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Mn2(SO4)3 = O2 + MnSO4 + SO3

Input interpretation

Mn2(SO4)3 ⟶ O_2 oxygen + MnSO_4 manganese(II) sulfate + SO_3 sulfur trioxide
Mn2(SO4)3 ⟶ O_2 oxygen + MnSO_4 manganese(II) sulfate + SO_3 sulfur trioxide

Balanced equation

Balance the chemical equation algebraically: Mn2(SO4)3 ⟶ O_2 + MnSO_4 + SO_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Mn2(SO4)3 ⟶ c_2 O_2 + c_3 MnSO_4 + c_4 SO_3 Set the number of atoms in the reactants equal to the number of atoms in the products for Mn, S and O: Mn: | 2 c_1 = c_3 S: | 3 c_1 = c_3 + c_4 O: | 12 c_1 = 2 c_2 + 4 c_3 + 3 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 = 4 c_4 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 Mn2(SO4)3 ⟶ O_2 + 4 MnSO_4 + 2 SO_3
Balance the chemical equation algebraically: Mn2(SO4)3 ⟶ O_2 + MnSO_4 + SO_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Mn2(SO4)3 ⟶ c_2 O_2 + c_3 MnSO_4 + c_4 SO_3 Set the number of atoms in the reactants equal to the number of atoms in the products for Mn, S and O: Mn: | 2 c_1 = c_3 S: | 3 c_1 = c_3 + c_4 O: | 12 c_1 = 2 c_2 + 4 c_3 + 3 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 = 4 c_4 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 Mn2(SO4)3 ⟶ O_2 + 4 MnSO_4 + 2 SO_3

Structures

Mn2(SO4)3 ⟶ + +
Mn2(SO4)3 ⟶ + +

Names

Mn2(SO4)3 ⟶ oxygen + manganese(II) sulfate + sulfur trioxide
Mn2(SO4)3 ⟶ oxygen + manganese(II) sulfate + sulfur trioxide

Equilibrium constant

Construct the equilibrium constant, K, expression for: Mn2(SO4)3 ⟶ O_2 + MnSO_4 + SO_3 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 Mn2(SO4)3 ⟶ O_2 + 4 MnSO_4 + 2 SO_3 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 Mn2(SO4)3 | 2 | -2 O_2 | 1 | 1 MnSO_4 | 4 | 4 SO_3 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Mn2(SO4)3 | 2 | -2 | ([Mn2(SO4)3])^(-2) O_2 | 1 | 1 | [O2] MnSO_4 | 4 | 4 | ([MnSO4])^4 SO_3 | 2 | 2 | ([SO3])^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 = ([Mn2(SO4)3])^(-2) [O2] ([MnSO4])^4 ([SO3])^2 = ([O2] ([MnSO4])^4 ([SO3])^2)/([Mn2(SO4)3])^2
Construct the equilibrium constant, K, expression for: Mn2(SO4)3 ⟶ O_2 + MnSO_4 + SO_3 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 Mn2(SO4)3 ⟶ O_2 + 4 MnSO_4 + 2 SO_3 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 Mn2(SO4)3 | 2 | -2 O_2 | 1 | 1 MnSO_4 | 4 | 4 SO_3 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Mn2(SO4)3 | 2 | -2 | ([Mn2(SO4)3])^(-2) O_2 | 1 | 1 | [O2] MnSO_4 | 4 | 4 | ([MnSO4])^4 SO_3 | 2 | 2 | ([SO3])^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 = ([Mn2(SO4)3])^(-2) [O2] ([MnSO4])^4 ([SO3])^2 = ([O2] ([MnSO4])^4 ([SO3])^2)/([Mn2(SO4)3])^2

Rate of reaction

Construct the rate of reaction expression for: Mn2(SO4)3 ⟶ O_2 + MnSO_4 + SO_3 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 Mn2(SO4)3 ⟶ O_2 + 4 MnSO_4 + 2 SO_3 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 Mn2(SO4)3 | 2 | -2 O_2 | 1 | 1 MnSO_4 | 4 | 4 SO_3 | 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 Mn2(SO4)3 | 2 | -2 | -1/2 (Δ[Mn2(SO4)3])/(Δt) O_2 | 1 | 1 | (Δ[O2])/(Δt) MnSO_4 | 4 | 4 | 1/4 (Δ[MnSO4])/(Δt) SO_3 | 2 | 2 | 1/2 (Δ[SO3])/(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[Mn2(SO4)3])/(Δt) = (Δ[O2])/(Δt) = 1/4 (Δ[MnSO4])/(Δt) = 1/2 (Δ[SO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: Mn2(SO4)3 ⟶ O_2 + MnSO_4 + SO_3 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 Mn2(SO4)3 ⟶ O_2 + 4 MnSO_4 + 2 SO_3 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 Mn2(SO4)3 | 2 | -2 O_2 | 1 | 1 MnSO_4 | 4 | 4 SO_3 | 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 Mn2(SO4)3 | 2 | -2 | -1/2 (Δ[Mn2(SO4)3])/(Δt) O_2 | 1 | 1 | (Δ[O2])/(Δt) MnSO_4 | 4 | 4 | 1/4 (Δ[MnSO4])/(Δt) SO_3 | 2 | 2 | 1/2 (Δ[SO3])/(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[Mn2(SO4)3])/(Δt) = (Δ[O2])/(Δt) = 1/4 (Δ[MnSO4])/(Δt) = 1/2 (Δ[SO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| Mn2(SO4)3 | oxygen | manganese(II) sulfate | sulfur trioxide formula | Mn2(SO4)3 | O_2 | MnSO_4 | SO_3 Hill formula | Mn2O12S3 | O_2 | MnSO_4 | O_3S name | | oxygen | manganese(II) sulfate | sulfur trioxide IUPAC name | | molecular oxygen | manganese(+2) cation sulfate | sulfur trioxide
| Mn2(SO4)3 | oxygen | manganese(II) sulfate | sulfur trioxide formula | Mn2(SO4)3 | O_2 | MnSO_4 | SO_3 Hill formula | Mn2O12S3 | O_2 | MnSO_4 | O_3S name | | oxygen | manganese(II) sulfate | sulfur trioxide IUPAC name | | molecular oxygen | manganese(+2) cation sulfate | sulfur trioxide

Substance properties

| Mn2(SO4)3 | oxygen | manganese(II) sulfate | sulfur trioxide molar mass | 398 g/mol | 31.998 g/mol | 150.99 g/mol | 80.06 g/mol phase | | gas (at STP) | solid (at STP) | liquid (at STP) melting point | | -218 °C | 710 °C | 16.8 °C boiling point | | -183 °C | | 44.7 °C density | | 0.001429 g/cm^3 (at 0 °C) | 3.25 g/cm^3 | 1.97 g/cm^3 solubility in water | | | soluble | reacts surface tension | | 0.01347 N/m | | dynamic viscosity | | 2.055×10^-5 Pa s (at 25 °C) | | 0.00159 Pa s (at 30 °C) odor | | odorless | |
| Mn2(SO4)3 | oxygen | manganese(II) sulfate | sulfur trioxide molar mass | 398 g/mol | 31.998 g/mol | 150.99 g/mol | 80.06 g/mol phase | | gas (at STP) | solid (at STP) | liquid (at STP) melting point | | -218 °C | 710 °C | 16.8 °C boiling point | | -183 °C | | 44.7 °C density | | 0.001429 g/cm^3 (at 0 °C) | 3.25 g/cm^3 | 1.97 g/cm^3 solubility in water | | | soluble | reacts surface tension | | 0.01347 N/m | | dynamic viscosity | | 2.055×10^-5 Pa s (at 25 °C) | | 0.00159 Pa s (at 30 °C) odor | | odorless | |

Units

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