HNO3 + Cd = H2O + N2O + Cd(NO3)2

HNO_3 nitric acid + Cd cadmium ⟶ H_2O water + N_2O nitrous oxide + Cd(NO3)2

Balance the chemical equation algebraically: HNO_3 + Cd ⟶ H_2O + N_2O + Cd(NO3)2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HNO_3 + c_2 Cd ⟶ c_3 H_2O + c_4 N_2O + c_5 Cd(NO3)2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, N, O and Cd: H: | c_1 = 2 c_3 N: | c_1 = 2 c_4 + 2 c_5 O: | 3 c_1 = c_3 + c_4 + 6 c_5 Cd: | 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_4 = 1 and solve the system of equations for the remaining coefficients: c_1 = 10 c_2 = 4 c_3 = 5 c_4 = 1 c_5 = 4 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 10 HNO_3 + 4 Cd ⟶ 5 H_2O + N_2O + 4 Cd(NO3)2

+ ⟶ + + Cd(NO3)2

nitric acid + cadmium ⟶ water + nitrous oxide + Cd(NO3)2

Construct the equilibrium constant, K, expression for: HNO_3 + Cd ⟶ H_2O + N_2O + Cd(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: 10 HNO_3 + 4 Cd ⟶ 5 H_2O + N_2O + 4 Cd(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 | 10 | -10 Cd | 4 | -4 H_2O | 5 | 5 N_2O | 1 | 1 Cd(NO3)2 | 4 | 4 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) Cd | 4 | -4 | ([Cd])^(-4) H_2O | 5 | 5 | ([H2O])^5 N_2O | 1 | 1 | [N2O] Cd(NO3)2 | 4 | 4 | ([Cd(NO3)2])^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 = ([HNO3])^(-10) ([Cd])^(-4) ([H2O])^5 [N2O] ([Cd(NO3)2])^4 = (([H2O])^5 [N2O] ([Cd(NO3)2])^4)/(([HNO3])^10 ([Cd])^4)

Construct the rate of reaction expression for: HNO_3 + Cd ⟶ H_2O + N_2O + Cd(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: 10 HNO_3 + 4 Cd ⟶ 5 H_2O + N_2O + 4 Cd(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 | 10 | -10 Cd | 4 | -4 H_2O | 5 | 5 N_2O | 1 | 1 Cd(NO3)2 | 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 HNO_3 | 10 | -10 | -1/10 (Δ[HNO3])/(Δt) Cd | 4 | -4 | -1/4 (Δ[Cd])/(Δt) H_2O | 5 | 5 | 1/5 (Δ[H2O])/(Δt) N_2O | 1 | 1 | (Δ[N2O])/(Δt) Cd(NO3)2 | 4 | 4 | 1/4 (Δ[Cd(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 = -1/10 (Δ[HNO3])/(Δt) = -1/4 (Δ[Cd])/(Δt) = 1/5 (Δ[H2O])/(Δt) = (Δ[N2O])/(Δt) = 1/4 (Δ[Cd(NO3)2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| nitric acid | cadmium | water | nitrous oxide | Cd(NO3)2 formula | HNO_3 | Cd | H_2O | N_2O | Cd(NO3)2 Hill formula | HNO_3 | Cd | H_2O | N_2O | CdN2O6 name | nitric acid | cadmium | water | nitrous oxide |

| nitric acid | cadmium | water | nitrous oxide | Cd(NO3)2 molar mass | 63.012 g/mol | 112.414 g/mol | 18.015 g/mol | 44.013 g/mol | 236.42 g/mol phase | liquid (at STP) | solid (at STP) | liquid (at STP) | gas (at STP) | melting point | -41.6 °C | 320.9 °C | 0 °C | -91 °C | boiling point | 83 °C | 765 °C | 99.9839 °C | -88 °C | density | 1.5129 g/cm^3 | 8.65 g/cm^3 | 1 g/cm^3 | 0.001799 g/cm^3 (at 25 °C) | solubility in water | miscible | insoluble | | | 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 | |