HNO3 + Sn = H2O + NO2 + SnO2

HNO_3 (nitric acid) + Sn (white tin) ⟶ H_2O (water) + NO_2 (nitrogen dioxide) + SnO_2 (stannic oxide)

Balance the chemical equation algebraically: HNO_3 + Sn ⟶ H_2O + NO_2 + SnO_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HNO_3 + c_2 Sn ⟶ c_3 H_2O + c_4 NO_2 + c_5 SnO_2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, N, O and Sn: H: | c_1 = 2 c_3 N: | c_1 = c_4 O: | 3 c_1 = c_3 + 2 c_4 + 2 c_5 Sn: | c_2 = c_5 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 = 4 c_2 = 1 c_3 = 2 c_4 = 4 c_5 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 HNO_3 + Sn ⟶ 2 H_2O + 4 NO_2 + SnO_2

+ ⟶ + +

nitric acid + white tin ⟶ water + nitrogen dioxide + stannic oxide

| nitric acid | white tin | water | nitrogen dioxide | stannic oxide molecular entropy | 156 J/(mol K) | 51.2 J/(mol K) | 69.91 J/(mol K) | 240 J/(mol K) | 52 J/(mol K) total entropy | 624 J/(mol K) | 51.2 J/(mol K) | 139.8 J/(mol K) | 960 J/(mol K) | 52 J/(mol K) | S_initial = 675.2 J/(mol K) | | S_final = 1152 J/(mol K) | | ΔS_rxn^0 | 1152 J/(mol K) - 675.2 J/(mol K) = 476.6 J/(mol K) (endoentropic) | | | |

Construct the equilibrium constant, K, expression for: HNO_3 + Sn ⟶ H_2O + NO_2 + SnO_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: 4 HNO_3 + Sn ⟶ 2 H_2O + 4 NO_2 + SnO_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 | 4 | -4 Sn | 1 | -1 H_2O | 2 | 2 NO_2 | 4 | 4 SnO_2 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HNO_3 | 4 | -4 | ([HNO3])^(-4) Sn | 1 | -1 | ([Sn])^(-1) H_2O | 2 | 2 | ([H2O])^2 NO_2 | 4 | 4 | ([NO2])^4 SnO_2 | 1 | 1 | [SnO2] 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])^(-4) ([Sn])^(-1) ([H2O])^2 ([NO2])^4 [SnO2] = (([H2O])^2 ([NO2])^4 [SnO2])/(([HNO3])^4 [Sn])

Construct the rate of reaction expression for: HNO_3 + Sn ⟶ H_2O + NO_2 + SnO_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: 4 HNO_3 + Sn ⟶ 2 H_2O + 4 NO_2 + SnO_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 | 4 | -4 Sn | 1 | -1 H_2O | 2 | 2 NO_2 | 4 | 4 SnO_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 HNO_3 | 4 | -4 | -1/4 (Δ[HNO3])/(Δt) Sn | 1 | -1 | -(Δ[Sn])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(Δt) NO_2 | 4 | 4 | 1/4 (Δ[NO2])/(Δt) SnO_2 | 1 | 1 | (Δ[SnO2])/(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[HNO3])/(Δt) = -(Δ[Sn])/(Δt) = 1/2 (Δ[H2O])/(Δt) = 1/4 (Δ[NO2])/(Δt) = (Δ[SnO2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| nitric acid | white tin | water | nitrogen dioxide | stannic oxide formula | HNO_3 | Sn | H_2O | NO_2 | SnO_2 Hill formula | HNO_3 | Sn | H_2O | NO_2 | O_2Sn name | nitric acid | white tin | water | nitrogen dioxide | stannic oxide IUPAC name | nitric acid | tin | water | Nitrogen dioxide |