KOH + KClO2 + (CN)2 = H2O + KCl + N2 + K2CO3

KOH potassium hydroxide + KClO2 + C_2N_2 cyanogen ⟶ H_2O water + KCl potassium chloride + N_2 nitrogen + K_2CO_3 pearl ash

Balance the chemical equation algebraically: KOH + KClO2 + C_2N_2 ⟶ H_2O + KCl + N_2 + K_2CO_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 KOH + c_2 KClO2 + c_3 C_2N_2 ⟶ c_4 H_2O + c_5 KCl + c_6 N_2 + c_7 K_2CO_3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, K, O, Cl, C and N: H: | c_1 = 2 c_4 K: | c_1 + c_2 = c_5 + 2 c_7 O: | c_1 + 2 c_2 = c_4 + 3 c_7 Cl: | c_2 = c_5 C: | 2 c_3 = c_7 N: | 2 c_3 = 2 c_6 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 = 2 c_6 = 1 c_7 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 KOH + 2 KClO2 + C_2N_2 ⟶ 2 H_2O + 2 KCl + N_2 + 2 K_2CO_3

+ KClO2 + ⟶ + + +

potassium hydroxide + KClO2 + cyanogen ⟶ water + potassium chloride + nitrogen + pearl ash

Construct the equilibrium constant, K, expression for: KOH + KClO2 + C_2N_2 ⟶ H_2O + KCl + N_2 + K_2CO_3 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 KOH + 2 KClO2 + C_2N_2 ⟶ 2 H_2O + 2 KCl + N_2 + 2 K_2CO_3 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 | 4 | -4 KClO2 | 2 | -2 C_2N_2 | 1 | -1 H_2O | 2 | 2 KCl | 2 | 2 N_2 | 1 | 1 K_2CO_3 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression KOH | 4 | -4 | ([KOH])^(-4) KClO2 | 2 | -2 | ([KClO2])^(-2) C_2N_2 | 1 | -1 | ([C2N2])^(-1) H_2O | 2 | 2 | ([H2O])^2 KCl | 2 | 2 | ([KCl])^2 N_2 | 1 | 1 | [N2] K_2CO_3 | 2 | 2 | ([K2CO3])^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])^(-4) ([KClO2])^(-2) ([C2N2])^(-1) ([H2O])^2 ([KCl])^2 [N2] ([K2CO3])^2 = (([H2O])^2 ([KCl])^2 [N2] ([K2CO3])^2)/(([KOH])^4 ([KClO2])^2 [C2N2])

Construct the rate of reaction expression for: KOH + KClO2 + C_2N_2 ⟶ H_2O + KCl + N_2 + K_2CO_3 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 KOH + 2 KClO2 + C_2N_2 ⟶ 2 H_2O + 2 KCl + N_2 + 2 K_2CO_3 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 | 4 | -4 KClO2 | 2 | -2 C_2N_2 | 1 | -1 H_2O | 2 | 2 KCl | 2 | 2 N_2 | 1 | 1 K_2CO_3 | 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 | 4 | -4 | -1/4 (Δ[KOH])/(Δt) KClO2 | 2 | -2 | -1/2 (Δ[KClO2])/(Δt) C_2N_2 | 1 | -1 | -(Δ[C2N2])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(Δt) KCl | 2 | 2 | 1/2 (Δ[KCl])/(Δt) N_2 | 1 | 1 | (Δ[N2])/(Δt) K_2CO_3 | 2 | 2 | 1/2 (Δ[K2CO3])/(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[KOH])/(Δt) = -1/2 (Δ[KClO2])/(Δt) = -(Δ[C2N2])/(Δt) = 1/2 (Δ[H2O])/(Δt) = 1/2 (Δ[KCl])/(Δt) = (Δ[N2])/(Δt) = 1/2 (Δ[K2CO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| potassium hydroxide | KClO2 | cyanogen | water | potassium chloride | nitrogen | pearl ash formula | KOH | KClO2 | C_2N_2 | H_2O | KCl | N_2 | K_2CO_3 Hill formula | HKO | ClKO2 | C_2N_2 | H_2O | ClK | N_2 | CK_2O_3 name | potassium hydroxide | | cyanogen | water | potassium chloride | nitrogen | pearl ash IUPAC name | potassium hydroxide | | oxalonitrile | water | potassium chloride | molecular nitrogen | dipotassium carbonate

| potassium hydroxide | KClO2 | cyanogen | water | potassium chloride | nitrogen | pearl ash molar mass | 56.105 g/mol | 106.5 g/mol | 52.036 g/mol | 18.015 g/mol | 74.55 g/mol | 28.014 g/mol | 138.2 g/mol phase | solid (at STP) | | gas (at STP) | liquid (at STP) | solid (at STP) | gas (at STP) | solid (at STP) melting point | 406 °C | | | 0 °C | 770 °C | -210 °C | 891 °C boiling point | 1327 °C | | -21.17 °C | 99.9839 °C | 1420 °C | -195.79 °C | density | 2.044 g/cm^3 | | 0.002127 g/cm^3 (at 25 °C) | 1 g/cm^3 | 1.98 g/cm^3 | 0.001251 g/cm^3 (at 0 °C) | 2.43 g/cm^3 solubility in water | soluble | | very soluble | | soluble | insoluble | soluble surface tension | | | 0.02282 N/m | 0.0728 N/m | | 0.0066 N/m | dynamic viscosity | 0.001 Pa s (at 550 °C) | | 9.8×10^-6 Pa s (at 15 °C) | 8.9×10^-4 Pa s (at 25 °C) | | 1.78×10^-5 Pa s (at 25 °C) | odor | | | | odorless | odorless | odorless |