CuSO4 + Cr = Cu + Cr2(SO4)3

Input interpretation

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CuSO_4 copper(II) sulfate + Cr chromium ⟶ Cu copper + Cr_2(SO_4)_3 chromium sulfate

Balanced equation

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Balance the chemical equation algebraically: CuSO_4 + Cr ⟶ Cu + Cr_2(SO_4)_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 CuSO_4 + c_2 Cr ⟶ c_3 Cu + c_4 Cr_2(SO_4)_3 Set the number of atoms in the reactants equal to the number of atoms in the products for Cu, O, S and Cr: Cu: | c_1 = c_3 O: | 4 c_1 = 12 c_4 S: | c_1 = 3 c_4 Cr: | c_2 = 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_4 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3 c_2 = 2 c_3 = 3 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 CuSO_4 + 2 Cr ⟶ 3 Cu + Cr_2(SO_4)_3

+ ⟶ +

Names

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copper(II) sulfate + chromium ⟶ copper + chromium sulfate

Equilibrium constant

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Construct the equilibrium constant, K, expression for: CuSO_4 + Cr ⟶ Cu + Cr_2(SO_4)_3 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: 3 CuSO_4 + 2 Cr ⟶ 3 Cu + Cr_2(SO_4)_3 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 | 3 | -3 Cr | 2 | -2 Cu | 3 | 3 Cr_2(SO_4)_3 | 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 | 3 | -3 | ([CuSO4])^(-3) Cr | 2 | -2 | ([Cr])^(-2) Cu | 3 | 3 | ([Cu])^3 Cr_2(SO_4)_3 | 1 | 1 | [Cr2(SO4)3] 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])^(-3) ([Cr])^(-2) ([Cu])^3 [Cr2(SO4)3] = (([Cu])^3 [Cr2(SO4)3])/(([CuSO4])^3 ([Cr])^2)

Rate of reaction

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Construct the rate of reaction expression for: CuSO_4 + Cr ⟶ Cu + Cr_2(SO_4)_3 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: 3 CuSO_4 + 2 Cr ⟶ 3 Cu + Cr_2(SO_4)_3 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 | 3 | -3 Cr | 2 | -2 Cu | 3 | 3 Cr_2(SO_4)_3 | 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 | 3 | -3 | -1/3 (Δ[CuSO4])/(Δt) Cr | 2 | -2 | -1/2 (Δ[Cr])/(Δt) Cu | 3 | 3 | 1/3 (Δ[Cu])/(Δt) Cr_2(SO_4)_3 | 1 | 1 | (Δ[Cr2(SO4)3])/(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 = -1/3 (Δ[CuSO4])/(Δt) = -1/2 (Δ[Cr])/(Δt) = 1/3 (Δ[Cu])/(Δt) = (Δ[Cr2(SO4)3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)