HNO3 + Zn = H2O + NO2 + NH4NO3 + Zn(NO3)2

HNO_3 nitric acid + Zn zinc ⟶ H_2O water + NO_2 nitrogen dioxide + NH_4NO_3 ammonium nitrate + Zn(NO3)2

Balance the chemical equation algebraically: HNO_3 + Zn ⟶ H_2O + NO_2 + NH_4NO_3 + Zn(NO3)2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HNO_3 + c_2 Zn ⟶ c_3 H_2O + c_4 NO_2 + c_5 NH_4NO_3 + c_6 Zn(NO3)2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, N, O and Zn: H: | c_1 = 2 c_3 + 4 c_5 N: | c_1 = c_4 + 2 c_5 + 2 c_6 O: | 3 c_1 = c_3 + 2 c_4 + 3 c_5 + 6 c_6 Zn: | c_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_5 = 1 and solve the system of equations for the remaining coefficients: c_2 = c_1/4 + 3/2 c_3 = c_1/2 - 2 c_4 = c_1/2 - 5 c_5 = 1 c_6 = c_1/4 + 3/2 The resulting system of equations is still underdetermined, so an additional coefficient must be set arbitrarily. Set c_1 = 14 and solve for the remaining coefficients: c_1 = 14 c_2 = 5 c_3 = 5 c_4 = 2 c_5 = 1 c_6 = 5 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 14 HNO_3 + 5 Zn ⟶ 5 H_2O + 2 NO_2 + NH_4NO_3 + 5 Zn(NO3)2

+ ⟶ + + + Zn(NO3)2

nitric acid + zinc ⟶ water + nitrogen dioxide + ammonium nitrate + Zn(NO3)2

Construct the equilibrium constant, K, expression for: HNO_3 + Zn ⟶ H_2O + NO_2 + NH_4NO_3 + Zn(NO3)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: 14 HNO_3 + 5 Zn ⟶ 5 H_2O + 2 NO_2 + NH_4NO_3 + 5 Zn(NO3)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 HNO_3 | 14 | -14 Zn | 5 | -5 H_2O | 5 | 5 NO_2 | 2 | 2 NH_4NO_3 | 1 | 1 Zn(NO3)2 | 5 | 5 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HNO_3 | 14 | -14 | ([HNO3])^(-14) Zn | 5 | -5 | ([Zn])^(-5) H_2O | 5 | 5 | ([H2O])^5 NO_2 | 2 | 2 | ([NO2])^2 NH_4NO_3 | 1 | 1 | [NH4NO3] Zn(NO3)2 | 5 | 5 | ([Zn(NO3)2])^5 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 = ([HNO3])^(-14) ([Zn])^(-5) ([H2O])^5 ([NO2])^2 [NH4NO3] ([Zn(NO3)2])^5 = (([H2O])^5 ([NO2])^2 [NH4NO3] ([Zn(NO3)2])^5)/(([HNO3])^14 ([Zn])^5)

Construct the rate of reaction expression for: HNO_3 + Zn ⟶ H_2O + NO_2 + NH_4NO_3 + Zn(NO3)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: 14 HNO_3 + 5 Zn ⟶ 5 H_2O + 2 NO_2 + NH_4NO_3 + 5 Zn(NO3)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 HNO_3 | 14 | -14 Zn | 5 | -5 H_2O | 5 | 5 NO_2 | 2 | 2 NH_4NO_3 | 1 | 1 Zn(NO3)2 | 5 | 5 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 HNO_3 | 14 | -14 | -1/14 (Δ[HNO3])/(Δt) Zn | 5 | -5 | -1/5 (Δ[Zn])/(Δt) H_2O | 5 | 5 | 1/5 (Δ[H2O])/(Δt) NO_2 | 2 | 2 | 1/2 (Δ[NO2])/(Δt) NH_4NO_3 | 1 | 1 | (Δ[NH4NO3])/(Δt) Zn(NO3)2 | 5 | 5 | 1/5 (Δ[Zn(NO3)2])/(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 = -1/14 (Δ[HNO3])/(Δt) = -1/5 (Δ[Zn])/(Δt) = 1/5 (Δ[H2O])/(Δt) = 1/2 (Δ[NO2])/(Δt) = (Δ[NH4NO3])/(Δt) = 1/5 (Δ[Zn(NO3)2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| nitric acid | zinc | water | nitrogen dioxide | ammonium nitrate | Zn(NO3)2 formula | HNO_3 | Zn | H_2O | NO_2 | NH_4NO_3 | Zn(NO3)2 Hill formula | HNO_3 | Zn | H_2O | NO_2 | H_4N_2O_3 | N2O6Zn name | nitric acid | zinc | water | nitrogen dioxide | ammonium nitrate | IUPAC name | nitric acid | zinc | water | Nitrogen dioxide | |

| nitric acid | zinc | water | nitrogen dioxide | ammonium nitrate | Zn(NO3)2 molar mass | 63.012 g/mol | 65.38 g/mol | 18.015 g/mol | 46.005 g/mol | 80.04 g/mol | 189.4 g/mol phase | liquid (at STP) | solid (at STP) | liquid (at STP) | gas (at STP) | solid (at STP) | melting point | -41.6 °C | 420 °C | 0 °C | -11 °C | 169 °C | boiling point | 83 °C | 907 °C | 99.9839 °C | 21 °C | 210 °C | density | 1.5129 g/cm^3 | 7.14 g/cm^3 | 1 g/cm^3 | 0.00188 g/cm^3 (at 25 °C) | 1.73 g/cm^3 | solubility in water | miscible | insoluble | | reacts | | surface tension | | | 0.0728 N/m | | | dynamic viscosity | 7.6×10^-4 Pa s (at 25 °C) | | 8.9×10^-4 Pa s (at 25 °C) | 4.02×10^-4 Pa s (at 25 °C) | | odor | | odorless | odorless | | odorless |