4 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 | 4 | -4 | -1/4 (Δ[KMnO4])/(Δt) K_2CO_3 | 2 | -2 | -1/2 (Δ[K2CO3])/(Δt) O_2 | 1 | 1 | (Δ[O2])/(Δt) CO_2 | 2 | 2 | 1/2 (Δ[CO2])/(Δt) K_2MnO_4 | 4 | 4 | 1/4 (Δ[K2MnO4])/(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[KMnO4])/(Δt) = -1/2 (Δ[K2CO3])/(Δt) = (Δ[O2])/(Δt) = 1/2 (Δ[CO2])/(Δt) = 1/4 (Δ[K2MnO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| potassium permanganate | pearl ash | oxygen | carbon dioxide | potassium manganate formula | KMnO_4 | K_2CO_3 | O_2 | CO_2 | K_2MnO_4 Hill formula | KMnO_4 | CK_2O_3 | O_2 | CO_2 | K_2MnO_4 name | potassium permanganate | pearl ash | oxygen | carbon dioxide | potassium manganate IUPAC name | potassium permanganate | dipotassium carbonate | molecular oxygen | carbon dioxide | dipotassium dioxido-dioxomanganese

| potassium permanganate | pearl ash | oxygen | carbon dioxide | potassium manganate molar mass | 158.03 g/mol | 138.2 g/mol | 31.998 g/mol | 44.009 g/mol | 197.13 g/mol phase | solid (at STP) | solid (at STP) | gas (at STP) | gas (at STP) | solid (at STP) melting point | 240 °C | 891 °C | -218 °C | -56.56 °C (at triple point) | 190 °C boiling point | | | -183 °C | -78.5 °C (at sublimation point) | density | 1 g/cm^3 | 2.43 g/cm^3 | 0.001429 g/cm^3 (at 0 °C) | 0.00184212 g/cm^3 (at 20 °C) | solubility in water | | soluble | | | decomposes surface tension | | | 0.01347 N/m | | dynamic viscosity | | | 2.055×10^-5 Pa s (at 25 °C) | 1.491×10^-5 Pa s (at 25 °C) | odor | odorless | | odorless | odorless |