HNO3 + NH4HS = H2O + S + NO2 + NH4HO3

HNO_3 nitric acid + NH_4SH ammonium bisulfide ⟶ H_2O water + S mixed sulfur + NO_2 nitrogen dioxide + NH4HO3

Balance the chemical equation algebraically: HNO_3 + NH_4SH ⟶ H_2O + S + NO_2 + NH4HO3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HNO_3 + c_2 NH_4SH ⟶ c_3 H_2O + c_4 S + c_5 NO_2 + c_6 NH4HO3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, N, O and S: H: | c_1 + 5 c_2 = 2 c_3 + 5 c_6 N: | c_1 + c_2 = c_5 + c_6 O: | 3 c_1 = c_3 + 2 c_5 + 3 c_6 S: | c_2 = 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_3 = 1 and solve the system of equations for the remaining coefficients: c_2 = (4 c_1)/15 - 1/5 c_3 = 1 c_4 = (4 c_1)/15 - 1/5 c_5 = (4 c_1)/5 + 2/5 c_6 = (7 c_1)/15 - 3/5 The resulting system of equations is still underdetermined, so an additional coefficient must be set arbitrarily. Set c_1 = 12 and solve for the remaining coefficients: c_1 = 12 c_2 = 3 c_3 = 1 c_4 = 3 c_5 = 10 c_6 = 5 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 12 HNO_3 + 3 NH_4SH ⟶ H_2O + 3 S + 10 NO_2 + 5 NH4HO3

+ ⟶ + + + NH4HO3

nitric acid + ammonium bisulfide ⟶ water + mixed sulfur + nitrogen dioxide + NH4HO3

Construct the equilibrium constant, K, expression for: HNO_3 + NH_4SH ⟶ H_2O + S + NO_2 + NH4HO3 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: 12 HNO_3 + 3 NH_4SH ⟶ H_2O + 3 S + 10 NO_2 + 5 NH4HO3 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 HNO_3 | 12 | -12 NH_4SH | 3 | -3 H_2O | 1 | 1 S | 3 | 3 NO_2 | 10 | 10 NH4HO3 | 5 | 5 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HNO_3 | 12 | -12 | ([HNO3])^(-12) NH_4SH | 3 | -3 | ([NH4SH])^(-3) H_2O | 1 | 1 | [H2O] S | 3 | 3 | ([S])^3 NO_2 | 10 | 10 | ([NO2])^10 NH4HO3 | 5 | 5 | ([NH4HO3])^5 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 = ([HNO3])^(-12) ([NH4SH])^(-3) [H2O] ([S])^3 ([NO2])^10 ([NH4HO3])^5 = ([H2O] ([S])^3 ([NO2])^10 ([NH4HO3])^5)/(([HNO3])^12 ([NH4SH])^3)

Construct the rate of reaction expression for: HNO_3 + NH_4SH ⟶ H_2O + S + NO_2 + NH4HO3 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: 12 HNO_3 + 3 NH_4SH ⟶ H_2O + 3 S + 10 NO_2 + 5 NH4HO3 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 HNO_3 | 12 | -12 NH_4SH | 3 | -3 H_2O | 1 | 1 S | 3 | 3 NO_2 | 10 | 10 NH4HO3 | 5 | 5 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 HNO_3 | 12 | -12 | -1/12 (Δ[HNO3])/(Δt) NH_4SH | 3 | -3 | -1/3 (Δ[NH4SH])/(Δt) H_2O | 1 | 1 | (Δ[H2O])/(Δt) S | 3 | 3 | 1/3 (Δ[S])/(Δt) NO_2 | 10 | 10 | 1/10 (Δ[NO2])/(Δt) NH4HO3 | 5 | 5 | 1/5 (Δ[NH4HO3])/(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 = -1/12 (Δ[HNO3])/(Δt) = -1/3 (Δ[NH4SH])/(Δt) = (Δ[H2O])/(Δt) = 1/3 (Δ[S])/(Δt) = 1/10 (Δ[NO2])/(Δt) = 1/5 (Δ[NH4HO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| nitric acid | ammonium bisulfide | water | mixed sulfur | nitrogen dioxide | NH4HO3 formula | HNO_3 | NH_4SH | H_2O | S | NO_2 | NH4HO3 Hill formula | HNO_3 | H_5NS | H_2O | S | NO_2 | H5NO3 name | nitric acid | ammonium bisulfide | water | mixed sulfur | nitrogen dioxide | IUPAC name | nitric acid | azanium sulfanide | water | sulfur | Nitrogen dioxide |

| nitric acid | ammonium bisulfide | water | mixed sulfur | nitrogen dioxide | NH4HO3 molar mass | 63.012 g/mol | 51.11 g/mol | 18.015 g/mol | 32.06 g/mol | 46.005 g/mol | 67.04 g/mol phase | liquid (at STP) | solid (at STP) | liquid (at STP) | solid (at STP) | gas (at STP) | melting point | -41.6 °C | 120 °C | 0 °C | 112.8 °C | -11 °C | boiling point | 83 °C | | 99.9839 °C | 444.7 °C | 21 °C | density | 1.5129 g/cm^3 | 1.18 g/cm^3 | 1 g/cm^3 | 2.07 g/cm^3 | 0.00188 g/cm^3 (at 25 °C) | solubility in water | miscible | soluble | | | reacts | surface tension | | | 0.0728 N/m | | | dynamic viscosity | 7.6×10^-4 Pa s (at 25 °C) | | 8.9×10^-4 Pa s (at 25 °C) | | 4.02×10^-4 Pa s (at 25 °C) | odor | | | odorless | | |