HNO3 + Sc2O3 = H2O + Sc(NO3)3

HNO_3 nitric acid + Sc_2O_3 scandium(III) oxide ⟶ H_2O water + N_3O_9Sc_1 scandium nitrate

Balance the chemical equation algebraically: HNO_3 + Sc_2O_3 ⟶ H_2O + N_3O_9Sc_1 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HNO_3 + c_2 Sc_2O_3 ⟶ c_3 H_2O + c_4 N_3O_9Sc_1 Set the number of atoms in the reactants equal to the number of atoms in the products for H, N, O and Sc: H: | c_1 = 2 c_3 N: | c_1 = 3 c_4 O: | 3 c_1 + 3 c_2 = c_3 + 9 c_4 Sc: | 2 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 6 c_2 = 1 c_3 = 3 c_4 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 6 HNO_3 + Sc_2O_3 ⟶ 3 H_2O + 2 N_3O_9Sc_1

+ ⟶ +

nitric acid + scandium(III) oxide ⟶ water + scandium nitrate

Construct the equilibrium constant, K, expression for: HNO_3 + Sc_2O_3 ⟶ H_2O + N_3O_9Sc_1 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: 6 HNO_3 + Sc_2O_3 ⟶ 3 H_2O + 2 N_3O_9Sc_1 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 | 6 | -6 Sc_2O_3 | 1 | -1 H_2O | 3 | 3 N_3O_9Sc_1 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HNO_3 | 6 | -6 | ([HNO3])^(-6) Sc_2O_3 | 1 | -1 | ([Sc2O3])^(-1) H_2O | 3 | 3 | ([H2O])^3 N_3O_9Sc_1 | 2 | 2 | ([N3O9Sc1])^2 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])^(-6) ([Sc2O3])^(-1) ([H2O])^3 ([N3O9Sc1])^2 = (([H2O])^3 ([N3O9Sc1])^2)/(([HNO3])^6 [Sc2O3])

Construct the rate of reaction expression for: HNO_3 + Sc_2O_3 ⟶ H_2O + N_3O_9Sc_1 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: 6 HNO_3 + Sc_2O_3 ⟶ 3 H_2O + 2 N_3O_9Sc_1 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 | 6 | -6 Sc_2O_3 | 1 | -1 H_2O | 3 | 3 N_3O_9Sc_1 | 2 | 2 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 | 6 | -6 | -1/6 (Δ[HNO3])/(Δt) Sc_2O_3 | 1 | -1 | -(Δ[Sc2O3])/(Δt) H_2O | 3 | 3 | 1/3 (Δ[H2O])/(Δt) N_3O_9Sc_1 | 2 | 2 | 1/2 (Δ[N3O9Sc1])/(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 = -1/6 (Δ[HNO3])/(Δt) = -(Δ[Sc2O3])/(Δt) = 1/3 (Δ[H2O])/(Δt) = 1/2 (Δ[N3O9Sc1])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| nitric acid | scandium(III) oxide | water | scandium nitrate formula | HNO_3 | Sc_2O_3 | H_2O | N_3O_9Sc_1 Hill formula | HNO_3 | O_3Sc_2 | H_2O | N_3O_9Sc name | nitric acid | scandium(III) oxide | water | scandium nitrate IUPAC name | nitric acid | | water | scandium(3+) trinitrate

| nitric acid | scandium(III) oxide | water | scandium nitrate molar mass | 63.012 g/mol | 137.91 g/mol | 18.015 g/mol | 230.97 g/mol phase | liquid (at STP) | solid (at STP) | liquid (at STP) | melting point | -41.6 °C | 1000 °C | 0 °C | boiling point | 83 °C | | 99.9839 °C | density | 1.5129 g/cm^3 | 8.35 g/cm^3 | 1 g/cm^3 | solubility in water | miscible | | | 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 |