H2SO4 + Cu = H2 + Cu(SO4)2

H_2SO_4 sulfuric acid + Cu copper ⟶ H_2 hydrogen + Cu(SO4)2

Balance the chemical equation algebraically: H_2SO_4 + Cu ⟶ H_2 + Cu(SO4)2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 Cu ⟶ c_3 H_2 + c_4 Cu(SO4)2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S and Cu: H: | 2 c_1 = 2 c_3 O: | 4 c_1 = 8 c_4 S: | c_1 = 2 c_4 Cu: | 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 1 c_3 = 2 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 H_2SO_4 + Cu ⟶ 2 H_2 + Cu(SO4)2

+ ⟶ + Cu(SO4)2

sulfuric acid + copper ⟶ hydrogen + Cu(SO4)2

Construct the equilibrium constant, K, expression for: H_2SO_4 + Cu ⟶ H_2 + Cu(SO4)2 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: 2 H_2SO_4 + Cu ⟶ 2 H_2 + Cu(SO4)2 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_2SO_4 | 2 | -2 Cu | 1 | -1 H_2 | 2 | 2 Cu(SO4)2 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 2 | -2 | ([H2SO4])^(-2) Cu | 1 | -1 | ([Cu])^(-1) H_2 | 2 | 2 | ([H2])^2 Cu(SO4)2 | 1 | 1 | [Cu(SO4)2] 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 = ([H2SO4])^(-2) ([Cu])^(-1) ([H2])^2 [Cu(SO4)2] = (([H2])^2 [Cu(SO4)2])/(([H2SO4])^2 [Cu])

Construct the rate of reaction expression for: H_2SO_4 + Cu ⟶ H_2 + Cu(SO4)2 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: 2 H_2SO_4 + Cu ⟶ 2 H_2 + Cu(SO4)2 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_2SO_4 | 2 | -2 Cu | 1 | -1 H_2 | 2 | 2 Cu(SO4)2 | 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_2SO_4 | 2 | -2 | -1/2 (Δ[H2SO4])/(Δt) Cu | 1 | -1 | -(Δ[Cu])/(Δt) H_2 | 2 | 2 | 1/2 (Δ[H2])/(Δt) Cu(SO4)2 | 1 | 1 | (Δ[Cu(SO4)2])/(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 = -1/2 (Δ[H2SO4])/(Δt) = -(Δ[Cu])/(Δt) = 1/2 (Δ[H2])/(Δt) = (Δ[Cu(SO4)2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sulfuric acid | copper | hydrogen | Cu(SO4)2 formula | H_2SO_4 | Cu | H_2 | Cu(SO4)2 Hill formula | H_2O_4S | Cu | H_2 | CuO8S2 name | sulfuric acid | copper | hydrogen | IUPAC name | sulfuric acid | copper | molecular hydrogen |

| sulfuric acid | copper | hydrogen | Cu(SO4)2 molar mass | 98.07 g/mol | 63.546 g/mol | 2.016 g/mol | 255.7 g/mol phase | liquid (at STP) | solid (at STP) | gas (at STP) | melting point | 10.371 °C | 1083 °C | -259.2 °C | boiling point | 279.6 °C | 2567 °C | -252.8 °C | density | 1.8305 g/cm^3 | 8.96 g/cm^3 | 8.99×10^-5 g/cm^3 (at 0 °C) | solubility in water | very soluble | insoluble | | surface tension | 0.0735 N/m | | | dynamic viscosity | 0.021 Pa s (at 25 °C) | | 8.9×10^-6 Pa s (at 25 °C) | odor | odorless | odorless | odorless |