H2O + HNO3 = NO3 + H3O

H_2O water + HNO_3 nitric acid ⟶ (NO_3)^- nitrate anion + (H_3O)^+ hydronium cation

Balance the chemical equation algebraically: H_2O + HNO_3 ⟶ (NO_3)^- + (H_3O)^+ Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 HNO_3 ⟶ c_3 (NO_3)^- + c_4 (H_3O)^+ Set the number of atoms and the charges in the reactants equal to the number of atoms and the charges in the products for H, O and N: H: | 2 c_1 + c_2 = 3 c_4 O: | c_1 + 3 c_2 = 3 c_3 + c_4 N: | c_2 = c_3 Charges: | 0 = c_4 - 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 1 c_3 = 1 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | H_2O + HNO_3 ⟶ (NO_3)^- + (H_3O)^+

+ ⟶ +

water + nitric acid ⟶ nitrate anion + hydronium cation

Construct the equilibrium constant, K, expression for: H_2O + HNO_3 ⟶ (NO_3)^- + (H_3O)^+ 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: H_2O + HNO_3 ⟶ (NO_3)^- + (H_3O)^+ 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 | 1 | -1 HNO_3 | 1 | -1 (NO_3)^- | 1 | 1 (H_3O)^+ | 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 | 1 | -1 | ([H2O])^(-1) HNO_3 | 1 | -1 | ([HNO3])^(-1) (NO_3)^- | 1 | 1 | [NO3-1] (H_3O)^+ | 1 | 1 | [H3O+1] 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])^(-1) ([HNO3])^(-1) [NO3-1] [H3O+1] = ([NO3-1] [H3O+1])/([H2O] [HNO3])

Construct the rate of reaction expression for: H_2O + HNO_3 ⟶ (NO_3)^- + (H_3O)^+ 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: H_2O + HNO_3 ⟶ (NO_3)^- + (H_3O)^+ 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 | 1 | -1 HNO_3 | 1 | -1 (NO_3)^- | 1 | 1 (H_3O)^+ | 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 | 1 | -1 | -(Δ[H2O])/(Δt) HNO_3 | 1 | -1 | -(Δ[HNO3])/(Δt) (NO_3)^- | 1 | 1 | (Δ[NO3-1])/(Δt) (H_3O)^+ | 1 | 1 | (Δ[H3O+1])/(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 = -(Δ[H2O])/(Δt) = -(Δ[HNO3])/(Δt) = (Δ[NO3-1])/(Δt) = (Δ[H3O+1])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | nitric acid | nitrate anion | hydronium cation formula | H_2O | HNO_3 | (NO_3)^- | (H_3O)^+ name | water | nitric acid | nitrate anion | hydronium cation

| water | nitric acid | nitrate anion | hydronium cation molar mass | 18.015 g/mol | 63.012 g/mol | 62.005 g/mol | 19.022 g/mol phase | liquid (at STP) | liquid (at STP) | | melting point | 0 °C | -41.6 °C | | boiling point | 99.9839 °C | 83 °C | | density | 1 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) | 7.6×10^-4 Pa s (at 25 °C) | | odor | odorless | | |