Zn + CuSO4 + 5H2O = H2O + Cu + ZnSO4

Input interpretation

Image
Text

Zn zinc + CuSO_4 copper(II) sulfate + 5 H_2O water ⟶ H_2O water + Cu copper + ZnSO_4 zinc sulfate

Balanced equation

Image
Text

Balance the chemical equation algebraically: Zn + CuSO_4 + H_2O ⟶ H_2O + Cu + ZnSO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Zn + c_2 CuSO_4 + c_3 H_2O ⟶ c_4 H_2O + c_5 Cu + c_6 ZnSO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for Zn, Cu, O, S and H: Zn: | c_1 = c_6 Cu: | c_2 = c_5 O: | 4 c_2 + c_3 = c_4 + 4 c_6 S: | c_2 = c_6 H: | 2 c_3 = 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_4 = c_3 c_5 = 1 c_6 = 1 The resulting system of equations is still underdetermined, so an additional coefficient must be set arbitrarily. Set c_3 = 1 and solve for the remaining coefficients: c_1 = 1 c_2 = 1 c_3 = 1 c_4 = 1 c_5 = 1 c_6 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | Zn + CuSO_4 + H_2O ⟶ H_2O + Cu + ZnSO_4

+ + ⟶ + +

Names

Image
Text

zinc + copper(II) sulfate + water ⟶ water + copper + zinc sulfate

Equilibrium constant

Image
Text

Construct the equilibrium constant, K, expression for: Zn + CuSO_4 + H_2O ⟶ H_2O + Cu + ZnSO_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: Zn + CuSO_4 + H_2O ⟶ H_2O + Cu + ZnSO_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 Zn | 1 | -1 CuSO_4 | 1 | -1 H_2O | 1 | -1 H_2O | 1 | 1 Cu | 1 | 1 ZnSO_4 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Zn | 1 | -1 | ([Zn])^(-1) CuSO_4 | 1 | -1 | ([CuSO4])^(-1) H_2O | 1 | -1 | ([H2O])^(-1) H_2O | 1 | 1 | [H2O] Cu | 1 | 1 | [Cu] ZnSO_4 | 1 | 1 | [ZnSO4] 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 = ([Zn])^(-1) ([CuSO4])^(-1) ([H2O])^(-1) [H2O] [Cu] [ZnSO4] = ([H2O] [Cu] [ZnSO4])/([Zn] [CuSO4] [H2O])

Rate of reaction

Image
Text

Construct the rate of reaction expression for: Zn + CuSO_4 + H_2O ⟶ H_2O + Cu + ZnSO_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: Zn + CuSO_4 + H_2O ⟶ H_2O + Cu + ZnSO_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 Zn | 1 | -1 CuSO_4 | 1 | -1 H_2O | 1 | -1 H_2O | 1 | 1 Cu | 1 | 1 ZnSO_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 Zn | 1 | -1 | -(Δ[Zn])/(Δt) CuSO_4 | 1 | -1 | -(Δ[CuSO4])/(Δt) H_2O | 1 | -1 | -(Δ[H2O])/(Δt) H_2O | 1 | 1 | (Δ[H2O])/(Δt) Cu | 1 | 1 | (Δ[Cu])/(Δt) ZnSO_4 | 1 | 1 | (Δ[ZnSO4])/(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[Zn])/(Δt) = -(Δ[CuSO4])/(Δt) = -(Δ[H2O])/(Δt) = (Δ[H2O])/(Δt) = (Δ[Cu])/(Δt) = (Δ[ZnSO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)