H2O + HNO3 + S = NO + H2SO3

H_2O water + HNO_3 nitric acid + S mixed sulfur ⟶ NO nitric oxide + H_2SO_3 sulfurous acid

Balance the chemical equation algebraically: H_2O + HNO_3 + S ⟶ NO + H_2SO_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 HNO_3 + c_3 S ⟶ c_4 NO + c_5 H_2SO_3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, N and S: H: | 2 c_1 + c_2 = 2 c_5 O: | c_1 + 3 c_2 = c_4 + 3 c_5 N: | c_2 = c_4 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 4 c_3 = 3 c_4 = 4 c_5 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | H_2O + 4 HNO_3 + 3 S ⟶ 4 NO + 3 H_2SO_3

+ + ⟶ +

water + nitric acid + mixed sulfur ⟶ nitric oxide + sulfurous acid

Construct the equilibrium constant, K, expression for: H_2O + HNO_3 + S ⟶ NO + H_2SO_3 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 + 4 HNO_3 + 3 S ⟶ 4 NO + 3 H_2SO_3 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 | 4 | -4 S | 3 | -3 NO | 4 | 4 H_2SO_3 | 3 | 3 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 | 4 | -4 | ([HNO3])^(-4) S | 3 | -3 | ([S])^(-3) NO | 4 | 4 | ([NO])^4 H_2SO_3 | 3 | 3 | ([H2SO3])^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 = ([H2O])^(-1) ([HNO3])^(-4) ([S])^(-3) ([NO])^4 ([H2SO3])^3 = (([NO])^4 ([H2SO3])^3)/([H2O] ([HNO3])^4 ([S])^3)

Construct the rate of reaction expression for: H_2O + HNO_3 + S ⟶ NO + H_2SO_3 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 + 4 HNO_3 + 3 S ⟶ 4 NO + 3 H_2SO_3 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 | 4 | -4 S | 3 | -3 NO | 4 | 4 H_2SO_3 | 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 H_2O | 1 | -1 | -(Δ[H2O])/(Δt) HNO_3 | 4 | -4 | -1/4 (Δ[HNO3])/(Δt) S | 3 | -3 | -1/3 (Δ[S])/(Δt) NO | 4 | 4 | 1/4 (Δ[NO])/(Δt) H_2SO_3 | 3 | 3 | 1/3 (Δ[H2SO3])/(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) = -1/4 (Δ[HNO3])/(Δt) = -1/3 (Δ[S])/(Δt) = 1/4 (Δ[NO])/(Δt) = 1/3 (Δ[H2SO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | nitric acid | mixed sulfur | nitric oxide | sulfurous acid formula | H_2O | HNO_3 | S | NO | H_2SO_3 Hill formula | H_2O | HNO_3 | S | NO | H_2O_3S name | water | nitric acid | mixed sulfur | nitric oxide | sulfurous acid IUPAC name | water | nitric acid | sulfur | nitric oxide | sulfurous acid