H2O + Cl2 + SO2 = H2SO4 + HCl

water + chlorine + sulfur dioxide ⟶ sulfuric acid + hydrogen chloride

Balance the chemical equation algebraically: + + ⟶ + Add stoichiometric coefficients, c_i, to the reactants and products: c_1 + c_2 + c_3 ⟶ c_4 + c_5 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, Cl and S: H: | 2 c_1 = 2 c_4 + c_5 O: | c_1 + 2 c_3 = 4 c_4 Cl: | 2 c_2 = c_5 S: | c_3 = 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 = 2 c_2 = 1 c_3 = 1 c_4 = 1 c_5 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 + + ⟶ + 2

+ + ⟶ +

water + chlorine + sulfur dioxide ⟶ sulfuric acid + hydrogen chloride

| water | chlorine | sulfur dioxide | sulfuric acid | hydrogen chloride molecular enthalpy | -285.8 kJ/mol | 0 kJ/mol | -296.8 kJ/mol | -814 kJ/mol | -92.3 kJ/mol total enthalpy | -571.7 kJ/mol | 0 kJ/mol | -296.8 kJ/mol | -814 kJ/mol | -184.6 kJ/mol | H_initial = -868.5 kJ/mol | | | H_final = -998.6 kJ/mol | ΔH_rxn^0 | -998.6 kJ/mol - -868.5 kJ/mol = -130.1 kJ/mol (exothermic) | | | |

| water | chlorine | sulfur dioxide | sulfuric acid | hydrogen chloride molecular free energy | -237.1 kJ/mol | 0 kJ/mol | -300.1 kJ/mol | -690 kJ/mol | -95.3 kJ/mol total free energy | -474.2 kJ/mol | 0 kJ/mol | -300.1 kJ/mol | -690 kJ/mol | -190.6 kJ/mol | G_initial = -774.3 kJ/mol | | | G_final = -880.6 kJ/mol | ΔG_rxn^0 | -880.6 kJ/mol - -774.3 kJ/mol = -106.3 kJ/mol (exergonic) | | | |

| water | chlorine | sulfur dioxide | sulfuric acid | hydrogen chloride molecular entropy | 69.91 J/(mol K) | 223 J/(mol K) | 248 J/(mol K) | 157 J/(mol K) | 187 J/(mol K) total entropy | 139.8 J/(mol K) | 223 J/(mol K) | 248 J/(mol K) | 157 J/(mol K) | 374 J/(mol K) | S_initial = 610.8 J/(mol K) | | | S_final = 531 J/(mol K) | ΔS_rxn^0 | 531 J/(mol K) - 610.8 J/(mol K) = -79.82 J/(mol K) (exoentropic) | | | |

| water | chlorine | sulfur dioxide | sulfuric acid | hydrogen chloride Hill formula | H_2O | Cl_2 | O_2S | H_2O_4S | ClH name | water | chlorine | sulfur dioxide | sulfuric acid | hydrogen chloride IUPAC name | water | molecular chlorine | sulfur dioxide | sulfuric acid | hydrogen chloride