HNO3 + Cr = H2O + NO + Cr(NO3)3

HNO_3 nitric acid + Cr chromium ⟶ H_2O water + NO nitric oxide + CrN_3O_9 chromium nitrate

Balance the chemical equation algebraically: HNO_3 + Cr ⟶ H_2O + NO + 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 NO + 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 N: | c_1 = c_4 + 3 c_5 O: | 3 c_1 = c_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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 4 c_2 = 1 c_3 = 2 c_4 = 1 c_5 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 HNO_3 + Cr ⟶ 2 H_2O + NO + CrN_3O_9

+ ⟶ + +

nitric acid + chromium ⟶ water + nitric oxide + chromium nitrate

Construct the equilibrium constant, K, expression for: HNO_3 + Cr ⟶ H_2O + NO + 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: 4 HNO_3 + Cr ⟶ 2 H_2O + NO + 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 | 4 | -4 Cr | 1 | -1 H_2O | 2 | 2 NO | 1 | 1 CrN_3O_9 | 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) Cr | 1 | -1 | ([Cr])^(-1) H_2O | 2 | 2 | ([H2O])^2 NO | 1 | 1 | [NO] CrN_3O_9 | 1 | 1 | [CrN3O9] 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) ([Cr])^(-1) ([H2O])^2 [NO] [CrN3O9] = (([H2O])^2 [NO] [CrN3O9])/(([HNO3])^4 [Cr])

Construct the rate of reaction expression for: HNO_3 + Cr ⟶ H_2O + NO + 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: 4 HNO_3 + Cr ⟶ 2 H_2O + NO + 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 | 4 | -4 Cr | 1 | -1 H_2O | 2 | 2 NO | 1 | 1 CrN_3O_9 | 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) Cr | 1 | -1 | -(Δ[Cr])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(Δt) NO | 1 | 1 | (Δ[NO])/(Δt) CrN_3O_9 | 1 | 1 | (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 = -1/4 (Δ[HNO3])/(Δt) = -(Δ[Cr])/(Δt) = 1/2 (Δ[H2O])/(Δt) = (Δ[NO])/(Δt) = (Δ[CrN3O9])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| nitric acid | chromium | water | nitric oxide | chromium nitrate formula | HNO_3 | Cr | H_2O | NO | CrN_3O_9 name | nitric acid | chromium | water | nitric oxide | chromium nitrate IUPAC name | nitric acid | chromium | water | nitric oxide | chromium(+3) cation trinitrate