Cl2 + NH2NH2 = HCl + N2

Cl_2 chlorine + NH_2NH_2 diazane ⟶ HCl hydrogen chloride + N_2 nitrogen

Balance the chemical equation algebraically: Cl_2 + NH_2NH_2 ⟶ HCl + N_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Cl_2 + c_2 NH_2NH_2 ⟶ c_3 HCl + c_4 N_2 Set the number of atoms in the reactants equal to the number of atoms in the products for Cl, H and N: Cl: | 2 c_1 = c_3 H: | 4 c_2 = c_3 N: | 2 c_2 = 2 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 = 4 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 Cl_2 + NH_2NH_2 ⟶ 4 HCl + N_2

+ ⟶ +

chlorine + diazane ⟶ hydrogen chloride + nitrogen

| chlorine | diazane | hydrogen chloride | nitrogen molecular enthalpy | 0 kJ/mol | 50.6 kJ/mol | -92.3 kJ/mol | 0 kJ/mol total enthalpy | 0 kJ/mol | 50.6 kJ/mol | -369.2 kJ/mol | 0 kJ/mol | H_initial = 50.6 kJ/mol | | H_final = -369.2 kJ/mol | ΔH_rxn^0 | -369.2 kJ/mol - 50.6 kJ/mol = -419.8 kJ/mol (exothermic) | | |

| chlorine | diazane | hydrogen chloride | nitrogen molecular free energy | 0 kJ/mol | 149.3 kJ/mol | -95.3 kJ/mol | 0 kJ/mol total free energy | 0 kJ/mol | 149.3 kJ/mol | -381.2 kJ/mol | 0 kJ/mol | G_initial = 149.3 kJ/mol | | G_final = -381.2 kJ/mol | ΔG_rxn^0 | -381.2 kJ/mol - 149.3 kJ/mol = -530.5 kJ/mol (exergonic) | | |

| chlorine | diazane | hydrogen chloride | nitrogen molecular entropy | 223 J/(mol K) | 121 J/(mol K) | 187 J/(mol K) | 192 J/(mol K) total entropy | 446 J/(mol K) | 121 J/(mol K) | 748 J/(mol K) | 192 J/(mol K) | S_initial = 567 J/(mol K) | | S_final = 940 J/(mol K) | ΔS_rxn^0 | 940 J/(mol K) - 567 J/(mol K) = 373 J/(mol K) (endoentropic) | | |

Construct the equilibrium constant, K, expression for: Cl_2 + NH_2NH_2 ⟶ HCl + 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 Cl_2 + NH_2NH_2 ⟶ 4 HCl + 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 Cl_2 | 2 | -2 NH_2NH_2 | 1 | -1 HCl | 4 | 4 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 Cl_2 | 2 | -2 | ([Cl2])^(-2) NH_2NH_2 | 1 | -1 | ([NH2NH2])^(-1) HCl | 4 | 4 | ([HCl])^4 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 = ([Cl2])^(-2) ([NH2NH2])^(-1) ([HCl])^4 [N2] = (([HCl])^4 [N2])/(([Cl2])^2 [NH2NH2])

Construct the rate of reaction expression for: Cl_2 + NH_2NH_2 ⟶ HCl + 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 Cl_2 + NH_2NH_2 ⟶ 4 HCl + 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 Cl_2 | 2 | -2 NH_2NH_2 | 1 | -1 HCl | 4 | 4 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 Cl_2 | 2 | -2 | -1/2 (Δ[Cl2])/(Δt) NH_2NH_2 | 1 | -1 | -(Δ[NH2NH2])/(Δt) HCl | 4 | 4 | 1/4 (Δ[HCl])/(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[Cl2])/(Δt) = -(Δ[NH2NH2])/(Δt) = 1/4 (Δ[HCl])/(Δt) = (Δ[N2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| chlorine | diazane | hydrogen chloride | nitrogen formula | Cl_2 | NH_2NH_2 | HCl | N_2 Hill formula | Cl_2 | H_4N_2 | ClH | N_2 name | chlorine | diazane | hydrogen chloride | nitrogen IUPAC name | molecular chlorine | hydrazine | hydrogen chloride | molecular nitrogen

| chlorine | diazane | hydrogen chloride | nitrogen molar mass | 70.9 g/mol | 32.046 g/mol | 36.46 g/mol | 28.014 g/mol phase | gas (at STP) | liquid (at STP) | gas (at STP) | gas (at STP) melting point | -101 °C | 1 °C | -114.17 °C | -210 °C boiling point | -34 °C | 113.5 °C | -85 °C | -195.79 °C density | 0.003214 g/cm^3 (at 0 °C) | 1.011 g/cm^3 | 0.00149 g/cm^3 (at 25 °C) | 0.001251 g/cm^3 (at 0 °C) solubility in water | | miscible | miscible | insoluble surface tension | | 0.0667 N/m | | 0.0066 N/m dynamic viscosity | | 8.76×10^-4 Pa s (at 25 °C) | | 1.78×10^-5 Pa s (at 25 °C) odor | | | | odorless