HCl + NaNO3 + Au = H2O + NaCl + NO + AuCl

HCl hydrogen chloride + NaNO_3 sodium nitrate + Au gold ⟶ H_2O water + NaCl sodium chloride + NO nitric oxide + AuCl gold(I) chloride

Balance the chemical equation algebraically: HCl + NaNO_3 + Au ⟶ H_2O + NaCl + NO + AuCl Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HCl + c_2 NaNO_3 + c_3 Au ⟶ c_4 H_2O + c_5 NaCl + c_6 NO + c_7 AuCl Set the number of atoms in the reactants equal to the number of atoms in the products for Cl, H, N, Na, O and Au: Cl: | c_1 = c_5 + c_7 H: | c_1 = 2 c_4 N: | c_2 = c_6 Na: | c_2 = c_5 O: | 3 c_2 = c_4 + c_6 Au: | c_3 = c_7 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 = 3 c_4 = 2 c_5 = 1 c_6 = 1 c_7 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 HCl + NaNO_3 + 3 Au ⟶ 2 H_2O + NaCl + NO + 3 AuCl

+ + ⟶ + + +

hydrogen chloride + sodium nitrate + gold ⟶ water + sodium chloride + nitric oxide + gold(I) chloride

| hydrogen chloride | sodium nitrate | gold | water | sodium chloride | nitric oxide | gold(I) chloride molecular enthalpy | -92.3 kJ/mol | -467.9 kJ/mol | 0 kJ/mol | -285.8 kJ/mol | -411.2 kJ/mol | 91.3 kJ/mol | -34.7 kJ/mol total enthalpy | -369.2 kJ/mol | -467.9 kJ/mol | 0 kJ/mol | -571.7 kJ/mol | -411.2 kJ/mol | 91.3 kJ/mol | -104.1 kJ/mol | H_initial = -837.1 kJ/mol | | | H_final = -995.7 kJ/mol | | | ΔH_rxn^0 | -995.7 kJ/mol - -837.1 kJ/mol = -158.6 kJ/mol (exothermic) | | | | | |

Construct the equilibrium constant, K, expression for: HCl + NaNO_3 + Au ⟶ H_2O + NaCl + NO + AuCl 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 HCl + NaNO_3 + 3 Au ⟶ 2 H_2O + NaCl + NO + 3 AuCl 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 HCl | 4 | -4 NaNO_3 | 1 | -1 Au | 3 | -3 H_2O | 2 | 2 NaCl | 1 | 1 NO | 1 | 1 AuCl | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HCl | 4 | -4 | ([HCl])^(-4) NaNO_3 | 1 | -1 | ([NaNO3])^(-1) Au | 3 | -3 | ([Au])^(-3) H_2O | 2 | 2 | ([H2O])^2 NaCl | 1 | 1 | [NaCl] NO | 1 | 1 | [NO] AuCl | 3 | 3 | ([AuCl])^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 = ([HCl])^(-4) ([NaNO3])^(-1) ([Au])^(-3) ([H2O])^2 [NaCl] [NO] ([AuCl])^3 = (([H2O])^2 [NaCl] [NO] ([AuCl])^3)/(([HCl])^4 [NaNO3] ([Au])^3)

Construct the rate of reaction expression for: HCl + NaNO_3 + Au ⟶ H_2O + NaCl + NO + AuCl 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 HCl + NaNO_3 + 3 Au ⟶ 2 H_2O + NaCl + NO + 3 AuCl 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 HCl | 4 | -4 NaNO_3 | 1 | -1 Au | 3 | -3 H_2O | 2 | 2 NaCl | 1 | 1 NO | 1 | 1 AuCl | 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 HCl | 4 | -4 | -1/4 (Δ[HCl])/(Δt) NaNO_3 | 1 | -1 | -(Δ[NaNO3])/(Δt) Au | 3 | -3 | -1/3 (Δ[Au])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(Δt) NaCl | 1 | 1 | (Δ[NaCl])/(Δt) NO | 1 | 1 | (Δ[NO])/(Δt) AuCl | 3 | 3 | 1/3 (Δ[AuCl])/(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[HCl])/(Δt) = -(Δ[NaNO3])/(Δt) = -1/3 (Δ[Au])/(Δt) = 1/2 (Δ[H2O])/(Δt) = (Δ[NaCl])/(Δt) = (Δ[NO])/(Δt) = 1/3 (Δ[AuCl])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| hydrogen chloride | sodium nitrate | gold | water | sodium chloride | nitric oxide | gold(I) chloride formula | HCl | NaNO_3 | Au | H_2O | NaCl | NO | AuCl Hill formula | ClH | NNaO_3 | Au | H_2O | ClNa | NO | AuCl name | hydrogen chloride | sodium nitrate | gold | water | sodium chloride | nitric oxide | gold(I) chloride IUPAC name | hydrogen chloride | sodium nitrate | gold | water | sodium chloride | nitric oxide | gold(+1) cation chloride