CuSO4 + Mg = Cu + MgSO4

copper(II) sulfate + magnesium ⟶ copper + magnesium sulfate

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

+ ⟶ +

copper(II) sulfate + magnesium ⟶ copper + magnesium sulfate

| copper(II) sulfate | magnesium | copper | magnesium sulfate molecular enthalpy | -771.4 kJ/mol | 0 kJ/mol | 0 kJ/mol | -1285 kJ/mol total enthalpy | -771.4 kJ/mol | 0 kJ/mol | 0 kJ/mol | -1285 kJ/mol | H_initial = -771.4 kJ/mol | | H_final = -1285 kJ/mol | ΔH_rxn^0 | -1285 kJ/mol - -771.4 kJ/mol = -513.5 kJ/mol (exothermic) | | |

Construct the equilibrium constant, K, expression for: + ⟶ + 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: + ⟶ + 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 | 1 | -1 | 1 | -1 | 1 | 1 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression | 1 | -1 | ([CuSO4])^(-1) | 1 | -1 | ([Mg])^(-1) | 1 | 1 | [Cu] | 1 | 1 | [MgSO4] 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) ([Mg])^(-1) [Cu] [MgSO4] = ([Cu] [MgSO4])/([CuSO4] [Mg])

Construct the rate of reaction expression for: + ⟶ + 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: + ⟶ + 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 | 1 | -1 | 1 | -1 | 1 | 1 | 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 | 1 | -1 | -(Δ[CuSO4])/(Δt) | 1 | -1 | -(Δ[Mg])/(Δt) | 1 | 1 | (Δ[Cu])/(Δt) | 1 | 1 | (Δ[MgSO4])/(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) = -(Δ[Mg])/(Δt) = (Δ[Cu])/(Δt) = (Δ[MgSO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| copper(II) sulfate | magnesium | copper | magnesium sulfate Hill formula | CuO_4S | Mg | Cu | MgO_4S name | copper(II) sulfate | magnesium | copper | magnesium sulfate IUPAC name | copper sulfate | magnesium | copper | magnesium sulfate

| copper(II) sulfate | magnesium | copper | magnesium sulfate molar mass | 159.6 g/mol | 24.305 g/mol | 63.546 g/mol | 120.4 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | solid (at STP) melting point | 200 °C | 648 °C | 1083 °C | boiling point | | 1090 °C | 2567 °C | density | 3.603 g/cm^3 | 1.738 g/cm^3 | 8.96 g/cm^3 | solubility in water | | reacts | insoluble | soluble odor | | | odorless |