HNO3 + Cr = H2O + NH4NO3 + Cr(NO3)3

HNO_3 nitric acid + Cr chromium ⟶ H_2O water + NH_4NO_3 ammonium nitrate + CrN_3O_9 chromium nitrate

Balance the chemical equation algebraically: HNO_3 + Cr ⟶ H_2O + NH_4NO_3 + CrN_3O_9 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HNO_3 + c_2 Cr ⟶ c_3 H_2O + c_4 NH_4NO_3 + c_5 CrN_3O_9 Set the number of atoms in the reactants equal to the number of atoms in the products for H, N, O and Cr: H: | c_1 = 2 c_3 + 4 c_4 N: | c_1 = 2 c_4 + 3 c_5 O: | 3 c_1 = c_3 + 3 c_4 + 9 c_5 Cr: | 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 = 8/3 c_3 = 3 c_4 = 1 c_5 = 8/3 Multiply by the least common denominator, 3, to eliminate fractional coefficients: c_1 = 30 c_2 = 8 c_3 = 9 c_4 = 3 c_5 = 8 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 30 HNO_3 + 8 Cr ⟶ 9 H_2O + 3 NH_4NO_3 + 8 CrN_3O_9

+ ⟶ + +

nitric acid + chromium ⟶ water + ammonium nitrate + chromium nitrate

Construct the equilibrium constant, K, expression for: HNO_3 + Cr ⟶ H_2O + NH_4NO_3 + CrN_3O_9 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: 30 HNO_3 + 8 Cr ⟶ 9 H_2O + 3 NH_4NO_3 + 8 CrN_3O_9 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 | 30 | -30 Cr | 8 | -8 H_2O | 9 | 9 NH_4NO_3 | 3 | 3 CrN_3O_9 | 8 | 8 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HNO_3 | 30 | -30 | ([HNO3])^(-30) Cr | 8 | -8 | ([Cr])^(-8) H_2O | 9 | 9 | ([H2O])^9 NH_4NO_3 | 3 | 3 | ([NH4NO3])^3 CrN_3O_9 | 8 | 8 | ([CrN3O9])^8 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])^(-30) ([Cr])^(-8) ([H2O])^9 ([NH4NO3])^3 ([CrN3O9])^8 = (([H2O])^9 ([NH4NO3])^3 ([CrN3O9])^8)/(([HNO3])^30 ([Cr])^8)

Construct the rate of reaction expression for: HNO_3 + Cr ⟶ H_2O + NH_4NO_3 + CrN_3O_9 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: 30 HNO_3 + 8 Cr ⟶ 9 H_2O + 3 NH_4NO_3 + 8 CrN_3O_9 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 | 30 | -30 Cr | 8 | -8 H_2O | 9 | 9 NH_4NO_3 | 3 | 3 CrN_3O_9 | 8 | 8 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 | 30 | -30 | -1/30 (Δ[HNO3])/(Δt) Cr | 8 | -8 | -1/8 (Δ[Cr])/(Δt) H_2O | 9 | 9 | 1/9 (Δ[H2O])/(Δt) NH_4NO_3 | 3 | 3 | 1/3 (Δ[NH4NO3])/(Δt) CrN_3O_9 | 8 | 8 | 1/8 (Δ[CrN3O9])/(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 = -1/30 (Δ[HNO3])/(Δt) = -1/8 (Δ[Cr])/(Δt) = 1/9 (Δ[H2O])/(Δt) = 1/3 (Δ[NH4NO3])/(Δt) = 1/8 (Δ[CrN3O9])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| nitric acid | chromium | water | ammonium nitrate | chromium nitrate formula | HNO_3 | Cr | H_2O | NH_4NO_3 | CrN_3O_9 Hill formula | HNO_3 | Cr | H_2O | H_4N_2O_3 | CrN_3O_9 name | nitric acid | chromium | water | ammonium nitrate | chromium nitrate IUPAC name | nitric acid | chromium | water | | chromium(+3) cation trinitrate

| nitric acid | chromium | water | ammonium nitrate | chromium nitrate molar mass | 63.012 g/mol | 51.9961 g/mol | 18.015 g/mol | 80.04 g/mol | 238.01 g/mol phase | liquid (at STP) | solid (at STP) | liquid (at STP) | solid (at STP) | solid (at STP) melting point | -41.6 °C | 1857 °C | 0 °C | 169 °C | 66 °C boiling point | 83 °C | 2672 °C | 99.9839 °C | 210 °C | density | 1.5129 g/cm^3 | 7.14 g/cm^3 | 1 g/cm^3 | 1.73 g/cm^3 | 1.8 g/cm^3 solubility in water | miscible | insoluble | | | soluble 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) | | odor | | odorless | odorless | odorless |