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H2O + Mn(NO3)2 + (NH4)2S2O8 = H2SO4 + HNO3 + HMnO4 + (NH4)2SO4

Input interpretation

H_2O water + Mn(NO_3)_2 manganese(II) nitrate + (NH_4)_2S_2O_8 ammonium persulfate ⟶ H_2SO_4 sulfuric acid + HNO_3 nitric acid + HMnO4 + (NH_4)_2SO_4 ammonium sulfate
H_2O water + Mn(NO_3)_2 manganese(II) nitrate + (NH_4)_2S_2O_8 ammonium persulfate ⟶ H_2SO_4 sulfuric acid + HNO_3 nitric acid + HMnO4 + (NH_4)_2SO_4 ammonium sulfate

Balanced equation

Balance the chemical equation algebraically: H_2O + Mn(NO_3)_2 + (NH_4)_2S_2O_8 ⟶ H_2SO_4 + HNO_3 + HMnO4 + (NH_4)_2SO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 Mn(NO_3)_2 + c_3 (NH_4)_2S_2O_8 ⟶ c_4 H_2SO_4 + c_5 HNO_3 + c_6 HMnO4 + c_7 (NH_4)_2SO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, Mn, N and S: H: | 2 c_1 + 8 c_3 = 2 c_4 + c_5 + c_6 + 8 c_7 O: | c_1 + 6 c_2 + 8 c_3 = 4 c_4 + 3 c_5 + 4 c_6 + 4 c_7 Mn: | c_2 = c_6 N: | 2 c_2 + 2 c_3 = c_5 + 2 c_7 S: | 2 c_3 = c_4 + c_7 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_4 = 1 and solve the system of equations for the remaining coefficients: c_2 = (3 c_1)/7 - 2/7 c_3 = (5 c_1)/42 + 17/21 c_4 = 1 c_5 = (13 c_1)/21 - 4/21 c_6 = (3 c_1)/7 - 2/7 c_7 = (5 c_1)/21 + 13/21 Multiply by the least common denominator, 8, to eliminate fractional coefficients: c_2 = (3 c_1)/7 - 16/7 c_3 = (5 c_1)/42 + 136/21 c_4 = 8 c_5 = (13 c_1)/21 - 32/21 c_6 = (3 c_1)/7 - 16/7 c_7 = (5 c_1)/21 + 104/21 The resulting system of equations is still underdetermined, so an additional coefficient must be set arbitrarily. Set c_1 = 38 and solve for the remaining coefficients: c_1 = 38 c_2 = 14 c_3 = 11 c_4 = 8 c_5 = 22 c_6 = 14 c_7 = 14 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 38 H_2O + 14 Mn(NO_3)_2 + 11 (NH_4)_2S_2O_8 ⟶ 8 H_2SO_4 + 22 HNO_3 + 14 HMnO4 + 14 (NH_4)_2SO_4
Balance the chemical equation algebraically: H_2O + Mn(NO_3)_2 + (NH_4)_2S_2O_8 ⟶ H_2SO_4 + HNO_3 + HMnO4 + (NH_4)_2SO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 Mn(NO_3)_2 + c_3 (NH_4)_2S_2O_8 ⟶ c_4 H_2SO_4 + c_5 HNO_3 + c_6 HMnO4 + c_7 (NH_4)_2SO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, Mn, N and S: H: | 2 c_1 + 8 c_3 = 2 c_4 + c_5 + c_6 + 8 c_7 O: | c_1 + 6 c_2 + 8 c_3 = 4 c_4 + 3 c_5 + 4 c_6 + 4 c_7 Mn: | c_2 = c_6 N: | 2 c_2 + 2 c_3 = c_5 + 2 c_7 S: | 2 c_3 = c_4 + c_7 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_4 = 1 and solve the system of equations for the remaining coefficients: c_2 = (3 c_1)/7 - 2/7 c_3 = (5 c_1)/42 + 17/21 c_4 = 1 c_5 = (13 c_1)/21 - 4/21 c_6 = (3 c_1)/7 - 2/7 c_7 = (5 c_1)/21 + 13/21 Multiply by the least common denominator, 8, to eliminate fractional coefficients: c_2 = (3 c_1)/7 - 16/7 c_3 = (5 c_1)/42 + 136/21 c_4 = 8 c_5 = (13 c_1)/21 - 32/21 c_6 = (3 c_1)/7 - 16/7 c_7 = (5 c_1)/21 + 104/21 The resulting system of equations is still underdetermined, so an additional coefficient must be set arbitrarily. Set c_1 = 38 and solve for the remaining coefficients: c_1 = 38 c_2 = 14 c_3 = 11 c_4 = 8 c_5 = 22 c_6 = 14 c_7 = 14 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 38 H_2O + 14 Mn(NO_3)_2 + 11 (NH_4)_2S_2O_8 ⟶ 8 H_2SO_4 + 22 HNO_3 + 14 HMnO4 + 14 (NH_4)_2SO_4

Structures

+ + ⟶ + + HMnO4 +
+ + ⟶ + + HMnO4 +

Names

water + manganese(II) nitrate + ammonium persulfate ⟶ sulfuric acid + nitric acid + HMnO4 + ammonium sulfate
water + manganese(II) nitrate + ammonium persulfate ⟶ sulfuric acid + nitric acid + HMnO4 + ammonium sulfate

Equilibrium constant

Construct the equilibrium constant, K, expression for: H_2O + Mn(NO_3)_2 + (NH_4)_2S_2O_8 ⟶ H_2SO_4 + HNO_3 + HMnO4 + (NH_4)_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: 38 H_2O + 14 Mn(NO_3)_2 + 11 (NH_4)_2S_2O_8 ⟶ 8 H_2SO_4 + 22 HNO_3 + 14 HMnO4 + 14 (NH_4)_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_2O | 38 | -38 Mn(NO_3)_2 | 14 | -14 (NH_4)_2S_2O_8 | 11 | -11 H_2SO_4 | 8 | 8 HNO_3 | 22 | 22 HMnO4 | 14 | 14 (NH_4)_2SO_4 | 14 | 14 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 38 | -38 | ([H2O])^(-38) Mn(NO_3)_2 | 14 | -14 | ([Mn(NO3)2])^(-14) (NH_4)_2S_2O_8 | 11 | -11 | ([(NH4)2S2O8])^(-11) H_2SO_4 | 8 | 8 | ([H2SO4])^8 HNO_3 | 22 | 22 | ([HNO3])^22 HMnO4 | 14 | 14 | ([HMnO4])^14 (NH_4)_2SO_4 | 14 | 14 | ([(NH4)2SO4])^14 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 = ([H2O])^(-38) ([Mn(NO3)2])^(-14) ([(NH4)2S2O8])^(-11) ([H2SO4])^8 ([HNO3])^22 ([HMnO4])^14 ([(NH4)2SO4])^14 = (([H2SO4])^8 ([HNO3])^22 ([HMnO4])^14 ([(NH4)2SO4])^14)/(([H2O])^38 ([Mn(NO3)2])^14 ([(NH4)2S2O8])^11)
Construct the equilibrium constant, K, expression for: H_2O + Mn(NO_3)_2 + (NH_4)_2S_2O_8 ⟶ H_2SO_4 + HNO_3 + HMnO4 + (NH_4)_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: 38 H_2O + 14 Mn(NO_3)_2 + 11 (NH_4)_2S_2O_8 ⟶ 8 H_2SO_4 + 22 HNO_3 + 14 HMnO4 + 14 (NH_4)_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_2O | 38 | -38 Mn(NO_3)_2 | 14 | -14 (NH_4)_2S_2O_8 | 11 | -11 H_2SO_4 | 8 | 8 HNO_3 | 22 | 22 HMnO4 | 14 | 14 (NH_4)_2SO_4 | 14 | 14 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 38 | -38 | ([H2O])^(-38) Mn(NO_3)_2 | 14 | -14 | ([Mn(NO3)2])^(-14) (NH_4)_2S_2O_8 | 11 | -11 | ([(NH4)2S2O8])^(-11) H_2SO_4 | 8 | 8 | ([H2SO4])^8 HNO_3 | 22 | 22 | ([HNO3])^22 HMnO4 | 14 | 14 | ([HMnO4])^14 (NH_4)_2SO_4 | 14 | 14 | ([(NH4)2SO4])^14 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 = ([H2O])^(-38) ([Mn(NO3)2])^(-14) ([(NH4)2S2O8])^(-11) ([H2SO4])^8 ([HNO3])^22 ([HMnO4])^14 ([(NH4)2SO4])^14 = (([H2SO4])^8 ([HNO3])^22 ([HMnO4])^14 ([(NH4)2SO4])^14)/(([H2O])^38 ([Mn(NO3)2])^14 ([(NH4)2S2O8])^11)

Rate of reaction

Construct the rate of reaction expression for: H_2O + Mn(NO_3)_2 + (NH_4)_2S_2O_8 ⟶ H_2SO_4 + HNO_3 + HMnO4 + (NH_4)_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: 38 H_2O + 14 Mn(NO_3)_2 + 11 (NH_4)_2S_2O_8 ⟶ 8 H_2SO_4 + 22 HNO_3 + 14 HMnO4 + 14 (NH_4)_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_2O | 38 | -38 Mn(NO_3)_2 | 14 | -14 (NH_4)_2S_2O_8 | 11 | -11 H_2SO_4 | 8 | 8 HNO_3 | 22 | 22 HMnO4 | 14 | 14 (NH_4)_2SO_4 | 14 | 14 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_2O | 38 | -38 | -1/38 (Δ[H2O])/(Δt) Mn(NO_3)_2 | 14 | -14 | -1/14 (Δ[Mn(NO3)2])/(Δt) (NH_4)_2S_2O_8 | 11 | -11 | -1/11 (Δ[(NH4)2S2O8])/(Δt) H_2SO_4 | 8 | 8 | 1/8 (Δ[H2SO4])/(Δt) HNO_3 | 22 | 22 | 1/22 (Δ[HNO3])/(Δt) HMnO4 | 14 | 14 | 1/14 (Δ[HMnO4])/(Δt) (NH_4)_2SO_4 | 14 | 14 | 1/14 (Δ[(NH4)2SO4])/(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 = -1/38 (Δ[H2O])/(Δt) = -1/14 (Δ[Mn(NO3)2])/(Δt) = -1/11 (Δ[(NH4)2S2O8])/(Δt) = 1/8 (Δ[H2SO4])/(Δt) = 1/22 (Δ[HNO3])/(Δt) = 1/14 (Δ[HMnO4])/(Δt) = 1/14 (Δ[(NH4)2SO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: H_2O + Mn(NO_3)_2 + (NH_4)_2S_2O_8 ⟶ H_2SO_4 + HNO_3 + HMnO4 + (NH_4)_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: 38 H_2O + 14 Mn(NO_3)_2 + 11 (NH_4)_2S_2O_8 ⟶ 8 H_2SO_4 + 22 HNO_3 + 14 HMnO4 + 14 (NH_4)_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_2O | 38 | -38 Mn(NO_3)_2 | 14 | -14 (NH_4)_2S_2O_8 | 11 | -11 H_2SO_4 | 8 | 8 HNO_3 | 22 | 22 HMnO4 | 14 | 14 (NH_4)_2SO_4 | 14 | 14 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_2O | 38 | -38 | -1/38 (Δ[H2O])/(Δt) Mn(NO_3)_2 | 14 | -14 | -1/14 (Δ[Mn(NO3)2])/(Δt) (NH_4)_2S_2O_8 | 11 | -11 | -1/11 (Δ[(NH4)2S2O8])/(Δt) H_2SO_4 | 8 | 8 | 1/8 (Δ[H2SO4])/(Δt) HNO_3 | 22 | 22 | 1/22 (Δ[HNO3])/(Δt) HMnO4 | 14 | 14 | 1/14 (Δ[HMnO4])/(Δt) (NH_4)_2SO_4 | 14 | 14 | 1/14 (Δ[(NH4)2SO4])/(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 = -1/38 (Δ[H2O])/(Δt) = -1/14 (Δ[Mn(NO3)2])/(Δt) = -1/11 (Δ[(NH4)2S2O8])/(Δt) = 1/8 (Δ[H2SO4])/(Δt) = 1/22 (Δ[HNO3])/(Δt) = 1/14 (Δ[HMnO4])/(Δt) = 1/14 (Δ[(NH4)2SO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| water | manganese(II) nitrate | ammonium persulfate | sulfuric acid | nitric acid | HMnO4 | ammonium sulfate formula | H_2O | Mn(NO_3)_2 | (NH_4)_2S_2O_8 | H_2SO_4 | HNO_3 | HMnO4 | (NH_4)_2SO_4 Hill formula | H_2O | MnN_2O_6 | H_8N_2O_8S_2 | H_2O_4S | HNO_3 | HMnO4 | H_8N_2O_4S name | water | manganese(II) nitrate | ammonium persulfate | sulfuric acid | nitric acid | | ammonium sulfate IUPAC name | water | manganese(2+) dinitrate | diammonium sulfonatooxy sulfate | sulfuric acid | nitric acid | |
| water | manganese(II) nitrate | ammonium persulfate | sulfuric acid | nitric acid | HMnO4 | ammonium sulfate formula | H_2O | Mn(NO_3)_2 | (NH_4)_2S_2O_8 | H_2SO_4 | HNO_3 | HMnO4 | (NH_4)_2SO_4 Hill formula | H_2O | MnN_2O_6 | H_8N_2O_8S_2 | H_2O_4S | HNO_3 | HMnO4 | H_8N_2O_4S name | water | manganese(II) nitrate | ammonium persulfate | sulfuric acid | nitric acid | | ammonium sulfate IUPAC name | water | manganese(2+) dinitrate | diammonium sulfonatooxy sulfate | sulfuric acid | nitric acid | |

Substance properties

| water | manganese(II) nitrate | ammonium persulfate | sulfuric acid | nitric acid | HMnO4 | ammonium sulfate molar mass | 18.015 g/mol | 178.95 g/mol | 228.2 g/mol | 98.07 g/mol | 63.012 g/mol | 119.94 g/mol | 132.1 g/mol phase | liquid (at STP) | | solid (at STP) | liquid (at STP) | liquid (at STP) | | solid (at STP) melting point | 0 °C | | 120 °C | 10.371 °C | -41.6 °C | | 280 °C boiling point | 99.9839 °C | | | 279.6 °C | 83 °C | | density | 1 g/cm^3 | 1.536 g/cm^3 | 1.98 g/cm^3 | 1.8305 g/cm^3 | 1.5129 g/cm^3 | | 1.77 g/cm^3 solubility in water | | | | very soluble | miscible | | surface tension | 0.0728 N/m | | | 0.0735 N/m | | | dynamic viscosity | 8.9×10^-4 Pa s (at 25 °C) | | | 0.021 Pa s (at 25 °C) | 7.6×10^-4 Pa s (at 25 °C) | | odor | odorless | | odorless | odorless | | | odorless
| water | manganese(II) nitrate | ammonium persulfate | sulfuric acid | nitric acid | HMnO4 | ammonium sulfate molar mass | 18.015 g/mol | 178.95 g/mol | 228.2 g/mol | 98.07 g/mol | 63.012 g/mol | 119.94 g/mol | 132.1 g/mol phase | liquid (at STP) | | solid (at STP) | liquid (at STP) | liquid (at STP) | | solid (at STP) melting point | 0 °C | | 120 °C | 10.371 °C | -41.6 °C | | 280 °C boiling point | 99.9839 °C | | | 279.6 °C | 83 °C | | density | 1 g/cm^3 | 1.536 g/cm^3 | 1.98 g/cm^3 | 1.8305 g/cm^3 | 1.5129 g/cm^3 | | 1.77 g/cm^3 solubility in water | | | | very soluble | miscible | | surface tension | 0.0728 N/m | | | 0.0735 N/m | | | dynamic viscosity | 8.9×10^-4 Pa s (at 25 °C) | | | 0.021 Pa s (at 25 °C) | 7.6×10^-4 Pa s (at 25 °C) | | odor | odorless | | odorless | odorless | | | odorless

Units

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