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H2SO4 + KMnO4 + C6H8O6 = H2O + K2SO4 + MnSO4 + C6H6O6

Input interpretation

H_2SO_4 sulfuric acid + KMnO_4 potassium permanganate + H_2C_6H_6O_6 ascorbic acid ⟶ H_2O water + K_2SO_4 potassium sulfate + MnSO_4 manganese(II) sulfate + HO_2CCH_2C(CO_2H)=CHCO_2H trans-aconitic acid
H_2SO_4 sulfuric acid + KMnO_4 potassium permanganate + H_2C_6H_6O_6 ascorbic acid ⟶ H_2O water + K_2SO_4 potassium sulfate + MnSO_4 manganese(II) sulfate + HO_2CCH_2C(CO_2H)=CHCO_2H trans-aconitic acid

Balanced equation

Balance the chemical equation algebraically: H_2SO_4 + KMnO_4 + H_2C_6H_6O_6 ⟶ H_2O + K_2SO_4 + MnSO_4 + HO_2CCH_2C(CO_2H)=CHCO_2H Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 KMnO_4 + c_3 H_2C_6H_6O_6 ⟶ c_4 H_2O + c_5 K_2SO_4 + c_6 MnSO_4 + c_7 HO_2CCH_2C(CO_2H)=CHCO_2H Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, K, Mn and C: H: | 2 c_1 + 8 c_3 = 2 c_4 + 6 c_7 O: | 4 c_1 + 4 c_2 + 6 c_3 = c_4 + 4 c_5 + 4 c_6 + 6 c_7 S: | c_1 = c_5 + c_6 K: | c_2 = 2 c_5 Mn: | c_2 = c_6 C: | 6 c_3 = 6 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_5 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3 c_2 = 2 c_3 = 5 c_4 = 8 c_5 = 1 c_6 = 2 c_7 = 5 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 H_2SO_4 + 2 KMnO_4 + 5 H_2C_6H_6O_6 ⟶ 8 H_2O + K_2SO_4 + 2 MnSO_4 + 5 HO_2CCH_2C(CO_2H)=CHCO_2H
Balance the chemical equation algebraically: H_2SO_4 + KMnO_4 + H_2C_6H_6O_6 ⟶ H_2O + K_2SO_4 + MnSO_4 + HO_2CCH_2C(CO_2H)=CHCO_2H Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 KMnO_4 + c_3 H_2C_6H_6O_6 ⟶ c_4 H_2O + c_5 K_2SO_4 + c_6 MnSO_4 + c_7 HO_2CCH_2C(CO_2H)=CHCO_2H Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, K, Mn and C: H: | 2 c_1 + 8 c_3 = 2 c_4 + 6 c_7 O: | 4 c_1 + 4 c_2 + 6 c_3 = c_4 + 4 c_5 + 4 c_6 + 6 c_7 S: | c_1 = c_5 + c_6 K: | c_2 = 2 c_5 Mn: | c_2 = c_6 C: | 6 c_3 = 6 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_5 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3 c_2 = 2 c_3 = 5 c_4 = 8 c_5 = 1 c_6 = 2 c_7 = 5 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 H_2SO_4 + 2 KMnO_4 + 5 H_2C_6H_6O_6 ⟶ 8 H_2O + K_2SO_4 + 2 MnSO_4 + 5 HO_2CCH_2C(CO_2H)=CHCO_2H

Structures

+ + ⟶ + + +
+ + ⟶ + + +

Names

sulfuric acid + potassium permanganate + ascorbic acid ⟶ water + potassium sulfate + manganese(II) sulfate + trans-aconitic acid
sulfuric acid + potassium permanganate + ascorbic acid ⟶ water + potassium sulfate + manganese(II) sulfate + trans-aconitic acid

Equilibrium constant

Construct the equilibrium constant, K, expression for: H_2SO_4 + KMnO_4 + H_2C_6H_6O_6 ⟶ H_2O + K_2SO_4 + MnSO_4 + HO_2CCH_2C(CO_2H)=CHCO_2H 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 KMnO_4 + 5 H_2C_6H_6O_6 ⟶ 8 H_2O + K_2SO_4 + 2 MnSO_4 + 5 HO_2CCH_2C(CO_2H)=CHCO_2H 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 KMnO_4 | 2 | -2 H_2C_6H_6O_6 | 5 | -5 H_2O | 8 | 8 K_2SO_4 | 1 | 1 MnSO_4 | 2 | 2 HO_2CCH_2C(CO_2H)=CHCO_2H | 5 | 5 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) KMnO_4 | 2 | -2 | ([KMnO4])^(-2) H_2C_6H_6O_6 | 5 | -5 | ([H2C6H6O6])^(-5) H_2O | 8 | 8 | ([H2O])^8 K_2SO_4 | 1 | 1 | [K2SO4] MnSO_4 | 2 | 2 | ([MnSO4])^2 HO_2CCH_2C(CO_2H)=CHCO_2H | 5 | 5 | ([HO2CCH2C(CO2H)=CHCO2H])^5 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) ([KMnO4])^(-2) ([H2C6H6O6])^(-5) ([H2O])^8 [K2SO4] ([MnSO4])^2 ([HO2CCH2C(CO2H)=CHCO2H])^5 = (([H2O])^8 [K2SO4] ([MnSO4])^2 ([HO2CCH2C(CO2H)=CHCO2H])^5)/(([H2SO4])^3 ([KMnO4])^2 ([H2C6H6O6])^5)
Construct the equilibrium constant, K, expression for: H_2SO_4 + KMnO_4 + H_2C_6H_6O_6 ⟶ H_2O + K_2SO_4 + MnSO_4 + HO_2CCH_2C(CO_2H)=CHCO_2H 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 KMnO_4 + 5 H_2C_6H_6O_6 ⟶ 8 H_2O + K_2SO_4 + 2 MnSO_4 + 5 HO_2CCH_2C(CO_2H)=CHCO_2H 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 KMnO_4 | 2 | -2 H_2C_6H_6O_6 | 5 | -5 H_2O | 8 | 8 K_2SO_4 | 1 | 1 MnSO_4 | 2 | 2 HO_2CCH_2C(CO_2H)=CHCO_2H | 5 | 5 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) KMnO_4 | 2 | -2 | ([KMnO4])^(-2) H_2C_6H_6O_6 | 5 | -5 | ([H2C6H6O6])^(-5) H_2O | 8 | 8 | ([H2O])^8 K_2SO_4 | 1 | 1 | [K2SO4] MnSO_4 | 2 | 2 | ([MnSO4])^2 HO_2CCH_2C(CO_2H)=CHCO_2H | 5 | 5 | ([HO2CCH2C(CO2H)=CHCO2H])^5 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) ([KMnO4])^(-2) ([H2C6H6O6])^(-5) ([H2O])^8 [K2SO4] ([MnSO4])^2 ([HO2CCH2C(CO2H)=CHCO2H])^5 = (([H2O])^8 [K2SO4] ([MnSO4])^2 ([HO2CCH2C(CO2H)=CHCO2H])^5)/(([H2SO4])^3 ([KMnO4])^2 ([H2C6H6O6])^5)

Rate of reaction

Construct the rate of reaction expression for: H_2SO_4 + KMnO_4 + H_2C_6H_6O_6 ⟶ H_2O + K_2SO_4 + MnSO_4 + HO_2CCH_2C(CO_2H)=CHCO_2H 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 KMnO_4 + 5 H_2C_6H_6O_6 ⟶ 8 H_2O + K_2SO_4 + 2 MnSO_4 + 5 HO_2CCH_2C(CO_2H)=CHCO_2H 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 KMnO_4 | 2 | -2 H_2C_6H_6O_6 | 5 | -5 H_2O | 8 | 8 K_2SO_4 | 1 | 1 MnSO_4 | 2 | 2 HO_2CCH_2C(CO_2H)=CHCO_2H | 5 | 5 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) KMnO_4 | 2 | -2 | -1/2 (Δ[KMnO4])/(Δt) H_2C_6H_6O_6 | 5 | -5 | -1/5 (Δ[H2C6H6O6])/(Δt) H_2O | 8 | 8 | 1/8 (Δ[H2O])/(Δt) K_2SO_4 | 1 | 1 | (Δ[K2SO4])/(Δt) MnSO_4 | 2 | 2 | 1/2 (Δ[MnSO4])/(Δt) HO_2CCH_2C(CO_2H)=CHCO_2H | 5 | 5 | 1/5 (Δ[HO2CCH2C(CO2H)=CHCO2H])/(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[KMnO4])/(Δt) = -1/5 (Δ[H2C6H6O6])/(Δt) = 1/8 (Δ[H2O])/(Δt) = (Δ[K2SO4])/(Δt) = 1/2 (Δ[MnSO4])/(Δt) = 1/5 (Δ[HO2CCH2C(CO2H)=CHCO2H])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: H_2SO_4 + KMnO_4 + H_2C_6H_6O_6 ⟶ H_2O + K_2SO_4 + MnSO_4 + HO_2CCH_2C(CO_2H)=CHCO_2H 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 KMnO_4 + 5 H_2C_6H_6O_6 ⟶ 8 H_2O + K_2SO_4 + 2 MnSO_4 + 5 HO_2CCH_2C(CO_2H)=CHCO_2H 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 KMnO_4 | 2 | -2 H_2C_6H_6O_6 | 5 | -5 H_2O | 8 | 8 K_2SO_4 | 1 | 1 MnSO_4 | 2 | 2 HO_2CCH_2C(CO_2H)=CHCO_2H | 5 | 5 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) KMnO_4 | 2 | -2 | -1/2 (Δ[KMnO4])/(Δt) H_2C_6H_6O_6 | 5 | -5 | -1/5 (Δ[H2C6H6O6])/(Δt) H_2O | 8 | 8 | 1/8 (Δ[H2O])/(Δt) K_2SO_4 | 1 | 1 | (Δ[K2SO4])/(Δt) MnSO_4 | 2 | 2 | 1/2 (Δ[MnSO4])/(Δt) HO_2CCH_2C(CO_2H)=CHCO_2H | 5 | 5 | 1/5 (Δ[HO2CCH2C(CO2H)=CHCO2H])/(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[KMnO4])/(Δt) = -1/5 (Δ[H2C6H6O6])/(Δt) = 1/8 (Δ[H2O])/(Δt) = (Δ[K2SO4])/(Δt) = 1/2 (Δ[MnSO4])/(Δt) = 1/5 (Δ[HO2CCH2C(CO2H)=CHCO2H])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| sulfuric acid | potassium permanganate | ascorbic acid | water | potassium sulfate | manganese(II) sulfate | trans-aconitic acid formula | H_2SO_4 | KMnO_4 | H_2C_6H_6O_6 | H_2O | K_2SO_4 | MnSO_4 | HO_2CCH_2C(CO_2H)=CHCO_2H Hill formula | H_2O_4S | KMnO_4 | C_6H_8O_6 | H_2O | K_2O_4S | MnSO_4 | C_6H_6O_6 name | sulfuric acid | potassium permanganate | ascorbic acid | water | potassium sulfate | manganese(II) sulfate | trans-aconitic acid IUPAC name | sulfuric acid | potassium permanganate | | water | dipotassium sulfate | manganese(+2) cation sulfate | (E)-prop-1-ene-1, 2, 3-tricarboxylic acid
| sulfuric acid | potassium permanganate | ascorbic acid | water | potassium sulfate | manganese(II) sulfate | trans-aconitic acid formula | H_2SO_4 | KMnO_4 | H_2C_6H_6O_6 | H_2O | K_2SO_4 | MnSO_4 | HO_2CCH_2C(CO_2H)=CHCO_2H Hill formula | H_2O_4S | KMnO_4 | C_6H_8O_6 | H_2O | K_2O_4S | MnSO_4 | C_6H_6O_6 name | sulfuric acid | potassium permanganate | ascorbic acid | water | potassium sulfate | manganese(II) sulfate | trans-aconitic acid IUPAC name | sulfuric acid | potassium permanganate | | water | dipotassium sulfate | manganese(+2) cation sulfate | (E)-prop-1-ene-1, 2, 3-tricarboxylic acid

Substance properties

| sulfuric acid | potassium permanganate | ascorbic acid | water | potassium sulfate | manganese(II) sulfate | trans-aconitic acid molar mass | 98.07 g/mol | 158.03 g/mol | 176.12 g/mol | 18.015 g/mol | 174.25 g/mol | 150.99 g/mol | 174.11 g/mol phase | liquid (at STP) | solid (at STP) | solid (at STP) | liquid (at STP) | | solid (at STP) | solid (at STP) melting point | 10.371 °C | 240 °C | 192 °C | 0 °C | | 710 °C | 190 °C boiling point | 279.6 °C | | 553 °C | 99.9839 °C | | | 385 °C density | 1.8305 g/cm^3 | 1 g/cm^3 | 1.694 g/cm^3 | 1 g/cm^3 | | 3.25 g/cm^3 | solubility in water | very soluble | | | | soluble | soluble | very 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 | | odorless | | |
| sulfuric acid | potassium permanganate | ascorbic acid | water | potassium sulfate | manganese(II) sulfate | trans-aconitic acid molar mass | 98.07 g/mol | 158.03 g/mol | 176.12 g/mol | 18.015 g/mol | 174.25 g/mol | 150.99 g/mol | 174.11 g/mol phase | liquid (at STP) | solid (at STP) | solid (at STP) | liquid (at STP) | | solid (at STP) | solid (at STP) melting point | 10.371 °C | 240 °C | 192 °C | 0 °C | | 710 °C | 190 °C boiling point | 279.6 °C | | 553 °C | 99.9839 °C | | | 385 °C density | 1.8305 g/cm^3 | 1 g/cm^3 | 1.694 g/cm^3 | 1 g/cm^3 | | 3.25 g/cm^3 | solubility in water | very soluble | | | | soluble | soluble | very 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 | | odorless | | |

Units

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