(NH4)S5 = S + (NH4)2S

NH4S5 ⟶ S mixed sulfur + (NH_4)_2S diammonium sulfide

Balance the chemical equation algebraically: NH4S5 ⟶ S + (NH_4)_2S Add stoichiometric coefficients, c_i, to the reactants and products: c_1 NH4S5 ⟶ c_2 S + c_3 (NH_4)_2S Set the number of atoms in the reactants equal to the number of atoms in the products for N, H and S: N: | c_1 = 2 c_3 H: | 4 c_1 = 8 c_3 S: | 5 c_1 = c_2 + c_3 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_1 = 2 c_2 = 9 c_3 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 NH4S5 ⟶ 9 S + (NH_4)_2S

NH4S5 ⟶ +

NH4S5 ⟶ mixed sulfur + diammonium sulfide

Construct the equilibrium constant, K, expression for: NH4S5 ⟶ S + (NH_4)_2S 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 NH4S5 ⟶ 9 S + (NH_4)_2S 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 NH4S5 | 2 | -2 S | 9 | 9 (NH_4)_2S | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression NH4S5 | 2 | -2 | ([NH4S5])^(-2) S | 9 | 9 | ([S])^9 (NH_4)_2S | 1 | 1 | [(NH4)2S] 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 = ([NH4S5])^(-2) ([S])^9 [(NH4)2S] = (([S])^9 [(NH4)2S])/([NH4S5])^2

Construct the rate of reaction expression for: NH4S5 ⟶ S + (NH_4)_2S 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 NH4S5 ⟶ 9 S + (NH_4)_2S 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 NH4S5 | 2 | -2 S | 9 | 9 (NH_4)_2S | 1 | 1 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 NH4S5 | 2 | -2 | -1/2 (Δ[NH4S5])/(Δt) S | 9 | 9 | 1/9 (Δ[S])/(Δt) (NH_4)_2S | 1 | 1 | (Δ[(NH4)2S])/(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[NH4S5])/(Δt) = 1/9 (Δ[S])/(Δt) = (Δ[(NH4)2S])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| NH4S5 | mixed sulfur | diammonium sulfide formula | NH4S5 | S | (NH_4)_2S Hill formula | H4NS5 | S | H_8N_2S name | | mixed sulfur | diammonium sulfide IUPAC name | | sulfur | diammonium sulfide

| NH4S5 | mixed sulfur | diammonium sulfide molar mass | 178.3 g/mol | 32.06 g/mol | 68.14 g/mol phase | | solid (at STP) | liquid (at STP) melting point | | 112.8 °C | -18 °C boiling point | | 444.7 °C | density | | 2.07 g/cm^3 | 0.997 g/cm^3 solubility in water | | | very soluble