H2O + O2 + SO2 = H2SO4

H_2O water + O_2 oxygen + SO_2 sulfur dioxide ⟶ H_2SO_4 sulfuric acid

Balance the chemical equation algebraically: H_2O + O_2 + SO_2 ⟶ H_2SO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 O_2 + c_3 SO_2 ⟶ c_4 H_2SO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O and S: H: | 2 c_1 = 2 c_4 O: | c_1 + 2 c_2 + 2 c_3 = 4 c_4 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 = 2 c_4 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 H_2O + O_2 + 2 SO_2 ⟶ 2 H_2SO_4

+ + ⟶

water + oxygen + sulfur dioxide ⟶ sulfuric acid

| water | oxygen | sulfur dioxide | sulfuric acid molecular enthalpy | -285.8 kJ/mol | 0 kJ/mol | -296.8 kJ/mol | -814 kJ/mol total enthalpy | -571.7 kJ/mol | 0 kJ/mol | -593.6 kJ/mol | -1628 kJ/mol | H_initial = -1165 kJ/mol | | | H_final = -1628 kJ/mol ΔH_rxn^0 | -1628 kJ/mol - -1165 kJ/mol = -462.7 kJ/mol (exothermic) | | |

| water | oxygen | sulfur dioxide | sulfuric acid molecular free energy | -237.1 kJ/mol | 231.7 kJ/mol | -300.1 kJ/mol | -690 kJ/mol total free energy | -474.2 kJ/mol | 231.7 kJ/mol | -600.2 kJ/mol | -1380 kJ/mol | G_initial = -842.7 kJ/mol | | | G_final = -1380 kJ/mol ΔG_rxn^0 | -1380 kJ/mol - -842.7 kJ/mol = -537.3 kJ/mol (exergonic) | | |

| water | oxygen | sulfur dioxide | sulfuric acid molecular entropy | 69.91 J/(mol K) | 205 J/(mol K) | 248 J/(mol K) | 157 J/(mol K) total entropy | 139.8 J/(mol K) | 205 J/(mol K) | 496 J/(mol K) | 314 J/(mol K) | S_initial = 840.8 J/(mol K) | | | S_final = 314 J/(mol K) ΔS_rxn^0 | 314 J/(mol K) - 840.8 J/(mol K) = -526.8 J/(mol K) (exoentropic) | | |

Construct the equilibrium constant, K, expression for: H_2O + O_2 + SO_2 ⟶ H_2SO_4 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: 2 H_2O + O_2 + 2 SO_2 ⟶ 2 H_2SO_4 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 | 2 | -2 O_2 | 1 | -1 SO_2 | 2 | -2 H_2SO_4 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 2 | -2 | ([H2O])^(-2) O_2 | 1 | -1 | ([O2])^(-1) SO_2 | 2 | -2 | ([SO2])^(-2) H_2SO_4 | 2 | 2 | ([H2SO4])^2 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])^(-2) ([O2])^(-1) ([SO2])^(-2) ([H2SO4])^2 = ([H2SO4])^2/(([H2O])^2 [O2] ([SO2])^2)

Construct the rate of reaction expression for: H_2O + O_2 + SO_2 ⟶ H_2SO_4 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: 2 H_2O + O_2 + 2 SO_2 ⟶ 2 H_2SO_4 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 | 2 | -2 O_2 | 1 | -1 SO_2 | 2 | -2 H_2SO_4 | 2 | 2 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 | 2 | -2 | -1/2 (Δ[H2O])/(Δt) O_2 | 1 | -1 | -(Δ[O2])/(Δt) SO_2 | 2 | -2 | -1/2 (Δ[SO2])/(Δt) H_2SO_4 | 2 | 2 | 1/2 (Δ[H2SO4])/(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 = -1/2 (Δ[H2O])/(Δt) = -(Δ[O2])/(Δt) = -1/2 (Δ[SO2])/(Δt) = 1/2 (Δ[H2SO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | oxygen | sulfur dioxide | sulfuric acid formula | H_2O | O_2 | SO_2 | H_2SO_4 Hill formula | H_2O | O_2 | O_2S | H_2O_4S name | water | oxygen | sulfur dioxide | sulfuric acid IUPAC name | water | molecular oxygen | sulfur dioxide | sulfuric acid

| water | oxygen | sulfur dioxide | sulfuric acid molar mass | 18.015 g/mol | 31.998 g/mol | 64.06 g/mol | 98.07 g/mol phase | liquid (at STP) | gas (at STP) | gas (at STP) | liquid (at STP) melting point | 0 °C | -218 °C | -73 °C | 10.371 °C boiling point | 99.9839 °C | -183 °C | -10 °C | 279.6 °C density | 1 g/cm^3 | 0.001429 g/cm^3 (at 0 °C) | 0.002619 g/cm^3 (at 25 °C) | 1.8305 g/cm^3 solubility in water | | | | very soluble surface tension | 0.0728 N/m | 0.01347 N/m | 0.02859 N/m | 0.0735 N/m dynamic viscosity | 8.9×10^-4 Pa s (at 25 °C) | 2.055×10^-5 Pa s (at 25 °C) | 1.282×10^-5 Pa s (at 25 °C) | 0.021 Pa s (at 25 °C) odor | odorless | odorless | | odorless