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H2SO4 + H2O2 + Mn3O4 = H2O + O2 + MnSO4

Input interpretation

H_2SO_4 sulfuric acid + H_2O_2 hydrogen peroxide + Mn_3O_4 manganese(II, III) oxide ⟶ H_2O water + O_2 oxygen + MnSO_4 manganese(II) sulfate
H_2SO_4 sulfuric acid + H_2O_2 hydrogen peroxide + Mn_3O_4 manganese(II, III) oxide ⟶ H_2O water + O_2 oxygen + MnSO_4 manganese(II) sulfate

Balanced equation

Balance the chemical equation algebraically: H_2SO_4 + H_2O_2 + Mn_3O_4 ⟶ H_2O + O_2 + MnSO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 H_2O_2 + c_3 Mn_3O_4 ⟶ c_4 H_2O + c_5 O_2 + c_6 MnSO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S and Mn: H: | 2 c_1 + 2 c_2 + c_3 = 2 c_4 O: | 4 c_1 + 2 c_2 + 2 c_3 = c_4 + 2 c_5 + 4 c_6 S: | c_1 = c_6 Mn: | 2 c_3 = c_6 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_5 = 1 and solve the system of equations for the remaining coefficients: c_2 = c_1/4 + 2 c_3 = c_1/2 c_4 = (3 c_1)/2 + 2 c_5 = 1 c_6 = c_1 The resulting system of equations is still underdetermined, so an additional coefficient must be set arbitrarily. Set c_1 = 4 and solve for the remaining coefficients: c_1 = 4 c_2 = 3 c_3 = 2 c_4 = 8 c_5 = 1 c_6 = 4 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 H_2SO_4 + 3 H_2O_2 + 2 Mn_3O_4 ⟶ 8 H_2O + O_2 + 4 MnSO_4
Balance the chemical equation algebraically: H_2SO_4 + H_2O_2 + Mn_3O_4 ⟶ H_2O + O_2 + MnSO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 H_2O_2 + c_3 Mn_3O_4 ⟶ c_4 H_2O + c_5 O_2 + c_6 MnSO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S and Mn: H: | 2 c_1 + 2 c_2 + c_3 = 2 c_4 O: | 4 c_1 + 2 c_2 + 2 c_3 = c_4 + 2 c_5 + 4 c_6 S: | c_1 = c_6 Mn: | 2 c_3 = c_6 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_5 = 1 and solve the system of equations for the remaining coefficients: c_2 = c_1/4 + 2 c_3 = c_1/2 c_4 = (3 c_1)/2 + 2 c_5 = 1 c_6 = c_1 The resulting system of equations is still underdetermined, so an additional coefficient must be set arbitrarily. Set c_1 = 4 and solve for the remaining coefficients: c_1 = 4 c_2 = 3 c_3 = 2 c_4 = 8 c_5 = 1 c_6 = 4 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 H_2SO_4 + 3 H_2O_2 + 2 Mn_3O_4 ⟶ 8 H_2O + O_2 + 4 MnSO_4

Structures

+ + ⟶ + +
+ + ⟶ + +

Names

sulfuric acid + hydrogen peroxide + manganese(II, III) oxide ⟶ water + oxygen + manganese(II) sulfate
sulfuric acid + hydrogen peroxide + manganese(II, III) oxide ⟶ water + oxygen + manganese(II) sulfate

Equilibrium constant

Construct the equilibrium constant, K, expression for: H_2SO_4 + H_2O_2 + Mn_3O_4 ⟶ H_2O + O_2 + MnSO_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: 4 H_2SO_4 + 3 H_2O_2 + 2 Mn_3O_4 ⟶ 8 H_2O + O_2 + 4 MnSO_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 | 4 | -4 H_2O_2 | 3 | -3 Mn_3O_4 | 2 | -2 H_2O | 8 | 8 O_2 | 1 | 1 MnSO_4 | 4 | 4 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 4 | -4 | ([H2SO4])^(-4) H_2O_2 | 3 | -3 | ([H2O2])^(-3) Mn_3O_4 | 2 | -2 | ([Mn3O4])^(-2) H_2O | 8 | 8 | ([H2O])^8 O_2 | 1 | 1 | [O2] MnSO_4 | 4 | 4 | ([MnSO4])^4 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])^(-4) ([H2O2])^(-3) ([Mn3O4])^(-2) ([H2O])^8 [O2] ([MnSO4])^4 = (([H2O])^8 [O2] ([MnSO4])^4)/(([H2SO4])^4 ([H2O2])^3 ([Mn3O4])^2)
Construct the equilibrium constant, K, expression for: H_2SO_4 + H_2O_2 + Mn_3O_4 ⟶ H_2O + O_2 + MnSO_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: 4 H_2SO_4 + 3 H_2O_2 + 2 Mn_3O_4 ⟶ 8 H_2O + O_2 + 4 MnSO_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 | 4 | -4 H_2O_2 | 3 | -3 Mn_3O_4 | 2 | -2 H_2O | 8 | 8 O_2 | 1 | 1 MnSO_4 | 4 | 4 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 4 | -4 | ([H2SO4])^(-4) H_2O_2 | 3 | -3 | ([H2O2])^(-3) Mn_3O_4 | 2 | -2 | ([Mn3O4])^(-2) H_2O | 8 | 8 | ([H2O])^8 O_2 | 1 | 1 | [O2] MnSO_4 | 4 | 4 | ([MnSO4])^4 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])^(-4) ([H2O2])^(-3) ([Mn3O4])^(-2) ([H2O])^8 [O2] ([MnSO4])^4 = (([H2O])^8 [O2] ([MnSO4])^4)/(([H2SO4])^4 ([H2O2])^3 ([Mn3O4])^2)

Rate of reaction

Construct the rate of reaction expression for: H_2SO_4 + H_2O_2 + Mn_3O_4 ⟶ H_2O + O_2 + MnSO_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: 4 H_2SO_4 + 3 H_2O_2 + 2 Mn_3O_4 ⟶ 8 H_2O + O_2 + 4 MnSO_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 | 4 | -4 H_2O_2 | 3 | -3 Mn_3O_4 | 2 | -2 H_2O | 8 | 8 O_2 | 1 | 1 MnSO_4 | 4 | 4 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 | 4 | -4 | -1/4 (Δ[H2SO4])/(Δt) H_2O_2 | 3 | -3 | -1/3 (Δ[H2O2])/(Δt) Mn_3O_4 | 2 | -2 | -1/2 (Δ[Mn3O4])/(Δt) H_2O | 8 | 8 | 1/8 (Δ[H2O])/(Δt) O_2 | 1 | 1 | (Δ[O2])/(Δt) MnSO_4 | 4 | 4 | 1/4 (Δ[MnSO4])/(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 = -1/4 (Δ[H2SO4])/(Δt) = -1/3 (Δ[H2O2])/(Δt) = -1/2 (Δ[Mn3O4])/(Δt) = 1/8 (Δ[H2O])/(Δt) = (Δ[O2])/(Δt) = 1/4 (Δ[MnSO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: H_2SO_4 + H_2O_2 + Mn_3O_4 ⟶ H_2O + O_2 + MnSO_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: 4 H_2SO_4 + 3 H_2O_2 + 2 Mn_3O_4 ⟶ 8 H_2O + O_2 + 4 MnSO_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 | 4 | -4 H_2O_2 | 3 | -3 Mn_3O_4 | 2 | -2 H_2O | 8 | 8 O_2 | 1 | 1 MnSO_4 | 4 | 4 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 | 4 | -4 | -1/4 (Δ[H2SO4])/(Δt) H_2O_2 | 3 | -3 | -1/3 (Δ[H2O2])/(Δt) Mn_3O_4 | 2 | -2 | -1/2 (Δ[Mn3O4])/(Δt) H_2O | 8 | 8 | 1/8 (Δ[H2O])/(Δt) O_2 | 1 | 1 | (Δ[O2])/(Δt) MnSO_4 | 4 | 4 | 1/4 (Δ[MnSO4])/(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 = -1/4 (Δ[H2SO4])/(Δt) = -1/3 (Δ[H2O2])/(Δt) = -1/2 (Δ[Mn3O4])/(Δt) = 1/8 (Δ[H2O])/(Δt) = (Δ[O2])/(Δt) = 1/4 (Δ[MnSO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| sulfuric acid | hydrogen peroxide | manganese(II, III) oxide | water | oxygen | manganese(II) sulfate formula | H_2SO_4 | H_2O_2 | Mn_3O_4 | H_2O | O_2 | MnSO_4 Hill formula | H_2O_4S | H_2O_2 | Mn_3O_4 | H_2O | O_2 | MnSO_4 name | sulfuric acid | hydrogen peroxide | manganese(II, III) oxide | water | oxygen | manganese(II) sulfate IUPAC name | sulfuric acid | hydrogen peroxide | | water | molecular oxygen | manganese(+2) cation sulfate
| sulfuric acid | hydrogen peroxide | manganese(II, III) oxide | water | oxygen | manganese(II) sulfate formula | H_2SO_4 | H_2O_2 | Mn_3O_4 | H_2O | O_2 | MnSO_4 Hill formula | H_2O_4S | H_2O_2 | Mn_3O_4 | H_2O | O_2 | MnSO_4 name | sulfuric acid | hydrogen peroxide | manganese(II, III) oxide | water | oxygen | manganese(II) sulfate IUPAC name | sulfuric acid | hydrogen peroxide | | water | molecular oxygen | manganese(+2) cation sulfate

Substance properties

| sulfuric acid | hydrogen peroxide | manganese(II, III) oxide | water | oxygen | manganese(II) sulfate molar mass | 98.07 g/mol | 34.014 g/mol | 142.882 g/mol | 18.015 g/mol | 31.998 g/mol | 150.99 g/mol phase | liquid (at STP) | liquid (at STP) | | liquid (at STP) | gas (at STP) | solid (at STP) melting point | 10.371 °C | -0.43 °C | | 0 °C | -218 °C | 710 °C boiling point | 279.6 °C | 150.2 °C | | 99.9839 °C | -183 °C | density | 1.8305 g/cm^3 | 1.44 g/cm^3 | 4.8 g/cm^3 | 1 g/cm^3 | 0.001429 g/cm^3 (at 0 °C) | 3.25 g/cm^3 solubility in water | very soluble | miscible | | | | soluble surface tension | 0.0735 N/m | 0.0804 N/m | | 0.0728 N/m | 0.01347 N/m | dynamic viscosity | 0.021 Pa s (at 25 °C) | 0.001249 Pa s (at 20 °C) | | 8.9×10^-4 Pa s (at 25 °C) | 2.055×10^-5 Pa s (at 25 °C) | odor | odorless | | | odorless | odorless |
| sulfuric acid | hydrogen peroxide | manganese(II, III) oxide | water | oxygen | manganese(II) sulfate molar mass | 98.07 g/mol | 34.014 g/mol | 142.882 g/mol | 18.015 g/mol | 31.998 g/mol | 150.99 g/mol phase | liquid (at STP) | liquid (at STP) | | liquid (at STP) | gas (at STP) | solid (at STP) melting point | 10.371 °C | -0.43 °C | | 0 °C | -218 °C | 710 °C boiling point | 279.6 °C | 150.2 °C | | 99.9839 °C | -183 °C | density | 1.8305 g/cm^3 | 1.44 g/cm^3 | 4.8 g/cm^3 | 1 g/cm^3 | 0.001429 g/cm^3 (at 0 °C) | 3.25 g/cm^3 solubility in water | very soluble | miscible | | | | soluble surface tension | 0.0735 N/m | 0.0804 N/m | | 0.0728 N/m | 0.01347 N/m | dynamic viscosity | 0.021 Pa s (at 25 °C) | 0.001249 Pa s (at 20 °C) | | 8.9×10^-4 Pa s (at 25 °C) | 2.055×10^-5 Pa s (at 25 °C) | odor | odorless | | | odorless | odorless |

Units

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