Na2SO4 + Cu(NO3)2 = CuSO4 + NaNO3

Na_2SO_4 sodium sulfate + Cu(NO_3)_2 copper(II) nitrate ⟶ CuSO_4 copper(II) sulfate + NaNO_3 sodium nitrate

Balance the chemical equation algebraically: Na_2SO_4 + Cu(NO_3)_2 ⟶ CuSO_4 + NaNO_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Na_2SO_4 + c_2 Cu(NO_3)_2 ⟶ c_3 CuSO_4 + c_4 NaNO_3 Set the number of atoms in the reactants equal to the number of atoms in the products for Na, O, S, Cu and N: Na: | 2 c_1 = c_4 O: | 4 c_1 + 6 c_2 = 4 c_3 + 3 c_4 S: | c_1 = c_3 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_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: | | Na_2SO_4 + Cu(NO_3)_2 ⟶ CuSO_4 + 2 NaNO_3

+ ⟶ +

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

Construct the equilibrium constant, K, expression for: Na_2SO_4 + Cu(NO_3)_2 ⟶ CuSO_4 + 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: Na_2SO_4 + Cu(NO_3)_2 ⟶ CuSO_4 + 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 Na_2SO_4 | 1 | -1 Cu(NO_3)_2 | 1 | -1 CuSO_4 | 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 Na_2SO_4 | 1 | -1 | ([Na2SO4])^(-1) Cu(NO_3)_2 | 1 | -1 | ([Cu(NO3)2])^(-1) CuSO_4 | 1 | 1 | [CuSO4] 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 = ([Na2SO4])^(-1) ([Cu(NO3)2])^(-1) [CuSO4] ([NaNO3])^2 = ([CuSO4] ([NaNO3])^2)/([Na2SO4] [Cu(NO3)2])

Construct the rate of reaction expression for: Na_2SO_4 + Cu(NO_3)_2 ⟶ CuSO_4 + 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: Na_2SO_4 + Cu(NO_3)_2 ⟶ CuSO_4 + 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 Na_2SO_4 | 1 | -1 Cu(NO_3)_2 | 1 | -1 CuSO_4 | 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 Na_2SO_4 | 1 | -1 | -(Δ[Na2SO4])/(Δt) Cu(NO_3)_2 | 1 | -1 | -(Δ[Cu(NO3)2])/(Δt) CuSO_4 | 1 | 1 | (Δ[CuSO4])/(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[Na2SO4])/(Δt) = -(Δ[Cu(NO3)2])/(Δt) = (Δ[CuSO4])/(Δt) = 1/2 (Δ[NaNO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sodium sulfate | copper(II) nitrate | copper(II) sulfate | sodium nitrate formula | Na_2SO_4 | Cu(NO_3)_2 | CuSO_4 | NaNO_3 Hill formula | Na_2O_4S | CuN_2O_6 | CuO_4S | NNaO_3 name | sodium sulfate | copper(II) nitrate | copper(II) sulfate | sodium nitrate IUPAC name | disodium sulfate | copper(II) nitrate | copper sulfate | sodium nitrate

| sodium sulfate | copper(II) nitrate | copper(II) sulfate | sodium nitrate molar mass | 142.04 g/mol | 187.55 g/mol | 159.6 g/mol | 84.994 g/mol phase | solid (at STP) | | solid (at STP) | solid (at STP) melting point | 884 °C | | 200 °C | 306 °C boiling point | 1429 °C | | | density | 2.68 g/cm^3 | | 3.603 g/cm^3 | 2.26 g/cm^3 solubility in water | soluble | | | soluble dynamic viscosity | | | | 0.003 Pa s (at 250 °C)