H2O + Al(NO3)3 = HNO3 + Al(OH)3

H_2O water + Al(NO_3)_3 aluminum nitrate ⟶ HNO_3 nitric acid + Al(OH)_3 aluminum hydroxide

Balance the chemical equation algebraically: H_2O + Al(NO_3)_3 ⟶ HNO_3 + Al(OH)_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 Al(NO_3)_3 ⟶ c_3 HNO_3 + c_4 Al(OH)_3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, Al and N: H: | 2 c_1 = c_3 + 3 c_4 O: | c_1 + 9 c_2 = 3 c_3 + 3 c_4 Al: | c_2 = c_4 N: | 3 c_2 = c_3 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 = 3 c_2 = 1 c_3 = 3 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 H_2O + Al(NO_3)_3 ⟶ 3 HNO_3 + Al(OH)_3

+ ⟶ +

water + aluminum nitrate ⟶ nitric acid + aluminum hydroxide

Construct the equilibrium constant, K, expression for: H_2O + Al(NO_3)_3 ⟶ HNO_3 + Al(OH)_3 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: 3 H_2O + Al(NO_3)_3 ⟶ 3 HNO_3 + Al(OH)_3 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 H_2O | 3 | -3 Al(NO_3)_3 | 1 | -1 HNO_3 | 3 | 3 Al(OH)_3 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 3 | -3 | ([H2O])^(-3) Al(NO_3)_3 | 1 | -1 | ([Al(NO3)3])^(-1) HNO_3 | 3 | 3 | ([HNO3])^3 Al(OH)_3 | 1 | 1 | [Al(OH)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 = ([H2O])^(-3) ([Al(NO3)3])^(-1) ([HNO3])^3 [Al(OH)3] = (([HNO3])^3 [Al(OH)3])/(([H2O])^3 [Al(NO3)3])

Construct the rate of reaction expression for: H_2O + Al(NO_3)_3 ⟶ HNO_3 + Al(OH)_3 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: 3 H_2O + Al(NO_3)_3 ⟶ 3 HNO_3 + Al(OH)_3 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 H_2O | 3 | -3 Al(NO_3)_3 | 1 | -1 HNO_3 | 3 | 3 Al(OH)_3 | 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 H_2O | 3 | -3 | -1/3 (Δ[H2O])/(Δt) Al(NO_3)_3 | 1 | -1 | -(Δ[Al(NO3)3])/(Δt) HNO_3 | 3 | 3 | 1/3 (Δ[HNO3])/(Δt) Al(OH)_3 | 1 | 1 | (Δ[Al(OH)3])/(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 = -1/3 (Δ[H2O])/(Δt) = -(Δ[Al(NO3)3])/(Δt) = 1/3 (Δ[HNO3])/(Δt) = (Δ[Al(OH)3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | aluminum nitrate | nitric acid | aluminum hydroxide formula | H_2O | Al(NO_3)_3 | HNO_3 | Al(OH)_3 Hill formula | H_2O | AlN_3O_9 | HNO_3 | AlH_3O_3 name | water | aluminum nitrate | nitric acid | aluminum hydroxide IUPAC name | water | aluminum(+3) cation trinitrate | nitric acid | aluminum hydroxide

| water | aluminum nitrate | nitric acid | aluminum hydroxide molar mass | 18.015 g/mol | 212.99 g/mol | 63.012 g/mol | 78.003 g/mol phase | liquid (at STP) | solid (at STP) | liquid (at STP) | melting point | 0 °C | 72.8 °C | -41.6 °C | boiling point | 99.9839 °C | | 83 °C | density | 1 g/cm^3 | 1.401 g/cm^3 | 1.5129 g/cm^3 | solubility in water | | | miscible | surface tension | 0.0728 N/m | | | dynamic viscosity | 8.9×10^-4 Pa s (at 25 °C) | 0.001338 Pa s (at 22 °C) | 7.6×10^-4 Pa s (at 25 °C) | odor | odorless | | |