H2O + K = H2 + K2O

H_2O water + K potassium ⟶ H_2 hydrogen + K_2O potassium oxide

Balance the chemical equation algebraically: H_2O + K ⟶ H_2 + K_2O Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 K ⟶ c_3 H_2 + c_4 K_2O Set the number of atoms in the reactants equal to the number of atoms in the products for H, O and K: H: | 2 c_1 = 2 c_3 O: | c_1 = c_4 K: | c_2 = 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 2 c_3 = 1 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | H_2O + 2 K ⟶ H_2 + K_2O

+ ⟶ +

water + potassium ⟶ hydrogen + potassium oxide

Construct the equilibrium constant, K, expression for: H_2O + K ⟶ H_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: H_2O + 2 K ⟶ H_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 H_2O | 1 | -1 K | 2 | -2 H_2 | 1 | 1 K_2O | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 1 | -1 | ([H2O])^(-1) K | 2 | -2 | ([K])^(-2) H_2 | 1 | 1 | [H2] K_2O | 1 | 1 | [K2O] 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 = ([H2O])^(-1) ([K])^(-2) [H2] [K2O] = ([H2] [K2O])/([H2O] ([K])^2)

Construct the rate of reaction expression for: H_2O + K ⟶ H_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: H_2O + 2 K ⟶ H_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 H_2O | 1 | -1 K | 2 | -2 H_2 | 1 | 1 K_2O | 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 H_2O | 1 | -1 | -(Δ[H2O])/(Δt) K | 2 | -2 | -1/2 (Δ[K])/(Δt) H_2 | 1 | 1 | (Δ[H2])/(Δt) K_2O | 1 | 1 | (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 = -(Δ[H2O])/(Δt) = -1/2 (Δ[K])/(Δt) = (Δ[H2])/(Δt) = (Δ[K2O])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | potassium | hydrogen | potassium oxide formula | H_2O | K | H_2 | K_2O name | water | potassium | hydrogen | potassium oxide IUPAC name | water | potassium | molecular hydrogen | dipotassium oxygen(2-)

| water | potassium | hydrogen | potassium oxide molar mass | 18.015 g/mol | 39.0983 g/mol | 2.016 g/mol | 94.196 g/mol phase | liquid (at STP) | solid (at STP) | gas (at STP) | melting point | 0 °C | 64 °C | -259.2 °C | boiling point | 99.9839 °C | 760 °C | -252.8 °C | density | 1 g/cm^3 | 0.86 g/cm^3 | 8.99×10^-5 g/cm^3 (at 0 °C) | solubility in water | | reacts | | surface tension | 0.0728 N/m | | | dynamic viscosity | 8.9×10^-4 Pa s (at 25 °C) | | 8.9×10^-6 Pa s (at 25 °C) | odor | odorless | | odorless |