HCl + HNO3 + HgS = H2O + H2SO4 + NO + HgCl2

HCl hydrogen chloride + HNO_3 nitric acid + HgS mercury(II) sulfide ⟶ H_2O water + H_2SO_4 sulfuric acid + NO nitric oxide + HgCl_2 mercuric chloride

Balance the chemical equation algebraically: HCl + HNO_3 + HgS ⟶ H_2O + H_2SO_4 + NO + HgCl_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HCl + c_2 HNO_3 + c_3 HgS ⟶ c_4 H_2O + c_5 H_2SO_4 + c_6 NO + c_7 HgCl_2 Set the number of atoms in the reactants equal to the number of atoms in the products for Cl, H, N, O, Hg and S: Cl: | c_1 = 2 c_7 H: | c_1 + c_2 = 2 c_4 + 2 c_5 N: | c_2 = c_6 O: | 3 c_2 = c_4 + 4 c_5 + c_6 Hg: | c_3 = c_7 S: | c_3 = 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 8/3 c_3 = 1 c_4 = 4/3 c_5 = 1 c_6 = 8/3 c_7 = 1 Multiply by the least common denominator, 3, to eliminate fractional coefficients: c_1 = 6 c_2 = 8 c_3 = 3 c_4 = 4 c_5 = 3 c_6 = 8 c_7 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 6 HCl + 8 HNO_3 + 3 HgS ⟶ 4 H_2O + 3 H_2SO_4 + 8 NO + 3 HgCl_2

+ + ⟶ + + +

hydrogen chloride + nitric acid + mercury(II) sulfide ⟶ water + sulfuric acid + nitric oxide + mercuric chloride

| hydrogen chloride | nitric acid | mercury(II) sulfide | water | sulfuric acid | nitric oxide | mercuric chloride molecular free energy | -95.3 kJ/mol | -80.7 kJ/mol | -50.6 kJ/mol | -237.1 kJ/mol | -690 kJ/mol | 87.6 kJ/mol | -178.6 kJ/mol total free energy | -571.8 kJ/mol | -645.6 kJ/mol | -151.8 kJ/mol | -948.4 kJ/mol | -2070 kJ/mol | 700.8 kJ/mol | -535.8 kJ/mol | G_initial = -1369 kJ/mol | | | G_final = -2853 kJ/mol | | | ΔG_rxn^0 | -2853 kJ/mol - -1369 kJ/mol = -1484 kJ/mol (exergonic) | | | | | |

Construct the equilibrium constant, K, expression for: HCl + HNO_3 + HgS ⟶ H_2O + H_2SO_4 + NO + HgCl_2 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 HCl + 8 HNO_3 + 3 HgS ⟶ 4 H_2O + 3 H_2SO_4 + 8 NO + 3 HgCl_2 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 | 6 | -6 HNO_3 | 8 | -8 HgS | 3 | -3 H_2O | 4 | 4 H_2SO_4 | 3 | 3 NO | 8 | 8 HgCl_2 | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HCl | 6 | -6 | ([HCl])^(-6) HNO_3 | 8 | -8 | ([HNO3])^(-8) HgS | 3 | -3 | ([HgS])^(-3) H_2O | 4 | 4 | ([H2O])^4 H_2SO_4 | 3 | 3 | ([H2SO4])^3 NO | 8 | 8 | ([NO])^8 HgCl_2 | 3 | 3 | ([HgCl2])^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])^(-6) ([HNO3])^(-8) ([HgS])^(-3) ([H2O])^4 ([H2SO4])^3 ([NO])^8 ([HgCl2])^3 = (([H2O])^4 ([H2SO4])^3 ([NO])^8 ([HgCl2])^3)/(([HCl])^6 ([HNO3])^8 ([HgS])^3)

Construct the rate of reaction expression for: HCl + HNO_3 + HgS ⟶ H_2O + H_2SO_4 + NO + HgCl_2 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 HCl + 8 HNO_3 + 3 HgS ⟶ 4 H_2O + 3 H_2SO_4 + 8 NO + 3 HgCl_2 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 | 6 | -6 HNO_3 | 8 | -8 HgS | 3 | -3 H_2O | 4 | 4 H_2SO_4 | 3 | 3 NO | 8 | 8 HgCl_2 | 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 | 6 | -6 | -1/6 (Δ[HCl])/(Δt) HNO_3 | 8 | -8 | -1/8 (Δ[HNO3])/(Δt) HgS | 3 | -3 | -1/3 (Δ[HgS])/(Δt) H_2O | 4 | 4 | 1/4 (Δ[H2O])/(Δt) H_2SO_4 | 3 | 3 | 1/3 (Δ[H2SO4])/(Δt) NO | 8 | 8 | 1/8 (Δ[NO])/(Δt) HgCl_2 | 3 | 3 | 1/3 (Δ[HgCl2])/(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[HCl])/(Δt) = -1/8 (Δ[HNO3])/(Δt) = -1/3 (Δ[HgS])/(Δt) = 1/4 (Δ[H2O])/(Δt) = 1/3 (Δ[H2SO4])/(Δt) = 1/8 (Δ[NO])/(Δt) = 1/3 (Δ[HgCl2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| hydrogen chloride | nitric acid | mercury(II) sulfide | water | sulfuric acid | nitric oxide | mercuric chloride formula | HCl | HNO_3 | HgS | H_2O | H_2SO_4 | NO | HgCl_2 Hill formula | ClH | HNO_3 | HgS | H_2O | H_2O_4S | NO | Cl_2Hg name | hydrogen chloride | nitric acid | mercury(II) sulfide | water | sulfuric acid | nitric oxide | mercuric chloride IUPAC name | hydrogen chloride | nitric acid | thioxomercury | water | sulfuric acid | nitric oxide | dichloromercury