HNO3 + V = H2O + NO + V2O5

HNO_3 (nitric acid) + V (vanadium) ⟶ H_2O (water) + NO (nitric oxide) + V_2O_5 (vanadium pentoxide)

Balance the chemical equation algebraically: HNO_3 + V ⟶ H_2O + NO + V_2O_5 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HNO_3 + c_2 V ⟶ c_3 H_2O + c_4 NO + c_5 V_2O_5 Set the number of atoms in the reactants equal to the number of atoms in the products for H, N, O and V: H: | c_1 = 2 c_3 N: | c_1 = c_4 O: | 3 c_1 = c_3 + c_4 + 5 c_5 V: | c_2 = 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_5 = 1 and solve the system of equations for the remaining coefficients: c_1 = 10/3 c_2 = 2 c_3 = 5/3 c_4 = 10/3 c_5 = 1 Multiply by the least common denominator, 3, to eliminate fractional coefficients: c_1 = 10 c_2 = 6 c_3 = 5 c_4 = 10 c_5 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 10 HNO_3 + 6 V ⟶ 5 H_2O + 10 NO + 3 V_2O_5

+ ⟶ + +

nitric acid + vanadium ⟶ water + nitric oxide + vanadium pentoxide

Construct the equilibrium constant, K, expression for: HNO_3 + V ⟶ H_2O + NO + V_2O_5 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 + 6 V ⟶ 5 H_2O + 10 NO + 3 V_2O_5 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 V | 6 | -6 H_2O | 5 | 5 NO | 10 | 10 V_2O_5 | 3 | 3 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) V | 6 | -6 | ([V])^(-6) H_2O | 5 | 5 | ([H2O])^5 NO | 10 | 10 | ([NO])^10 V_2O_5 | 3 | 3 | ([V2O5])^3 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) ([V])^(-6) ([H2O])^5 ([NO])^10 ([V2O5])^3 = (([H2O])^5 ([NO])^10 ([V2O5])^3)/(([HNO3])^10 ([V])^6)

Construct the rate of reaction expression for: HNO_3 + V ⟶ H_2O + NO + V_2O_5 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 + 6 V ⟶ 5 H_2O + 10 NO + 3 V_2O_5 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 V | 6 | -6 H_2O | 5 | 5 NO | 10 | 10 V_2O_5 | 3 | 3 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) V | 6 | -6 | -1/6 (Δ[V])/(Δt) H_2O | 5 | 5 | 1/5 (Δ[H2O])/(Δt) NO | 10 | 10 | 1/10 (Δ[NO])/(Δt) V_2O_5 | 3 | 3 | 1/3 (Δ[V2O5])/(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) = -1/6 (Δ[V])/(Δt) = 1/5 (Δ[H2O])/(Δt) = 1/10 (Δ[NO])/(Δt) = 1/3 (Δ[V2O5])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| nitric acid | vanadium | water | nitric oxide | vanadium pentoxide formula | HNO_3 | V | H_2O | NO | V_2O_5 Hill formula | HNO_3 | V | H_2O | NO | O_5V_2 name | nitric acid | vanadium | water | nitric oxide | vanadium pentoxide