H2SO4 + NH3 = H2O + HNO3 + S

H_2SO_4 sulfuric acid + NH_3 ammonia ⟶ H_2O water + HNO_3 nitric acid + S mixed sulfur

Balance the chemical equation algebraically: H_2SO_4 + NH_3 ⟶ H_2O + HNO_3 + S Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 NH_3 ⟶ c_3 H_2O + c_4 HNO_3 + c_5 S Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S and N: H: | 2 c_1 + 3 c_2 = 2 c_3 + c_4 O: | 4 c_1 = c_3 + 3 c_4 S: | c_1 = c_5 N: | 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 4/3 c_2 = 1 c_3 = 7/3 c_4 = 1 c_5 = 4/3 Multiply by the least common denominator, 3, to eliminate fractional coefficients: c_1 = 4 c_2 = 3 c_3 = 7 c_4 = 3 c_5 = 4 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 H_2SO_4 + 3 NH_3 ⟶ 7 H_2O + 3 HNO_3 + 4 S

+ ⟶ + +

sulfuric acid + ammonia ⟶ water + nitric acid + mixed sulfur

Construct the equilibrium constant, K, expression for: H_2SO_4 + NH_3 ⟶ H_2O + HNO_3 + S 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: 4 H_2SO_4 + 3 NH_3 ⟶ 7 H_2O + 3 HNO_3 + 4 S 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_2SO_4 | 4 | -4 NH_3 | 3 | -3 H_2O | 7 | 7 HNO_3 | 3 | 3 S | 4 | 4 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 4 | -4 | ([H2SO4])^(-4) NH_3 | 3 | -3 | ([NH3])^(-3) H_2O | 7 | 7 | ([H2O])^7 HNO_3 | 3 | 3 | ([HNO3])^3 S | 4 | 4 | ([S])^4 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 = ([H2SO4])^(-4) ([NH3])^(-3) ([H2O])^7 ([HNO3])^3 ([S])^4 = (([H2O])^7 ([HNO3])^3 ([S])^4)/(([H2SO4])^4 ([NH3])^3)

Construct the rate of reaction expression for: H_2SO_4 + NH_3 ⟶ H_2O + HNO_3 + S 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: 4 H_2SO_4 + 3 NH_3 ⟶ 7 H_2O + 3 HNO_3 + 4 S 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_2SO_4 | 4 | -4 NH_3 | 3 | -3 H_2O | 7 | 7 HNO_3 | 3 | 3 S | 4 | 4 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_2SO_4 | 4 | -4 | -1/4 (Δ[H2SO4])/(Δt) NH_3 | 3 | -3 | -1/3 (Δ[NH3])/(Δt) H_2O | 7 | 7 | 1/7 (Δ[H2O])/(Δt) HNO_3 | 3 | 3 | 1/3 (Δ[HNO3])/(Δt) S | 4 | 4 | 1/4 (Δ[S])/(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 = -1/4 (Δ[H2SO4])/(Δt) = -1/3 (Δ[NH3])/(Δt) = 1/7 (Δ[H2O])/(Δt) = 1/3 (Δ[HNO3])/(Δt) = 1/4 (Δ[S])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sulfuric acid | ammonia | water | nitric acid | mixed sulfur formula | H_2SO_4 | NH_3 | H_2O | HNO_3 | S Hill formula | H_2O_4S | H_3N | H_2O | HNO_3 | S name | sulfuric acid | ammonia | water | nitric acid | mixed sulfur IUPAC name | sulfuric acid | ammonia | water | nitric acid | sulfur

| sulfuric acid | ammonia | water | nitric acid | mixed sulfur molar mass | 98.07 g/mol | 17.031 g/mol | 18.015 g/mol | 63.012 g/mol | 32.06 g/mol phase | liquid (at STP) | gas (at STP) | liquid (at STP) | liquid (at STP) | solid (at STP) melting point | 10.371 °C | -77.73 °C | 0 °C | -41.6 °C | 112.8 °C boiling point | 279.6 °C | -33.33 °C | 99.9839 °C | 83 °C | 444.7 °C density | 1.8305 g/cm^3 | 6.96×10^-4 g/cm^3 (at 25 °C) | 1 g/cm^3 | 1.5129 g/cm^3 | 2.07 g/cm^3 solubility in water | very soluble | | | miscible | surface tension | 0.0735 N/m | 0.0234 N/m | 0.0728 N/m | | dynamic viscosity | 0.021 Pa s (at 25 °C) | 1.009×10^-5 Pa s (at 25 °C) | 8.9×10^-4 Pa s (at 25 °C) | 7.6×10^-4 Pa s (at 25 °C) | odor | odorless | | odorless | |