K + K2O2 = K2O

K potassium + K_2O_2 potassium peroxide ⟶ K_2O potassium oxide

Balance the chemical equation algebraically: K + K_2O_2 ⟶ K_2O Add stoichiometric coefficients, c_i, to the reactants and products: c_1 K + c_2 K_2O_2 ⟶ c_3 K_2O Set the number of atoms in the reactants equal to the number of atoms in the products for K and O: K: | c_1 + 2 c_2 = 2 c_3 O: | 2 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 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 K + K_2O_2 ⟶ 2 K_2O

+ ⟶

potassium + potassium peroxide ⟶ potassium oxide

Construct the equilibrium constant, K, expression for: K + K_2O_2 ⟶ K_2O 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 K + K_2O_2 ⟶ 2 K_2O 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 | 2 | -2 K_2O_2 | 1 | -1 K_2O | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression K | 2 | -2 | ([K])^(-2) K_2O_2 | 1 | -1 | ([K2O2])^(-1) K_2O | 2 | 2 | ([K2O])^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 = ([K])^(-2) ([K2O2])^(-1) ([K2O])^2 = ([K2O])^2/(([K])^2 [K2O2])

Construct the rate of reaction expression for: K + K_2O_2 ⟶ K_2O 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 K + K_2O_2 ⟶ 2 K_2O 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 | 2 | -2 K_2O_2 | 1 | -1 K_2O | 2 | 2 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 | 2 | -2 | -1/2 (Δ[K])/(Δt) K_2O_2 | 1 | -1 | -(Δ[K2O2])/(Δt) K_2O | 2 | 2 | 1/2 (Δ[K2O])/(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[K])/(Δt) = -(Δ[K2O2])/(Δt) = 1/2 (Δ[K2O])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| potassium | potassium peroxide | potassium oxide formula | K | K_2O_2 | K_2O name | potassium | potassium peroxide | potassium oxide IUPAC name | potassium | dipotassium peroxide | dipotassium oxygen(2-)

| potassium | potassium peroxide | potassium oxide molar mass | 39.0983 g/mol | 110.19 g/mol | 94.196 g/mol phase | solid (at STP) | solid (at STP) | melting point | 64 °C | 490 °C | boiling point | 760 °C | | density | 0.86 g/cm^3 | 1 g/cm^3 | solubility in water | reacts | reacts |