H2O + CuSO4 = [Cu(H2O)6]SO4

H_2O water + CuSO_4 copper(II) sulfate ⟶ Cu(H2O)6SO4

Balance the chemical equation algebraically: H_2O + CuSO_4 ⟶ Cu(H2O)6SO4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 CuSO_4 ⟶ c_3 Cu(H2O)6SO4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, Cu and S: H: | 2 c_1 = 12 c_3 O: | c_1 + 4 c_2 = 10 c_3 Cu: | c_2 = 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 6 c_2 = 1 c_3 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 6 H_2O + CuSO_4 ⟶ Cu(H2O)6SO4

+ ⟶ Cu(H2O)6SO4

water + copper(II) sulfate ⟶ Cu(H2O)6SO4

Construct the equilibrium constant, K, expression for: H_2O + CuSO_4 ⟶ Cu(H2O)6SO4 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: 6 H_2O + CuSO_4 ⟶ Cu(H2O)6SO4 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 H_2O | 6 | -6 CuSO_4 | 1 | -1 Cu(H2O)6SO4 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 6 | -6 | ([H2O])^(-6) CuSO_4 | 1 | -1 | ([CuSO4])^(-1) Cu(H2O)6SO4 | 1 | 1 | [Cu(H2O)6SO4] 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 = ([H2O])^(-6) ([CuSO4])^(-1) [Cu(H2O)6SO4] = ([Cu(H2O)6SO4])/(([H2O])^6 [CuSO4])

Construct the rate of reaction expression for: H_2O + CuSO_4 ⟶ Cu(H2O)6SO4 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: 6 H_2O + CuSO_4 ⟶ Cu(H2O)6SO4 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 H_2O | 6 | -6 CuSO_4 | 1 | -1 Cu(H2O)6SO4 | 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 H_2O | 6 | -6 | -1/6 (Δ[H2O])/(Δt) CuSO_4 | 1 | -1 | -(Δ[CuSO4])/(Δt) Cu(H2O)6SO4 | 1 | 1 | (Δ[Cu(H2O)6SO4])/(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 = -1/6 (Δ[H2O])/(Δt) = -(Δ[CuSO4])/(Δt) = (Δ[Cu(H2O)6SO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | copper(II) sulfate | Cu(H2O)6SO4 formula | H_2O | CuSO_4 | Cu(H2O)6SO4 Hill formula | H_2O | CuO_4S | H12CuO10S name | water | copper(II) sulfate | IUPAC name | water | copper sulfate |

| water | copper(II) sulfate | Cu(H2O)6SO4 molar mass | 18.015 g/mol | 159.6 g/mol | 267.69 g/mol phase | liquid (at STP) | solid (at STP) | melting point | 0 °C | 200 °C | boiling point | 99.9839 °C | | density | 1 g/cm^3 | 3.603 g/cm^3 | surface tension | 0.0728 N/m | | dynamic viscosity | 8.9×10^-4 Pa s (at 25 °C) | | odor | odorless | |