NaOH + Cu(NO3)2 = Cu(OH)2 + Na(NO3)

NaOH sodium hydroxide + Cu(NO_3)_2 copper(II) nitrate ⟶ Cu(OH)_2 copper hydroxide + NaNO_3 sodium nitrate

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

+ ⟶ +

sodium hydroxide + copper(II) nitrate ⟶ copper hydroxide + sodium nitrate

Construct the equilibrium constant, K, expression for: NaOH + Cu(NO_3)_2 ⟶ Cu(OH)_2 + 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: 2 NaOH + Cu(NO_3)_2 ⟶ Cu(OH)_2 + 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 NaOH | 2 | -2 Cu(NO_3)_2 | 1 | -1 Cu(OH)_2 | 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 NaOH | 2 | -2 | ([NaOH])^(-2) Cu(NO_3)_2 | 1 | -1 | ([Cu(NO3)2])^(-1) Cu(OH)_2 | 1 | 1 | [Cu(OH)2] 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 = ([NaOH])^(-2) ([Cu(NO3)2])^(-1) [Cu(OH)2] ([NaNO3])^2 = ([Cu(OH)2] ([NaNO3])^2)/(([NaOH])^2 [Cu(NO3)2])

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

| sodium hydroxide | copper(II) nitrate | copper hydroxide | sodium nitrate formula | NaOH | Cu(NO_3)_2 | Cu(OH)_2 | NaNO_3 Hill formula | HNaO | CuN_2O_6 | CuH_2O_2 | NNaO_3 name | sodium hydroxide | copper(II) nitrate | copper hydroxide | sodium nitrate IUPAC name | sodium hydroxide | copper(II) nitrate | copper dihydroxide | sodium nitrate

| sodium hydroxide | copper(II) nitrate | copper hydroxide | sodium nitrate molar mass | 39.997 g/mol | 187.55 g/mol | 97.56 g/mol | 84.994 g/mol phase | solid (at STP) | | | solid (at STP) melting point | 323 °C | | | 306 °C boiling point | 1390 °C | | | density | 2.13 g/cm^3 | | | 2.26 g/cm^3 solubility in water | soluble | | | soluble surface tension | 0.07435 N/m | | | dynamic viscosity | 0.004 Pa s (at 350 °C) | | | 0.003 Pa s (at 250 °C)