CuSO4 + Mn = Cu + MnSO4

CuSO_4 copper(II) sulfate + Mn manganese ⟶ Cu copper + MnSO_4 manganese(II) sulfate

Balance the chemical equation algebraically: CuSO_4 + Mn ⟶ Cu + MnSO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 CuSO_4 + c_2 Mn ⟶ c_3 Cu + c_4 MnSO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for Cu, O, S and Mn: Cu: | c_1 = c_3 O: | 4 c_1 = 4 c_4 S: | c_1 = c_4 Mn: | 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: | | CuSO_4 + Mn ⟶ Cu + MnSO_4

+ ⟶ +

copper(II) sulfate + manganese ⟶ copper + manganese(II) sulfate

Construct the equilibrium constant, K, expression for: CuSO_4 + Mn ⟶ Cu + MnSO_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 + Mn ⟶ Cu + MnSO_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 Mn | 1 | -1 Cu | 1 | 1 MnSO_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) Mn | 1 | -1 | ([Mn])^(-1) Cu | 1 | 1 | [Cu] MnSO_4 | 1 | 1 | [MnSO4] 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) ([Mn])^(-1) [Cu] [MnSO4] = ([Cu] [MnSO4])/([CuSO4] [Mn])

Construct the rate of reaction expression for: CuSO_4 + Mn ⟶ Cu + MnSO_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 + Mn ⟶ Cu + MnSO_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 Mn | 1 | -1 Cu | 1 | 1 MnSO_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) Mn | 1 | -1 | -(Δ[Mn])/(Δt) Cu | 1 | 1 | (Δ[Cu])/(Δt) MnSO_4 | 1 | 1 | (Δ[MnSO4])/(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[Mn])/(Δt) = (Δ[Cu])/(Δt) = (Δ[MnSO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| copper(II) sulfate | manganese | copper | manganese(II) sulfate formula | CuSO_4 | Mn | Cu | MnSO_4 Hill formula | CuO_4S | Mn | Cu | MnSO_4 name | copper(II) sulfate | manganese | copper | manganese(II) sulfate IUPAC name | copper sulfate | manganese | copper | manganese(+2) cation sulfate

| copper(II) sulfate | manganese | copper | manganese(II) sulfate molar mass | 159.6 g/mol | 54.938044 g/mol | 63.546 g/mol | 150.99 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | solid (at STP) melting point | 200 °C | 1244 °C | 1083 °C | 710 °C boiling point | | 1962 °C | 2567 °C | density | 3.603 g/cm^3 | 7.3 g/cm^3 | 8.96 g/cm^3 | 3.25 g/cm^3 solubility in water | | insoluble | insoluble | soluble odor | | | odorless |