NH3 + C + K2CO3 = H2O + KCN

NH_3 ammonia + C activated charcoal + K_2CO_3 pearl ash ⟶ H_2O water + KCN potassium cyanide

Balance the chemical equation algebraically: NH_3 + C + K_2CO_3 ⟶ H_2O + KCN Add stoichiometric coefficients, c_i, to the reactants and products: c_1 NH_3 + c_2 C + c_3 K_2CO_3 ⟶ c_4 H_2O + c_5 KCN Set the number of atoms in the reactants equal to the number of atoms in the products for H, N, C, K and O: H: | 3 c_1 = 2 c_4 N: | c_1 = c_5 C: | c_2 + c_3 = c_5 K: | 2 c_3 = c_5 O: | 3 c_3 = 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 1 c_3 = 1 c_4 = 3 c_5 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 NH_3 + C + K_2CO_3 ⟶ 3 H_2O + 2 KCN

+ + ⟶ +

ammonia + activated charcoal + pearl ash ⟶ water + potassium cyanide

Construct the equilibrium constant, K, expression for: NH_3 + C + K_2CO_3 ⟶ H_2O + KCN 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 NH_3 + C + K_2CO_3 ⟶ 3 H_2O + 2 KCN 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 NH_3 | 2 | -2 C | 1 | -1 K_2CO_3 | 1 | -1 H_2O | 3 | 3 KCN | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression NH_3 | 2 | -2 | ([NH3])^(-2) C | 1 | -1 | ([C])^(-1) K_2CO_3 | 1 | -1 | ([K2CO3])^(-1) H_2O | 3 | 3 | ([H2O])^3 KCN | 2 | 2 | ([KCN])^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 = ([NH3])^(-2) ([C])^(-1) ([K2CO3])^(-1) ([H2O])^3 ([KCN])^2 = (([H2O])^3 ([KCN])^2)/(([NH3])^2 [C] [K2CO3])

Construct the rate of reaction expression for: NH_3 + C + K_2CO_3 ⟶ H_2O + KCN 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 NH_3 + C + K_2CO_3 ⟶ 3 H_2O + 2 KCN 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 NH_3 | 2 | -2 C | 1 | -1 K_2CO_3 | 1 | -1 H_2O | 3 | 3 KCN | 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 NH_3 | 2 | -2 | -1/2 (Δ[NH3])/(Δt) C | 1 | -1 | -(Δ[C])/(Δt) K_2CO_3 | 1 | -1 | -(Δ[K2CO3])/(Δt) H_2O | 3 | 3 | 1/3 (Δ[H2O])/(Δt) KCN | 2 | 2 | 1/2 (Δ[KCN])/(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[NH3])/(Δt) = -(Δ[C])/(Δt) = -(Δ[K2CO3])/(Δt) = 1/3 (Δ[H2O])/(Δt) = 1/2 (Δ[KCN])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| ammonia | activated charcoal | pearl ash | water | potassium cyanide formula | NH_3 | C | K_2CO_3 | H_2O | KCN Hill formula | H_3N | C | CK_2O_3 | H_2O | CKN name | ammonia | activated charcoal | pearl ash | water | potassium cyanide IUPAC name | ammonia | carbon | dipotassium carbonate | water | potassium cyanide

| ammonia | activated charcoal | pearl ash | water | potassium cyanide molar mass | 17.031 g/mol | 12.011 g/mol | 138.2 g/mol | 18.015 g/mol | 65.116 g/mol phase | gas (at STP) | solid (at STP) | solid (at STP) | liquid (at STP) | melting point | -77.73 °C | 3550 °C | 891 °C | 0 °C | boiling point | -33.33 °C | 4027 °C | | 99.9839 °C | density | 6.96×10^-4 g/cm^3 (at 25 °C) | 2.26 g/cm^3 | 2.43 g/cm^3 | 1 g/cm^3 | solubility in water | | insoluble | soluble | | surface tension | 0.0234 N/m | | | 0.0728 N/m | dynamic viscosity | 1.009×10^-5 Pa s (at 25 °C) | | | 8.9×10^-4 Pa s (at 25 °C) | odor | | | | odorless |