NaOH + Cu = Na + Cu(OH)2

NaOH sodium hydroxide + Cu copper ⟶ Na sodium + Cu(OH)_2 copper hydroxide

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

+ ⟶ +

sodium hydroxide + copper ⟶ sodium + copper hydroxide

Construct the equilibrium constant, K, expression for: NaOH + Cu ⟶ Na + Cu(OH)_2 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 + Cu ⟶ 2 Na + Cu(OH)_2 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 Cu | 1 | -1 Na | 2 | 2 Cu(OH)_2 | 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) Cu | 1 | -1 | ([Cu])^(-1) Na | 2 | 2 | ([Na])^2 Cu(OH)_2 | 1 | 1 | [Cu(OH)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 = ([NaOH])^(-2) ([Cu])^(-1) ([Na])^2 [Cu(OH)2] = (([Na])^2 [Cu(OH)2])/(([NaOH])^2 [Cu])

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

| sodium hydroxide | copper | sodium | copper hydroxide formula | NaOH | Cu | Na | Cu(OH)_2 Hill formula | HNaO | Cu | Na | CuH_2O_2 name | sodium hydroxide | copper | sodium | copper hydroxide IUPAC name | sodium hydroxide | copper | sodium | copper dihydroxide

| sodium hydroxide | copper | sodium | copper hydroxide molar mass | 39.997 g/mol | 63.546 g/mol | 22.98976928 g/mol | 97.56 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | melting point | 323 °C | 1083 °C | 97.8 °C | boiling point | 1390 °C | 2567 °C | 883 °C | density | 2.13 g/cm^3 | 8.96 g/cm^3 | 0.968 g/cm^3 | solubility in water | soluble | insoluble | decomposes | surface tension | 0.07435 N/m | | | dynamic viscosity | 0.004 Pa s (at 350 °C) | | 1.413×10^-5 Pa s (at 527 °C) | odor | | odorless | |