HNO3 + Ag = H2O + AgNO3 + N2O

HNO_3 nitric acid + Ag silver ⟶ H_2O water + AgNO_3 silver nitrate + N_2O nitrous oxide

Balance the chemical equation algebraically: HNO_3 + Ag ⟶ H_2O + AgNO_3 + N_2O Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HNO_3 + c_2 Ag ⟶ c_3 H_2O + c_4 AgNO_3 + c_5 N_2O Set the number of atoms in the reactants equal to the number of atoms in the products for H, N, O and Ag: H: | c_1 = 2 c_3 N: | c_1 = c_4 + 2 c_5 O: | 3 c_1 = c_3 + 3 c_4 + c_5 Ag: | 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_5 = 1 and solve the system of equations for the remaining coefficients: c_1 = 10 c_2 = 8 c_3 = 5 c_4 = 8 c_5 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 10 HNO_3 + 8 Ag ⟶ 5 H_2O + 8 AgNO_3 + N_2O

+ ⟶ + +

nitric acid + silver ⟶ water + silver nitrate + nitrous oxide

| nitric acid | silver | water | silver nitrate | nitrous oxide molecular entropy | 156 J/(mol K) | 42.6 J/(mol K) | 69.91 J/(mol K) | 140.9 J/(mol K) | 220 J/(mol K) total entropy | 1560 J/(mol K) | 340.8 J/(mol K) | 349.6 J/(mol K) | 1127 J/(mol K) | 220 J/(mol K) | S_initial = 1901 J/(mol K) | | S_final = 1697 J/(mol K) | | ΔS_rxn^0 | 1697 J/(mol K) - 1901 J/(mol K) = -204 J/(mol K) (exoentropic) | | | |

Construct the equilibrium constant, K, expression for: HNO_3 + Ag ⟶ H_2O + AgNO_3 + N_2O 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: 10 HNO_3 + 8 Ag ⟶ 5 H_2O + 8 AgNO_3 + N_2O 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 | 10 | -10 Ag | 8 | -8 H_2O | 5 | 5 AgNO_3 | 8 | 8 N_2O | 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 | 10 | -10 | ([HNO3])^(-10) Ag | 8 | -8 | ([Ag])^(-8) H_2O | 5 | 5 | ([H2O])^5 AgNO_3 | 8 | 8 | ([AgNO3])^8 N_2O | 1 | 1 | [N2O] 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])^(-10) ([Ag])^(-8) ([H2O])^5 ([AgNO3])^8 [N2O] = (([H2O])^5 ([AgNO3])^8 [N2O])/(([HNO3])^10 ([Ag])^8)

Construct the rate of reaction expression for: HNO_3 + Ag ⟶ H_2O + AgNO_3 + N_2O 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: 10 HNO_3 + 8 Ag ⟶ 5 H_2O + 8 AgNO_3 + N_2O 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 | 10 | -10 Ag | 8 | -8 H_2O | 5 | 5 AgNO_3 | 8 | 8 N_2O | 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 | 10 | -10 | -1/10 (Δ[HNO3])/(Δt) Ag | 8 | -8 | -1/8 (Δ[Ag])/(Δt) H_2O | 5 | 5 | 1/5 (Δ[H2O])/(Δt) AgNO_3 | 8 | 8 | 1/8 (Δ[AgNO3])/(Δt) N_2O | 1 | 1 | (Δ[N2O])/(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 = -1/10 (Δ[HNO3])/(Δt) = -1/8 (Δ[Ag])/(Δt) = 1/5 (Δ[H2O])/(Δt) = 1/8 (Δ[AgNO3])/(Δt) = (Δ[N2O])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| nitric acid | silver | water | silver nitrate | nitrous oxide formula | HNO_3 | Ag | H_2O | AgNO_3 | N_2O name | nitric acid | silver | water | silver nitrate | nitrous oxide

| nitric acid | silver | water | silver nitrate | nitrous oxide molar mass | 63.012 g/mol | 107.8682 g/mol | 18.015 g/mol | 169.87 g/mol | 44.013 g/mol phase | liquid (at STP) | solid (at STP) | liquid (at STP) | solid (at STP) | gas (at STP) melting point | -41.6 °C | 960 °C | 0 °C | 212 °C | -91 °C boiling point | 83 °C | 2212 °C | 99.9839 °C | | -88 °C density | 1.5129 g/cm^3 | 10.49 g/cm^3 | 1 g/cm^3 | | 0.001799 g/cm^3 (at 25 °C) solubility in water | miscible | insoluble | | soluble | surface tension | | | 0.0728 N/m | | 0.00175 N/m dynamic viscosity | 7.6×10^-4 Pa s (at 25 °C) | | 8.9×10^-4 Pa s (at 25 °C) | | 1.491×10^-5 Pa s (at 25 °C) odor | | | odorless | odorless |