NaOH + CuS = Cu(OH)2 + Na2S

NaOH sodium hydroxide + CuS cupric sulfide ⟶ Cu(OH)_2 copper hydroxide + Na_2S sodium sulfide

Balance the chemical equation algebraically: NaOH + CuS ⟶ Cu(OH)_2 + Na_2S Add stoichiometric coefficients, c_i, to the reactants and products: c_1 NaOH + c_2 CuS ⟶ c_3 Cu(OH)_2 + c_4 Na_2S Set the number of atoms in the reactants equal to the number of atoms in the products for H, Na, O, Cu and S: H: | c_1 = 2 c_3 Na: | c_1 = 2 c_4 O: | c_1 = 2 c_3 Cu: | c_2 = c_3 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 1 c_3 = 1 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 NaOH + CuS ⟶ Cu(OH)_2 + Na_2S

+ ⟶ +

sodium hydroxide + cupric sulfide ⟶ copper hydroxide + sodium sulfide

Construct the equilibrium constant, K, expression for: NaOH + CuS ⟶ Cu(OH)_2 + Na_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 NaOH + CuS ⟶ Cu(OH)_2 + Na_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 NaOH | 2 | -2 CuS | 1 | -1 Cu(OH)_2 | 1 | 1 Na_2S | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression NaOH | 2 | -2 | ([NaOH])^(-2) CuS | 1 | -1 | ([CuS])^(-1) Cu(OH)_2 | 1 | 1 | [Cu(OH)2] Na_2S | 1 | 1 | [Na2S] 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 = ([NaOH])^(-2) ([CuS])^(-1) [Cu(OH)2] [Na2S] = ([Cu(OH)2] [Na2S])/(([NaOH])^2 [CuS])

Construct the rate of reaction expression for: NaOH + CuS ⟶ Cu(OH)_2 + Na_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 NaOH + CuS ⟶ Cu(OH)_2 + Na_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 NaOH | 2 | -2 CuS | 1 | -1 Cu(OH)_2 | 1 | 1 Na_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 NaOH | 2 | -2 | -1/2 (Δ[NaOH])/(Δt) CuS | 1 | -1 | -(Δ[CuS])/(Δt) Cu(OH)_2 | 1 | 1 | (Δ[Cu(OH)2])/(Δt) Na_2S | 1 | 1 | (Δ[Na2S])/(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[NaOH])/(Δt) = -(Δ[CuS])/(Δt) = (Δ[Cu(OH)2])/(Δt) = (Δ[Na2S])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sodium hydroxide | cupric sulfide | copper hydroxide | sodium sulfide formula | NaOH | CuS | Cu(OH)_2 | Na_2S Hill formula | HNaO | CuS | CuH_2O_2 | Na_2S_1 name | sodium hydroxide | cupric sulfide | copper hydroxide | sodium sulfide IUPAC name | sodium hydroxide | | copper dihydroxide |

| sodium hydroxide | cupric sulfide | copper hydroxide | sodium sulfide molar mass | 39.997 g/mol | 95.61 g/mol | 97.56 g/mol | 78.04 g/mol phase | solid (at STP) | solid (at STP) | | solid (at STP) melting point | 323 °C | 220 °C | | 1172 °C boiling point | 1390 °C | | | density | 2.13 g/cm^3 | 4.6 g/cm^3 | | 1.856 g/cm^3 solubility in water | soluble | | | surface tension | 0.07435 N/m | | | dynamic viscosity | 0.004 Pa s (at 350 °C) | 3.68×10^-5 Pa s (at 1250 °C) | |