Zn + NO2 = N2 + ZnO

Zn zinc + NO_2 nitrogen dioxide ⟶ N_2 nitrogen + ZnO zinc oxide

Balance the chemical equation algebraically: Zn + NO_2 ⟶ N_2 + ZnO Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Zn + c_2 NO_2 ⟶ c_3 N_2 + c_4 ZnO Set the number of atoms in the reactants equal to the number of atoms in the products for Zn, N and O: Zn: | c_1 = c_4 N: | c_2 = 2 c_3 O: | 2 c_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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 4 c_2 = 2 c_3 = 1 c_4 = 4 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 Zn + 2 NO_2 ⟶ N_2 + 4 ZnO

+ ⟶ +

zinc + nitrogen dioxide ⟶ nitrogen + zinc oxide

| zinc | nitrogen dioxide | nitrogen | zinc oxide molecular enthalpy | 0 kJ/mol | 33.2 kJ/mol | 0 kJ/mol | -350.5 kJ/mol total enthalpy | 0 kJ/mol | 66.4 kJ/mol | 0 kJ/mol | -1402 kJ/mol | H_initial = 66.4 kJ/mol | | H_final = -1402 kJ/mol | ΔH_rxn^0 | -1402 kJ/mol - 66.4 kJ/mol = -1468 kJ/mol (exothermic) | | |

| zinc | nitrogen dioxide | nitrogen | zinc oxide molecular entropy | 42 J/(mol K) | 240 J/(mol K) | 192 J/(mol K) | 44 J/(mol K) total entropy | 168 J/(mol K) | 480 J/(mol K) | 192 J/(mol K) | 176 J/(mol K) | S_initial = 648 J/(mol K) | | S_final = 368 J/(mol K) | ΔS_rxn^0 | 368 J/(mol K) - 648 J/(mol K) = -280 J/(mol K) (exoentropic) | | |

Construct the equilibrium constant, K, expression for: Zn + NO_2 ⟶ N_2 + ZnO 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 Zn + 2 NO_2 ⟶ N_2 + 4 ZnO 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 Zn | 4 | -4 NO_2 | 2 | -2 N_2 | 1 | 1 ZnO | 4 | 4 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Zn | 4 | -4 | ([Zn])^(-4) NO_2 | 2 | -2 | ([NO2])^(-2) N_2 | 1 | 1 | [N2] ZnO | 4 | 4 | ([ZnO])^4 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 = ([Zn])^(-4) ([NO2])^(-2) [N2] ([ZnO])^4 = ([N2] ([ZnO])^4)/(([Zn])^4 ([NO2])^2)

Construct the rate of reaction expression for: Zn + NO_2 ⟶ N_2 + ZnO 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 Zn + 2 NO_2 ⟶ N_2 + 4 ZnO 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 Zn | 4 | -4 NO_2 | 2 | -2 N_2 | 1 | 1 ZnO | 4 | 4 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 Zn | 4 | -4 | -1/4 (Δ[Zn])/(Δt) NO_2 | 2 | -2 | -1/2 (Δ[NO2])/(Δt) N_2 | 1 | 1 | (Δ[N2])/(Δt) ZnO | 4 | 4 | 1/4 (Δ[ZnO])/(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[Zn])/(Δt) = -1/2 (Δ[NO2])/(Δt) = (Δ[N2])/(Δt) = 1/4 (Δ[ZnO])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| zinc | nitrogen dioxide | nitrogen | zinc oxide formula | Zn | NO_2 | N_2 | ZnO Hill formula | Zn | NO_2 | N_2 | OZn name | zinc | nitrogen dioxide | nitrogen | zinc oxide IUPAC name | zinc | Nitrogen dioxide | molecular nitrogen | oxozinc

| zinc | nitrogen dioxide | nitrogen | zinc oxide molar mass | 65.38 g/mol | 46.005 g/mol | 28.014 g/mol | 81.38 g/mol phase | solid (at STP) | gas (at STP) | gas (at STP) | solid (at STP) melting point | 420 °C | -11 °C | -210 °C | 1975 °C boiling point | 907 °C | 21 °C | -195.79 °C | 2360 °C density | 7.14 g/cm^3 | 0.00188 g/cm^3 (at 25 °C) | 0.001251 g/cm^3 (at 0 °C) | 5.6 g/cm^3 solubility in water | insoluble | reacts | insoluble | surface tension | | | 0.0066 N/m | dynamic viscosity | | 4.02×10^-4 Pa s (at 25 °C) | 1.78×10^-5 Pa s (at 25 °C) | odor | odorless | | odorless | odorless