H2SO4 + Li = H2 + Li2SO4

H_2SO_4 (sulfuric acid) + Li (lithium) ⟶ H_2 (hydrogen) + Li_2SO_4 (lithium sulfate)

Balance the chemical equation algebraically: H_2SO_4 + Li ⟶ H_2 + Li_2SO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 Li ⟶ c_3 H_2 + c_4 Li_2SO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S and Li: H: | 2 c_1 = 2 c_3 O: | 4 c_1 = 4 c_4 S: | c_1 = c_4 Li: | 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 2 c_3 = 1 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | H_2SO_4 + 2 Li ⟶ H_2 + Li_2SO_4

+ ⟶ +

sulfuric acid + lithium ⟶ hydrogen + lithium sulfate

| sulfuric acid | lithium | hydrogen | lithium sulfate molecular enthalpy | -814 kJ/mol | 0 kJ/mol | 0 kJ/mol | -1437 kJ/mol total enthalpy | -814 kJ/mol | 0 kJ/mol | 0 kJ/mol | -1437 kJ/mol | H_initial = -814 kJ/mol | | H_final = -1437 kJ/mol | ΔH_rxn^0 | -1437 kJ/mol - -814 kJ/mol = -622.5 kJ/mol (exothermic) | | |

Construct the equilibrium constant, K, expression for: H_2SO_4 + Li ⟶ H_2 + Li_2SO_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: H_2SO_4 + 2 Li ⟶ H_2 + Li_2SO_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 H_2SO_4 | 1 | -1 Li | 2 | -2 H_2 | 1 | 1 Li_2SO_4 | 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 | 1 | -1 | ([H2SO4])^(-1) Li | 2 | -2 | ([Li])^(-2) H_2 | 1 | 1 | [H2] Li_2SO_4 | 1 | 1 | [Li2SO4] 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])^(-1) ([Li])^(-2) [H2] [Li2SO4] = ([H2] [Li2SO4])/([H2SO4] ([Li])^2)

Construct the rate of reaction expression for: H_2SO_4 + Li ⟶ H_2 + Li_2SO_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: H_2SO_4 + 2 Li ⟶ H_2 + Li_2SO_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 H_2SO_4 | 1 | -1 Li | 2 | -2 H_2 | 1 | 1 Li_2SO_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 H_2SO_4 | 1 | -1 | -(Δ[H2SO4])/(Δt) Li | 2 | -2 | -1/2 (Δ[Li])/(Δt) H_2 | 1 | 1 | (Δ[H2])/(Δt) Li_2SO_4 | 1 | 1 | (Δ[Li2SO4])/(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[H2SO4])/(Δt) = -1/2 (Δ[Li])/(Δt) = (Δ[H2])/(Δt) = (Δ[Li2SO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sulfuric acid | lithium | hydrogen | lithium sulfate formula | H_2SO_4 | Li | H_2 | Li_2SO_4 Hill formula | H_2O_4S | Li | H_2 | Li_2O_4S name | sulfuric acid | lithium | hydrogen | lithium sulfate IUPAC name | sulfuric acid | lithium | molecular hydrogen | dilithium sulfate