MnSO4 + (NH4)2S = (NH4)2SO4 + MnS

MnSO_4 manganese(II) sulfate + (NH_4)_2S diammonium sulfide ⟶ (NH_4)_2SO_4 ammonium sulfate + MnS manganese sulfide

Balance the chemical equation algebraically: MnSO_4 + (NH_4)_2S ⟶ (NH_4)_2SO_4 + MnS Add stoichiometric coefficients, c_i, to the reactants and products: c_1 MnSO_4 + c_2 (NH_4)_2S ⟶ c_3 (NH_4)_2SO_4 + c_4 MnS Set the number of atoms in the reactants equal to the number of atoms in the products for Mn, O, S, H and N: Mn: | c_1 = c_4 O: | 4 c_1 = 4 c_3 S: | c_1 + c_2 = c_3 + c_4 H: | 8 c_2 = 8 c_3 N: | 2 c_2 = 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 1 c_3 = 1 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | MnSO_4 + (NH_4)_2S ⟶ (NH_4)_2SO_4 + MnS

+ ⟶ +

manganese(II) sulfate + diammonium sulfide ⟶ ammonium sulfate + manganese sulfide

Construct the equilibrium constant, K, expression for: MnSO_4 + (NH_4)_2S ⟶ (NH_4)_2SO_4 + MnS 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: MnSO_4 + (NH_4)_2S ⟶ (NH_4)_2SO_4 + MnS 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 MnSO_4 | 1 | -1 (NH_4)_2S | 1 | -1 (NH_4)_2SO_4 | 1 | 1 MnS | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression MnSO_4 | 1 | -1 | ([MnSO4])^(-1) (NH_4)_2S | 1 | -1 | ([(NH4)2S])^(-1) (NH_4)_2SO_4 | 1 | 1 | [(NH4)2SO4] MnS | 1 | 1 | [MnS] 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 = ([MnSO4])^(-1) ([(NH4)2S])^(-1) [(NH4)2SO4] [MnS] = ([(NH4)2SO4] [MnS])/([MnSO4] [(NH4)2S])

Construct the rate of reaction expression for: MnSO_4 + (NH_4)_2S ⟶ (NH_4)_2SO_4 + MnS 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: MnSO_4 + (NH_4)_2S ⟶ (NH_4)_2SO_4 + MnS 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 MnSO_4 | 1 | -1 (NH_4)_2S | 1 | -1 (NH_4)_2SO_4 | 1 | 1 MnS | 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 MnSO_4 | 1 | -1 | -(Δ[MnSO4])/(Δt) (NH_4)_2S | 1 | -1 | -(Δ[(NH4)2S])/(Δt) (NH_4)_2SO_4 | 1 | 1 | (Δ[(NH4)2SO4])/(Δt) MnS | 1 | 1 | (Δ[MnS])/(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[MnSO4])/(Δt) = -(Δ[(NH4)2S])/(Δt) = (Δ[(NH4)2SO4])/(Δt) = (Δ[MnS])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| manganese(II) sulfate | diammonium sulfide | ammonium sulfate | manganese sulfide formula | MnSO_4 | (NH_4)_2S | (NH_4)_2SO_4 | MnS Hill formula | MnSO_4 | H_8N_2S | H_8N_2O_4S | MnS name | manganese(II) sulfate | diammonium sulfide | ammonium sulfate | manganese sulfide IUPAC name | manganese(+2) cation sulfate | diammonium sulfide | |

| manganese(II) sulfate | diammonium sulfide | ammonium sulfate | manganese sulfide molar mass | 150.99 g/mol | 68.14 g/mol | 132.1 g/mol | 87 g/mol phase | solid (at STP) | liquid (at STP) | solid (at STP) | solid (at STP) melting point | 710 °C | -18 °C | 280 °C | 1141 °C density | 3.25 g/cm^3 | 0.997 g/cm^3 | 1.77 g/cm^3 | 3.3 g/cm^3 solubility in water | soluble | very soluble | | dynamic viscosity | | | | 2.64×10^-5 Pa s (at 1250 °C) odor | | | odorless |