KOH + Se = H2O + K2SeO3 + K2Se

KOH potassium hydroxide + Se gray selenium ⟶ H_2O water + K_2SeO_3 selenious acid, dipotassium salt + K_2Se potassium selenide

Balance the chemical equation algebraically: KOH + Se ⟶ H_2O + K_2SeO_3 + K_2Se Add stoichiometric coefficients, c_i, to the reactants and products: c_1 KOH + c_2 Se ⟶ c_3 H_2O + c_4 K_2SeO_3 + c_5 K_2Se Set the number of atoms in the reactants equal to the number of atoms in the products for H, K, O and Se: H: | c_1 = 2 c_3 K: | c_1 = 2 c_4 + 2 c_5 O: | c_1 = c_3 + 3 c_4 Se: | c_2 = c_4 + c_5 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_4 = 1 and solve the system of equations for the remaining coefficients: c_1 = 6 c_2 = 3 c_3 = 3 c_4 = 1 c_5 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 6 KOH + 3 Se ⟶ 3 H_2O + K_2SeO_3 + 2 K_2Se

+ ⟶ + +

potassium hydroxide + gray selenium ⟶ water + selenious acid, dipotassium salt + potassium selenide

Construct the equilibrium constant, K, expression for: KOH + Se ⟶ H_2O + K_2SeO_3 + K_2Se 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: 6 KOH + 3 Se ⟶ 3 H_2O + K_2SeO_3 + 2 K_2Se 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 KOH | 6 | -6 Se | 3 | -3 H_2O | 3 | 3 K_2SeO_3 | 1 | 1 K_2Se | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression KOH | 6 | -6 | ([KOH])^(-6) Se | 3 | -3 | ([Se])^(-3) H_2O | 3 | 3 | ([H2O])^3 K_2SeO_3 | 1 | 1 | [K2SeO3] K_2Se | 2 | 2 | ([K2Se])^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 = ([KOH])^(-6) ([Se])^(-3) ([H2O])^3 [K2SeO3] ([K2Se])^2 = (([H2O])^3 [K2SeO3] ([K2Se])^2)/(([KOH])^6 ([Se])^3)

Construct the rate of reaction expression for: KOH + Se ⟶ H_2O + K_2SeO_3 + K_2Se 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: 6 KOH + 3 Se ⟶ 3 H_2O + K_2SeO_3 + 2 K_2Se 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 KOH | 6 | -6 Se | 3 | -3 H_2O | 3 | 3 K_2SeO_3 | 1 | 1 K_2Se | 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 KOH | 6 | -6 | -1/6 (Δ[KOH])/(Δt) Se | 3 | -3 | -1/3 (Δ[Se])/(Δt) H_2O | 3 | 3 | 1/3 (Δ[H2O])/(Δt) K_2SeO_3 | 1 | 1 | (Δ[K2SeO3])/(Δt) K_2Se | 2 | 2 | 1/2 (Δ[K2Se])/(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 = -1/6 (Δ[KOH])/(Δt) = -1/3 (Δ[Se])/(Δt) = 1/3 (Δ[H2O])/(Δt) = (Δ[K2SeO3])/(Δt) = 1/2 (Δ[K2Se])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| potassium hydroxide | gray selenium | water | selenious acid, dipotassium salt | potassium selenide formula | KOH | Se | H_2O | K_2SeO_3 | K_2Se Hill formula | HKO | Se | H_2O | K_2O_3Se | K_2Se name | potassium hydroxide | gray selenium | water | selenious acid, dipotassium salt | potassium selenide IUPAC name | potassium hydroxide | selenium | water | | dipotassium selenium(-2) anion

| potassium hydroxide | gray selenium | water | selenious acid, dipotassium salt | potassium selenide molar mass | 56.105 g/mol | 78.971 g/mol | 18.015 g/mol | 205.16 g/mol | 157.17 g/mol phase | solid (at STP) | solid (at STP) | liquid (at STP) | solid (at STP) | solid (at STP) melting point | 406 °C | 217 °C | 0 °C | 875 °C | 800 °C boiling point | 1327 °C | 684.9 °C | 99.9839 °C | | density | 2.044 g/cm^3 | 4.81 g/cm^3 | 1 g/cm^3 | | 2.29 g/cm^3 solubility in water | soluble | insoluble | | soluble | surface tension | | 0.1055 N/m | 0.0728 N/m | | dynamic viscosity | 0.001 Pa s (at 550 °C) | 0.221 Pa s (at 220 °C) | 8.9×10^-4 Pa s (at 25 °C) | | odor | | | odorless | |