(NH4)2SO4 = H2SO4 + NH3

(NH_4)_2SO_4 ammonium sulfate ⟶ H_2SO_4 sulfuric acid + NH_3 ammonia

Balance the chemical equation algebraically: (NH_4)_2SO_4 ⟶ H_2SO_4 + NH_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 (NH_4)_2SO_4 ⟶ c_2 H_2SO_4 + c_3 NH_3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, N, O and S: H: | 8 c_1 = 2 c_2 + 3 c_3 N: | 2 c_1 = c_3 O: | 4 c_1 = 4 c_2 S: | c_1 = c_2 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 = 1 c_3 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | (NH_4)_2SO_4 ⟶ H_2SO_4 + 2 NH_3

⟶ +

ammonium sulfate ⟶ sulfuric acid + ammonia

| ammonium sulfate | sulfuric acid | ammonia molecular enthalpy | -1181 kJ/mol | -814 kJ/mol | -45.9 kJ/mol total enthalpy | -1181 kJ/mol | -814 kJ/mol | -91.8 kJ/mol | H_initial = -1181 kJ/mol | H_final = -905.8 kJ/mol | ΔH_rxn^0 | -905.8 kJ/mol - -1181 kJ/mol = 275.1 kJ/mol (endothermic) | |

| ammonium sulfate | sulfuric acid | ammonia molecular free energy | -901.7 kJ/mol | -690 kJ/mol | -16.4 kJ/mol total free energy | -901.7 kJ/mol | -690 kJ/mol | -32.8 kJ/mol | G_initial = -901.7 kJ/mol | G_final = -722.8 kJ/mol | ΔG_rxn^0 | -722.8 kJ/mol - -901.7 kJ/mol = 178.9 kJ/mol (endergonic) | |

Construct the equilibrium constant, K, expression for: (NH_4)_2SO_4 ⟶ H_2SO_4 + NH_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: (NH_4)_2SO_4 ⟶ H_2SO_4 + 2 NH_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 (NH_4)_2SO_4 | 1 | -1 H_2SO_4 | 1 | 1 NH_3 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression (NH_4)_2SO_4 | 1 | -1 | ([(NH4)2SO4])^(-1) H_2SO_4 | 1 | 1 | [H2SO4] NH_3 | 2 | 2 | ([NH3])^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 = ([(NH4)2SO4])^(-1) [H2SO4] ([NH3])^2 = ([H2SO4] ([NH3])^2)/([(NH4)2SO4])

Construct the rate of reaction expression for: (NH_4)_2SO_4 ⟶ H_2SO_4 + NH_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: (NH_4)_2SO_4 ⟶ H_2SO_4 + 2 NH_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 (NH_4)_2SO_4 | 1 | -1 H_2SO_4 | 1 | 1 NH_3 | 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 (NH_4)_2SO_4 | 1 | -1 | -(Δ[(NH4)2SO4])/(Δt) H_2SO_4 | 1 | 1 | (Δ[H2SO4])/(Δt) NH_3 | 2 | 2 | 1/2 (Δ[NH3])/(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[(NH4)2SO4])/(Δt) = (Δ[H2SO4])/(Δt) = 1/2 (Δ[NH3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| ammonium sulfate | sulfuric acid | ammonia formula | (NH_4)_2SO_4 | H_2SO_4 | NH_3 Hill formula | H_8N_2O_4S | H_2O_4S | H_3N name | ammonium sulfate | sulfuric acid | ammonia

| ammonium sulfate | sulfuric acid | ammonia molar mass | 132.1 g/mol | 98.07 g/mol | 17.031 g/mol phase | solid (at STP) | liquid (at STP) | gas (at STP) melting point | 280 °C | 10.371 °C | -77.73 °C boiling point | | 279.6 °C | -33.33 °C density | 1.77 g/cm^3 | 1.8305 g/cm^3 | 6.96×10^-4 g/cm^3 (at 25 °C) solubility in water | | very soluble | surface tension | | 0.0735 N/m | 0.0234 N/m dynamic viscosity | | 0.021 Pa s (at 25 °C) | 1.009×10^-5 Pa s (at 25 °C) odor | odorless | odorless |