CuSO4 + Ag = Cu + Ag2SO4

CuSO_4 copper(II) sulfate + Ag silver ⟶ Cu copper + Ag_2SO_4 silver sulfate

Balance the chemical equation algebraically: CuSO_4 + Ag ⟶ Cu + Ag_2SO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 CuSO_4 + c_2 Ag ⟶ c_3 Cu + c_4 Ag_2SO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for Cu, O, S and Ag: Cu: | c_1 = c_3 O: | 4 c_1 = 4 c_4 S: | c_1 = c_4 Ag: | c_2 = 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 = 2 c_3 = 1 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | CuSO_4 + 2 Ag ⟶ Cu + Ag_2SO_4

+ ⟶ +

copper(II) sulfate + silver ⟶ copper + silver sulfate

| copper(II) sulfate | silver | copper | silver sulfate molecular enthalpy | -771.4 kJ/mol | 0 kJ/mol | 0 kJ/mol | -715.9 kJ/mol total enthalpy | -771.4 kJ/mol | 0 kJ/mol | 0 kJ/mol | -715.9 kJ/mol | H_initial = -771.4 kJ/mol | | H_final = -715.9 kJ/mol | ΔH_rxn^0 | -715.9 kJ/mol - -771.4 kJ/mol = 55.5 kJ/mol (endothermic) | | |

Construct the equilibrium constant, K, expression for: CuSO_4 + Ag ⟶ Cu + Ag_2SO_4 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: CuSO_4 + 2 Ag ⟶ Cu + Ag_2SO_4 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 CuSO_4 | 1 | -1 Ag | 2 | -2 Cu | 1 | 1 Ag_2SO_4 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression CuSO_4 | 1 | -1 | ([CuSO4])^(-1) Ag | 2 | -2 | ([Ag])^(-2) Cu | 1 | 1 | [Cu] Ag_2SO_4 | 1 | 1 | [Ag2SO4] 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 = ([CuSO4])^(-1) ([Ag])^(-2) [Cu] [Ag2SO4] = ([Cu] [Ag2SO4])/([CuSO4] ([Ag])^2)

Construct the rate of reaction expression for: CuSO_4 + Ag ⟶ Cu + Ag_2SO_4 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: CuSO_4 + 2 Ag ⟶ Cu + Ag_2SO_4 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 CuSO_4 | 1 | -1 Ag | 2 | -2 Cu | 1 | 1 Ag_2SO_4 | 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 CuSO_4 | 1 | -1 | -(Δ[CuSO4])/(Δt) Ag | 2 | -2 | -1/2 (Δ[Ag])/(Δt) Cu | 1 | 1 | (Δ[Cu])/(Δt) Ag_2SO_4 | 1 | 1 | (Δ[Ag2SO4])/(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[CuSO4])/(Δt) = -1/2 (Δ[Ag])/(Δt) = (Δ[Cu])/(Δt) = (Δ[Ag2SO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| copper(II) sulfate | silver | copper | silver sulfate formula | CuSO_4 | Ag | Cu | Ag_2SO_4 Hill formula | CuO_4S | Ag | Cu | Ag_2O_4S name | copper(II) sulfate | silver | copper | silver sulfate IUPAC name | copper sulfate | silver | copper | disilver sulfate

| copper(II) sulfate | silver | copper | silver sulfate molar mass | 159.6 g/mol | 107.8682 g/mol | 63.546 g/mol | 311.79 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | solid (at STP) melting point | 200 °C | 960 °C | 1083 °C | 652 °C boiling point | | 2212 °C | 2567 °C | density | 3.603 g/cm^3 | 10.49 g/cm^3 | 8.96 g/cm^3 | solubility in water | | insoluble | insoluble | slightly soluble odor | | | odorless |