Input interpretation
![H_2SO_4 (sulfuric acid) + MnO_2 (manganese dioxide) + FeSO_4 (duretter) ⟶ H_2O (water) + MnSO_4 (manganese(II) sulfate) + Fe_2(SO_4)_3·xH_2O (iron(III) sulfate hydrate)](../image_source/a2261546c0618e5d529446d173a6aa28.png)
H_2SO_4 (sulfuric acid) + MnO_2 (manganese dioxide) + FeSO_4 (duretter) ⟶ H_2O (water) + MnSO_4 (manganese(II) sulfate) + Fe_2(SO_4)_3·xH_2O (iron(III) sulfate hydrate)
Balanced equation
![Balance the chemical equation algebraically: H_2SO_4 + MnO_2 + FeSO_4 ⟶ H_2O + MnSO_4 + Fe_2(SO_4)_3·xH_2O Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 MnO_2 + c_3 FeSO_4 ⟶ c_4 H_2O + c_5 MnSO_4 + c_6 Fe_2(SO_4)_3·xH_2O Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, Mn and Fe: H: | 2 c_1 = 2 c_4 O: | 4 c_1 + 2 c_2 + 4 c_3 = c_4 + 4 c_5 + 12 c_6 S: | c_1 + c_3 = c_5 + 3 c_6 Mn: | c_2 = c_5 Fe: | c_3 = 2 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 1 c_3 = 2 c_4 = 2 c_5 = 1 c_6 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 H_2SO_4 + MnO_2 + 2 FeSO_4 ⟶ 2 H_2O + MnSO_4 + Fe_2(SO_4)_3·xH_2O](../image_source/4809b92eaebac63d30d85c89868211c6.png)
Balance the chemical equation algebraically: H_2SO_4 + MnO_2 + FeSO_4 ⟶ H_2O + MnSO_4 + Fe_2(SO_4)_3·xH_2O Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 MnO_2 + c_3 FeSO_4 ⟶ c_4 H_2O + c_5 MnSO_4 + c_6 Fe_2(SO_4)_3·xH_2O Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, Mn and Fe: H: | 2 c_1 = 2 c_4 O: | 4 c_1 + 2 c_2 + 4 c_3 = c_4 + 4 c_5 + 12 c_6 S: | c_1 + c_3 = c_5 + 3 c_6 Mn: | c_2 = c_5 Fe: | c_3 = 2 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 1 c_3 = 2 c_4 = 2 c_5 = 1 c_6 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 H_2SO_4 + MnO_2 + 2 FeSO_4 ⟶ 2 H_2O + MnSO_4 + Fe_2(SO_4)_3·xH_2O
Structures
![+ + ⟶ + +](../image_source/ce088de68496fbdbcf0aa2f206c53f5f.png)
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Names
![sulfuric acid + manganese dioxide + duretter ⟶ water + manganese(II) sulfate + iron(III) sulfate hydrate](../image_source/c05d59286966a5c612fa6bba834e6e17.png)
sulfuric acid + manganese dioxide + duretter ⟶ water + manganese(II) sulfate + iron(III) sulfate hydrate
Equilibrium constant
![Construct the equilibrium constant, K, expression for: H_2SO_4 + MnO_2 + FeSO_4 ⟶ H_2O + MnSO_4 + Fe_2(SO_4)_3·xH_2O 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 + MnO_2 + 2 FeSO_4 ⟶ 2 H_2O + MnSO_4 + Fe_2(SO_4)_3·xH_2O 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 MnO_2 | 1 | -1 FeSO_4 | 2 | -2 H_2O | 2 | 2 MnSO_4 | 1 | 1 Fe_2(SO_4)_3·xH_2O | 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) MnO_2 | 1 | -1 | ([MnO2])^(-1) FeSO_4 | 2 | -2 | ([FeSO4])^(-2) H_2O | 2 | 2 | ([H2O])^2 MnSO_4 | 1 | 1 | [MnSO4] Fe_2(SO_4)_3·xH_2O | 1 | 1 | [Fe2(SO4)3·xH2O] 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) ([MnO2])^(-1) ([FeSO4])^(-2) ([H2O])^2 [MnSO4] [Fe2(SO4)3·xH2O] = (([H2O])^2 [MnSO4] [Fe2(SO4)3·xH2O])/(([H2SO4])^2 [MnO2] ([FeSO4])^2)](../image_source/c0ddc53510da31ff01ae9c98125f7aac.png)
Construct the equilibrium constant, K, expression for: H_2SO_4 + MnO_2 + FeSO_4 ⟶ H_2O + MnSO_4 + Fe_2(SO_4)_3·xH_2O 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 + MnO_2 + 2 FeSO_4 ⟶ 2 H_2O + MnSO_4 + Fe_2(SO_4)_3·xH_2O 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 MnO_2 | 1 | -1 FeSO_4 | 2 | -2 H_2O | 2 | 2 MnSO_4 | 1 | 1 Fe_2(SO_4)_3·xH_2O | 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) MnO_2 | 1 | -1 | ([MnO2])^(-1) FeSO_4 | 2 | -2 | ([FeSO4])^(-2) H_2O | 2 | 2 | ([H2O])^2 MnSO_4 | 1 | 1 | [MnSO4] Fe_2(SO_4)_3·xH_2O | 1 | 1 | [Fe2(SO4)3·xH2O] 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) ([MnO2])^(-1) ([FeSO4])^(-2) ([H2O])^2 [MnSO4] [Fe2(SO4)3·xH2O] = (([H2O])^2 [MnSO4] [Fe2(SO4)3·xH2O])/(([H2SO4])^2 [MnO2] ([FeSO4])^2)
Rate of reaction
![Construct the rate of reaction expression for: H_2SO_4 + MnO_2 + FeSO_4 ⟶ H_2O + MnSO_4 + Fe_2(SO_4)_3·xH_2O 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 + MnO_2 + 2 FeSO_4 ⟶ 2 H_2O + MnSO_4 + Fe_2(SO_4)_3·xH_2O 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 MnO_2 | 1 | -1 FeSO_4 | 2 | -2 H_2O | 2 | 2 MnSO_4 | 1 | 1 Fe_2(SO_4)_3·xH_2O | 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) MnO_2 | 1 | -1 | -(Δ[MnO2])/(Δt) FeSO_4 | 2 | -2 | -1/2 (Δ[FeSO4])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(Δt) MnSO_4 | 1 | 1 | (Δ[MnSO4])/(Δt) Fe_2(SO_4)_3·xH_2O | 1 | 1 | (Δ[Fe2(SO4)3·xH2O])/(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[MnO2])/(Δt) = -1/2 (Δ[FeSO4])/(Δt) = 1/2 (Δ[H2O])/(Δt) = (Δ[MnSO4])/(Δt) = (Δ[Fe2(SO4)3·xH2O])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)](../image_source/b25a53502d8293363781e42bc76f8fbb.png)
Construct the rate of reaction expression for: H_2SO_4 + MnO_2 + FeSO_4 ⟶ H_2O + MnSO_4 + Fe_2(SO_4)_3·xH_2O 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 + MnO_2 + 2 FeSO_4 ⟶ 2 H_2O + MnSO_4 + Fe_2(SO_4)_3·xH_2O 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 MnO_2 | 1 | -1 FeSO_4 | 2 | -2 H_2O | 2 | 2 MnSO_4 | 1 | 1 Fe_2(SO_4)_3·xH_2O | 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) MnO_2 | 1 | -1 | -(Δ[MnO2])/(Δt) FeSO_4 | 2 | -2 | -1/2 (Δ[FeSO4])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(Δt) MnSO_4 | 1 | 1 | (Δ[MnSO4])/(Δt) Fe_2(SO_4)_3·xH_2O | 1 | 1 | (Δ[Fe2(SO4)3·xH2O])/(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[MnO2])/(Δt) = -1/2 (Δ[FeSO4])/(Δt) = 1/2 (Δ[H2O])/(Δt) = (Δ[MnSO4])/(Δt) = (Δ[Fe2(SO4)3·xH2O])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Chemical names and formulas
![| sulfuric acid | manganese dioxide | duretter | water | manganese(II) sulfate | iron(III) sulfate hydrate formula | H_2SO_4 | MnO_2 | FeSO_4 | H_2O | MnSO_4 | Fe_2(SO_4)_3·xH_2O Hill formula | H_2O_4S | MnO_2 | FeO_4S | H_2O | MnSO_4 | Fe_2O_12S_3 name | sulfuric acid | manganese dioxide | duretter | water | manganese(II) sulfate | iron(III) sulfate hydrate IUPAC name | sulfuric acid | dioxomanganese | iron(+2) cation sulfate | water | manganese(+2) cation sulfate | diferric trisulfate](../image_source/e7af273b9ca3829ba82b22326d8cdced.png)
| sulfuric acid | manganese dioxide | duretter | water | manganese(II) sulfate | iron(III) sulfate hydrate formula | H_2SO_4 | MnO_2 | FeSO_4 | H_2O | MnSO_4 | Fe_2(SO_4)_3·xH_2O Hill formula | H_2O_4S | MnO_2 | FeO_4S | H_2O | MnSO_4 | Fe_2O_12S_3 name | sulfuric acid | manganese dioxide | duretter | water | manganese(II) sulfate | iron(III) sulfate hydrate IUPAC name | sulfuric acid | dioxomanganese | iron(+2) cation sulfate | water | manganese(+2) cation sulfate | diferric trisulfate
Substance properties
![| sulfuric acid | manganese dioxide | duretter | water | manganese(II) sulfate | iron(III) sulfate hydrate molar mass | 98.07 g/mol | 86.936 g/mol | 151.9 g/mol | 18.015 g/mol | 150.99 g/mol | 399.9 g/mol phase | liquid (at STP) | solid (at STP) | | liquid (at STP) | solid (at STP) | melting point | 10.371 °C | 535 °C | | 0 °C | 710 °C | boiling point | 279.6 °C | | | 99.9839 °C | | density | 1.8305 g/cm^3 | 5.03 g/cm^3 | 2.841 g/cm^3 | 1 g/cm^3 | 3.25 g/cm^3 | solubility in water | very soluble | insoluble | | | soluble | slightly soluble surface tension | 0.0735 N/m | | | 0.0728 N/m | | dynamic viscosity | 0.021 Pa s (at 25 °C) | | | 8.9×10^-4 Pa s (at 25 °C) | | odor | odorless | | | odorless | |](../image_source/622d8ab1ea83ec7d5cd5f92b5867ed2a.png)
| sulfuric acid | manganese dioxide | duretter | water | manganese(II) sulfate | iron(III) sulfate hydrate molar mass | 98.07 g/mol | 86.936 g/mol | 151.9 g/mol | 18.015 g/mol | 150.99 g/mol | 399.9 g/mol phase | liquid (at STP) | solid (at STP) | | liquid (at STP) | solid (at STP) | melting point | 10.371 °C | 535 °C | | 0 °C | 710 °C | boiling point | 279.6 °C | | | 99.9839 °C | | density | 1.8305 g/cm^3 | 5.03 g/cm^3 | 2.841 g/cm^3 | 1 g/cm^3 | 3.25 g/cm^3 | solubility in water | very soluble | insoluble | | | soluble | slightly soluble surface tension | 0.0735 N/m | | | 0.0728 N/m | | dynamic viscosity | 0.021 Pa s (at 25 °C) | | | 8.9×10^-4 Pa s (at 25 °C) | | odor | odorless | | | odorless | |
Units