Cu + Ag2SO4 = CuSO4 + Ag

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

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

+ ⟶ +

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

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

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

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

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

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