NH3 + CuO = H2O + Cu + N2

NH_3 (ammonia) + CuO (cupric oxide) ⟶ H_2O (water) + Cu (copper) + N_2 (nitrogen)

Balance the chemical equation algebraically: NH_3 + CuO ⟶ H_2O + Cu + N_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 NH_3 + c_2 CuO ⟶ c_3 H_2O + c_4 Cu + c_5 N_2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, N, Cu and O: H: | 3 c_1 = 2 c_3 N: | c_1 = 2 c_5 Cu: | c_2 = c_4 O: | c_2 = c_3 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_5 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 3 c_3 = 3 c_4 = 3 c_5 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 NH_3 + 3 CuO ⟶ 3 H_2O + 3 Cu + N_2

+ ⟶ + +

ammonia + cupric oxide ⟶ water + copper + nitrogen

| ammonia | cupric oxide | water | copper | nitrogen molecular enthalpy | -45.9 kJ/mol | -157.3 kJ/mol | -285.8 kJ/mol | 0 kJ/mol | 0 kJ/mol total enthalpy | -91.8 kJ/mol | -471.9 kJ/mol | -857.5 kJ/mol | 0 kJ/mol | 0 kJ/mol | H_initial = -563.7 kJ/mol | | H_final = -857.5 kJ/mol | | ΔH_rxn^0 | -857.5 kJ/mol - -563.7 kJ/mol = -293.8 kJ/mol (exothermic) | | | |

| ammonia | cupric oxide | water | copper | nitrogen molecular entropy | 193 J/(mol K) | 43 J/(mol K) | 69.91 J/(mol K) | 33 J/(mol K) | 192 J/(mol K) total entropy | 386 J/(mol K) | 129 J/(mol K) | 209.7 J/(mol K) | 99 J/(mol K) | 192 J/(mol K) | S_initial = 515 J/(mol K) | | S_final = 500.7 J/(mol K) | | ΔS_rxn^0 | 500.7 J/(mol K) - 515 J/(mol K) = -14.27 J/(mol K) (exoentropic) | | | |

Construct the equilibrium constant, K, expression for: NH_3 + CuO ⟶ H_2O + 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: 2 NH_3 + 3 CuO ⟶ 3 H_2O + 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 NH_3 | 2 | -2 CuO | 3 | -3 H_2O | 3 | 3 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 NH_3 | 2 | -2 | ([NH3])^(-2) CuO | 3 | -3 | ([CuO])^(-3) H_2O | 3 | 3 | ([H2O])^3 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 = ([NH3])^(-2) ([CuO])^(-3) ([H2O])^3 ([Cu])^3 [N2] = (([H2O])^3 ([Cu])^3 [N2])/(([NH3])^2 ([CuO])^3)

Construct the rate of reaction expression for: NH_3 + CuO ⟶ H_2O + 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: 2 NH_3 + 3 CuO ⟶ 3 H_2O + 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 NH_3 | 2 | -2 CuO | 3 | -3 H_2O | 3 | 3 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 NH_3 | 2 | -2 | -1/2 (Δ[NH3])/(Δt) CuO | 3 | -3 | -1/3 (Δ[CuO])/(Δt) H_2O | 3 | 3 | 1/3 (Δ[H2O])/(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 = -1/2 (Δ[NH3])/(Δt) = -1/3 (Δ[CuO])/(Δt) = 1/3 (Δ[H2O])/(Δt) = 1/3 (Δ[Cu])/(Δt) = (Δ[N2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| ammonia | cupric oxide | water | copper | nitrogen formula | NH_3 | CuO | H_2O | Cu | N_2 Hill formula | H_3N | CuO | H_2O | Cu | N_2 name | ammonia | cupric oxide | water | copper | nitrogen IUPAC name | ammonia | | water | copper | molecular nitrogen

| ammonia | cupric oxide | water | copper | nitrogen molar mass | 17.031 g/mol | 79.545 g/mol | 18.015 g/mol | 63.546 g/mol | 28.014 g/mol phase | gas (at STP) | solid (at STP) | liquid (at STP) | solid (at STP) | gas (at STP) melting point | -77.73 °C | 1326 °C | 0 °C | 1083 °C | -210 °C boiling point | -33.33 °C | 2000 °C | 99.9839 °C | 2567 °C | -195.79 °C density | 6.96×10^-4 g/cm^3 (at 25 °C) | 6.315 g/cm^3 | 1 g/cm^3 | 8.96 g/cm^3 | 0.001251 g/cm^3 (at 0 °C) solubility in water | | insoluble | | insoluble | insoluble surface tension | 0.0234 N/m | | 0.0728 N/m | | 0.0066 N/m dynamic viscosity | 1.009×10^-5 Pa s (at 25 °C) | | 8.9×10^-4 Pa s (at 25 °C) | | 1.78×10^-5 Pa s (at 25 °C) odor | | | odorless | odorless | odorless