Cu(NO3)2 + Na2S = CuS + Na(NO3)

Cu(NO_3)_2 copper(II) nitrate + Na_2S sodium sulfide ⟶ CuS cupric sulfide + NaNO_3 sodium nitrate

Balance the chemical equation algebraically: Cu(NO_3)_2 + Na_2S ⟶ CuS + NaNO_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Cu(NO_3)_2 + c_2 Na_2S ⟶ c_3 CuS + c_4 NaNO_3 Set the number of atoms in the reactants equal to the number of atoms in the products for Cu, N, O, Na and S: Cu: | c_1 = c_3 N: | 2 c_1 = c_4 O: | 6 c_1 = 3 c_4 Na: | 2 c_2 = c_4 S: | 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 1 c_3 = 1 c_4 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | Cu(NO_3)_2 + Na_2S ⟶ CuS + 2 NaNO_3

+ ⟶ +

copper(II) nitrate + sodium sulfide ⟶ cupric sulfide + sodium nitrate

Construct the equilibrium constant, K, expression for: Cu(NO_3)_2 + Na_2S ⟶ CuS + NaNO_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: Cu(NO_3)_2 + Na_2S ⟶ CuS + 2 NaNO_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 Cu(NO_3)_2 | 1 | -1 Na_2S | 1 | -1 CuS | 1 | 1 NaNO_3 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Cu(NO_3)_2 | 1 | -1 | ([Cu(NO3)2])^(-1) Na_2S | 1 | -1 | ([Na2S])^(-1) CuS | 1 | 1 | [CuS] NaNO_3 | 2 | 2 | ([NaNO3])^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 = ([Cu(NO3)2])^(-1) ([Na2S])^(-1) [CuS] ([NaNO3])^2 = ([CuS] ([NaNO3])^2)/([Cu(NO3)2] [Na2S])

Construct the rate of reaction expression for: Cu(NO_3)_2 + Na_2S ⟶ CuS + NaNO_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: Cu(NO_3)_2 + Na_2S ⟶ CuS + 2 NaNO_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 Cu(NO_3)_2 | 1 | -1 Na_2S | 1 | -1 CuS | 1 | 1 NaNO_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 Cu(NO_3)_2 | 1 | -1 | -(Δ[Cu(NO3)2])/(Δt) Na_2S | 1 | -1 | -(Δ[Na2S])/(Δt) CuS | 1 | 1 | (Δ[CuS])/(Δt) NaNO_3 | 2 | 2 | 1/2 (Δ[NaNO3])/(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[Cu(NO3)2])/(Δt) = -(Δ[Na2S])/(Δt) = (Δ[CuS])/(Δt) = 1/2 (Δ[NaNO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| copper(II) nitrate | sodium sulfide | cupric sulfide | sodium nitrate formula | Cu(NO_3)_2 | Na_2S | CuS | NaNO_3 Hill formula | CuN_2O_6 | Na_2S_1 | CuS | NNaO_3 name | copper(II) nitrate | sodium sulfide | cupric sulfide | sodium nitrate

| copper(II) nitrate | sodium sulfide | cupric sulfide | sodium nitrate molar mass | 187.55 g/mol | 78.04 g/mol | 95.61 g/mol | 84.994 g/mol phase | | solid (at STP) | solid (at STP) | solid (at STP) melting point | | 1172 °C | 220 °C | 306 °C density | | 1.856 g/cm^3 | 4.6 g/cm^3 | 2.26 g/cm^3 solubility in water | | | | soluble dynamic viscosity | | | 3.68×10^-5 Pa s (at 1250 °C) | 0.003 Pa s (at 250 °C)