CuO + NH4Cl = H2O + HCl + Cu + N2

CuO cupric oxide + NH_4Cl ammonium chloride ⟶ H_2O water + HCl hydrogen chloride + Cu copper + N_2 nitrogen

Balance the chemical equation algebraically: CuO + NH_4Cl ⟶ H_2O + HCl + Cu + N_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 CuO + c_2 NH_4Cl ⟶ c_3 H_2O + c_4 HCl + c_5 Cu + c_6 N_2 Set the number of atoms in the reactants equal to the number of atoms in the products for Cu, O, Cl, H and N: Cu: | c_1 = c_5 O: | c_1 = c_3 Cl: | c_2 = c_4 H: | 4 c_2 = 2 c_3 + c_4 N: | c_2 = 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_6 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3 c_2 = 2 c_3 = 3 c_4 = 2 c_5 = 3 c_6 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 CuO + 2 NH_4Cl ⟶ 3 H_2O + 2 HCl + 3 Cu + N_2

+ ⟶ + + +

cupric oxide + ammonium chloride ⟶ water + hydrogen chloride + copper + nitrogen

| cupric oxide | ammonium chloride | water | hydrogen chloride | copper | nitrogen molecular enthalpy | -157.3 kJ/mol | -314.4 kJ/mol | -285.8 kJ/mol | -92.3 kJ/mol | 0 kJ/mol | 0 kJ/mol total enthalpy | -471.9 kJ/mol | -628.8 kJ/mol | -857.5 kJ/mol | -184.6 kJ/mol | 0 kJ/mol | 0 kJ/mol | H_initial = -1101 kJ/mol | | H_final = -1042 kJ/mol | | | ΔH_rxn^0 | -1042 kJ/mol - -1101 kJ/mol = 58.61 kJ/mol (endothermic) | | | | |

| cupric oxide | ammonium chloride | water | hydrogen chloride | copper | nitrogen molecular entropy | 43 J/(mol K) | 96 J/(mol K) | 69.91 J/(mol K) | 187 J/(mol K) | 33 J/(mol K) | 192 J/(mol K) total entropy | 129 J/(mol K) | 192 J/(mol K) | 209.7 J/(mol K) | 374 J/(mol K) | 99 J/(mol K) | 192 J/(mol K) | S_initial = 321 J/(mol K) | | S_final = 874.7 J/(mol K) | | | ΔS_rxn^0 | 874.7 J/(mol K) - 321 J/(mol K) = 553.7 J/(mol K) (endoentropic) | | | | |

Construct the equilibrium constant, K, expression for: CuO + NH_4Cl ⟶ H_2O + HCl + Cu + N_2 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: 3 CuO + 2 NH_4Cl ⟶ 3 H_2O + 2 HCl + 3 Cu + N_2 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 CuO | 3 | -3 NH_4Cl | 2 | -2 H_2O | 3 | 3 HCl | 2 | 2 Cu | 3 | 3 N_2 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression CuO | 3 | -3 | ([CuO])^(-3) NH_4Cl | 2 | -2 | ([NH4Cl])^(-2) H_2O | 3 | 3 | ([H2O])^3 HCl | 2 | 2 | ([HCl])^2 Cu | 3 | 3 | ([Cu])^3 N_2 | 1 | 1 | [N2] 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 = ([CuO])^(-3) ([NH4Cl])^(-2) ([H2O])^3 ([HCl])^2 ([Cu])^3 [N2] = (([H2O])^3 ([HCl])^2 ([Cu])^3 [N2])/(([CuO])^3 ([NH4Cl])^2)

Construct the rate of reaction expression for: CuO + NH_4Cl ⟶ H_2O + HCl + Cu + N_2 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: 3 CuO + 2 NH_4Cl ⟶ 3 H_2O + 2 HCl + 3 Cu + N_2 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 CuO | 3 | -3 NH_4Cl | 2 | -2 H_2O | 3 | 3 HCl | 2 | 2 Cu | 3 | 3 N_2 | 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 CuO | 3 | -3 | -1/3 (Δ[CuO])/(Δt) NH_4Cl | 2 | -2 | -1/2 (Δ[NH4Cl])/(Δt) H_2O | 3 | 3 | 1/3 (Δ[H2O])/(Δt) HCl | 2 | 2 | 1/2 (Δ[HCl])/(Δt) Cu | 3 | 3 | 1/3 (Δ[Cu])/(Δt) N_2 | 1 | 1 | (Δ[N2])/(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 = -1/3 (Δ[CuO])/(Δt) = -1/2 (Δ[NH4Cl])/(Δt) = 1/3 (Δ[H2O])/(Δt) = 1/2 (Δ[HCl])/(Δt) = 1/3 (Δ[Cu])/(Δt) = (Δ[N2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| cupric oxide | ammonium chloride | water | hydrogen chloride | copper | nitrogen formula | CuO | NH_4Cl | H_2O | HCl | Cu | N_2 Hill formula | CuO | ClH_4N | H_2O | ClH | Cu | N_2 name | cupric oxide | ammonium chloride | water | hydrogen chloride | copper | nitrogen IUPAC name | | ammonium chloride | water | hydrogen chloride | copper | molecular nitrogen