H2SO4 + Mg = H2S + H2O2 + MgSO4

H_2SO_4 sulfuric acid + Mg magnesium ⟶ H_2S hydrogen sulfide + H_2O_2 hydrogen peroxide + MgSO_4 magnesium sulfate

Balance the chemical equation algebraically: H_2SO_4 + Mg ⟶ H_2S + H_2O_2 + MgSO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 Mg ⟶ c_3 H_2S + c_4 H_2O_2 + c_5 MgSO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S and Mg: H: | 2 c_1 = 2 c_3 + 2 c_4 O: | 4 c_1 = 2 c_4 + 4 c_5 S: | c_1 = c_3 + c_5 Mg: | c_2 = c_5 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3 c_2 = 2 c_3 = 1 c_4 = 2 c_5 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 H_2SO_4 + 2 Mg ⟶ H_2S + 2 H_2O_2 + 2 MgSO_4

+ ⟶ + +

sulfuric acid + magnesium ⟶ hydrogen sulfide + hydrogen peroxide + magnesium sulfate

Construct the equilibrium constant, K, expression for: H_2SO_4 + Mg ⟶ H_2S + H_2O_2 + MgSO_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: 3 H_2SO_4 + 2 Mg ⟶ H_2S + 2 H_2O_2 + 2 MgSO_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 | 3 | -3 Mg | 2 | -2 H_2S | 1 | 1 H_2O_2 | 2 | 2 MgSO_4 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 3 | -3 | ([H2SO4])^(-3) Mg | 2 | -2 | ([Mg])^(-2) H_2S | 1 | 1 | [H2S] H_2O_2 | 2 | 2 | ([H2O2])^2 MgSO_4 | 2 | 2 | ([MgSO4])^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])^(-3) ([Mg])^(-2) [H2S] ([H2O2])^2 ([MgSO4])^2 = ([H2S] ([H2O2])^2 ([MgSO4])^2)/(([H2SO4])^3 ([Mg])^2)

Construct the rate of reaction expression for: H_2SO_4 + Mg ⟶ H_2S + H_2O_2 + MgSO_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: 3 H_2SO_4 + 2 Mg ⟶ H_2S + 2 H_2O_2 + 2 MgSO_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 | 3 | -3 Mg | 2 | -2 H_2S | 1 | 1 H_2O_2 | 2 | 2 MgSO_4 | 2 | 2 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 | 3 | -3 | -1/3 (Δ[H2SO4])/(Δt) Mg | 2 | -2 | -1/2 (Δ[Mg])/(Δt) H_2S | 1 | 1 | (Δ[H2S])/(Δt) H_2O_2 | 2 | 2 | 1/2 (Δ[H2O2])/(Δt) MgSO_4 | 2 | 2 | 1/2 (Δ[MgSO4])/(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[H2SO4])/(Δt) = -1/2 (Δ[Mg])/(Δt) = (Δ[H2S])/(Δt) = 1/2 (Δ[H2O2])/(Δt) = 1/2 (Δ[MgSO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sulfuric acid | magnesium | hydrogen sulfide | hydrogen peroxide | magnesium sulfate formula | H_2SO_4 | Mg | H_2S | H_2O_2 | MgSO_4 Hill formula | H_2O_4S | Mg | H_2S | H_2O_2 | MgO_4S name | sulfuric acid | magnesium | hydrogen sulfide | hydrogen peroxide | magnesium sulfate

| sulfuric acid | magnesium | hydrogen sulfide | hydrogen peroxide | magnesium sulfate molar mass | 98.07 g/mol | 24.305 g/mol | 34.08 g/mol | 34.014 g/mol | 120.4 g/mol phase | liquid (at STP) | solid (at STP) | gas (at STP) | liquid (at STP) | solid (at STP) melting point | 10.371 °C | 648 °C | -85 °C | -0.43 °C | boiling point | 279.6 °C | 1090 °C | -60 °C | 150.2 °C | density | 1.8305 g/cm^3 | 1.738 g/cm^3 | 0.001393 g/cm^3 (at 25 °C) | 1.44 g/cm^3 | solubility in water | very soluble | reacts | | miscible | soluble surface tension | 0.0735 N/m | | | 0.0804 N/m | dynamic viscosity | 0.021 Pa s (at 25 °C) | | 1.239×10^-5 Pa s (at 25 °C) | 0.001249 Pa s (at 20 °C) | odor | odorless | | | |