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H2SO4 + KMnO4 + C6H3(CH3)3 = H2O + K2SO4 + MnSO4 + C6H3(COOH)3

Input interpretation

H_2SO_4 sulfuric acid + KMnO_4 potassium permanganate + C_6H_5CH(CH_3)_2 cumene ⟶ H_2O water + K_2SO_4 potassium sulfate + MnSO_4 manganese(II) sulfate + C_6H_3(CO_2H)_3 trimellitic acid
H_2SO_4 sulfuric acid + KMnO_4 potassium permanganate + C_6H_5CH(CH_3)_2 cumene ⟶ H_2O water + K_2SO_4 potassium sulfate + MnSO_4 manganese(II) sulfate + C_6H_3(CO_2H)_3 trimellitic acid

Balanced equation

Balance the chemical equation algebraically: H_2SO_4 + KMnO_4 + C_6H_5CH(CH_3)_2 ⟶ H_2O + K_2SO_4 + MnSO_4 + C_6H_3(CO_2H)_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 KMnO_4 + c_3 C_6H_5CH(CH_3)_2 ⟶ c_4 H_2O + c_5 K_2SO_4 + c_6 MnSO_4 + c_7 C_6H_3(CO_2H)_3 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 + 12 c_3 = 2 c_4 + 6 c_7 O: | 4 c_1 + 4 c_2 = 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: | 9 c_3 = 9 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 27/5 c_2 = 18/5 c_3 = 1 c_4 = 42/5 c_5 = 9/5 c_6 = 18/5 c_7 = 1 Multiply by the least common denominator, 5, to eliminate fractional coefficients: c_1 = 27 c_2 = 18 c_3 = 5 c_4 = 42 c_5 = 9 c_6 = 18 c_7 = 5 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 27 H_2SO_4 + 18 KMnO_4 + 5 C_6H_5CH(CH_3)_2 ⟶ 42 H_2O + 9 K_2SO_4 + 18 MnSO_4 + 5 C_6H_3(CO_2H)_3
Balance the chemical equation algebraically: H_2SO_4 + KMnO_4 + C_6H_5CH(CH_3)_2 ⟶ H_2O + K_2SO_4 + MnSO_4 + C_6H_3(CO_2H)_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 KMnO_4 + c_3 C_6H_5CH(CH_3)_2 ⟶ c_4 H_2O + c_5 K_2SO_4 + c_6 MnSO_4 + c_7 C_6H_3(CO_2H)_3 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 + 12 c_3 = 2 c_4 + 6 c_7 O: | 4 c_1 + 4 c_2 = 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: | 9 c_3 = 9 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 27/5 c_2 = 18/5 c_3 = 1 c_4 = 42/5 c_5 = 9/5 c_6 = 18/5 c_7 = 1 Multiply by the least common denominator, 5, to eliminate fractional coefficients: c_1 = 27 c_2 = 18 c_3 = 5 c_4 = 42 c_5 = 9 c_6 = 18 c_7 = 5 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 27 H_2SO_4 + 18 KMnO_4 + 5 C_6H_5CH(CH_3)_2 ⟶ 42 H_2O + 9 K_2SO_4 + 18 MnSO_4 + 5 C_6H_3(CO_2H)_3

Structures

+ + ⟶ + + +
+ + ⟶ + + +

Names

sulfuric acid + potassium permanganate + cumene ⟶ water + potassium sulfate + manganese(II) sulfate + trimellitic acid
sulfuric acid + potassium permanganate + cumene ⟶ water + potassium sulfate + manganese(II) sulfate + trimellitic acid

Equilibrium constant

Construct the equilibrium constant, K, expression for: H_2SO_4 + KMnO_4 + C_6H_5CH(CH_3)_2 ⟶ H_2O + K_2SO_4 + MnSO_4 + C_6H_3(CO_2H)_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: 27 H_2SO_4 + 18 KMnO_4 + 5 C_6H_5CH(CH_3)_2 ⟶ 42 H_2O + 9 K_2SO_4 + 18 MnSO_4 + 5 C_6H_3(CO_2H)_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 H_2SO_4 | 27 | -27 KMnO_4 | 18 | -18 C_6H_5CH(CH_3)_2 | 5 | -5 H_2O | 42 | 42 K_2SO_4 | 9 | 9 MnSO_4 | 18 | 18 C_6H_3(CO_2H)_3 | 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 | 27 | -27 | ([H2SO4])^(-27) KMnO_4 | 18 | -18 | ([KMnO4])^(-18) C_6H_5CH(CH_3)_2 | 5 | -5 | ([C6H5CH(CH3)2])^(-5) H_2O | 42 | 42 | ([H2O])^42 K_2SO_4 | 9 | 9 | ([K2SO4])^9 MnSO_4 | 18 | 18 | ([MnSO4])^18 C_6H_3(CO_2H)_3 | 5 | 5 | ([C6H3(CO2H)3])^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])^(-27) ([KMnO4])^(-18) ([C6H5CH(CH3)2])^(-5) ([H2O])^42 ([K2SO4])^9 ([MnSO4])^18 ([C6H3(CO2H)3])^5 = (([H2O])^42 ([K2SO4])^9 ([MnSO4])^18 ([C6H3(CO2H)3])^5)/(([H2SO4])^27 ([KMnO4])^18 ([C6H5CH(CH3)2])^5)
Construct the equilibrium constant, K, expression for: H_2SO_4 + KMnO_4 + C_6H_5CH(CH_3)_2 ⟶ H_2O + K_2SO_4 + MnSO_4 + C_6H_3(CO_2H)_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: 27 H_2SO_4 + 18 KMnO_4 + 5 C_6H_5CH(CH_3)_2 ⟶ 42 H_2O + 9 K_2SO_4 + 18 MnSO_4 + 5 C_6H_3(CO_2H)_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 H_2SO_4 | 27 | -27 KMnO_4 | 18 | -18 C_6H_5CH(CH_3)_2 | 5 | -5 H_2O | 42 | 42 K_2SO_4 | 9 | 9 MnSO_4 | 18 | 18 C_6H_3(CO_2H)_3 | 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 | 27 | -27 | ([H2SO4])^(-27) KMnO_4 | 18 | -18 | ([KMnO4])^(-18) C_6H_5CH(CH_3)_2 | 5 | -5 | ([C6H5CH(CH3)2])^(-5) H_2O | 42 | 42 | ([H2O])^42 K_2SO_4 | 9 | 9 | ([K2SO4])^9 MnSO_4 | 18 | 18 | ([MnSO4])^18 C_6H_3(CO_2H)_3 | 5 | 5 | ([C6H3(CO2H)3])^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])^(-27) ([KMnO4])^(-18) ([C6H5CH(CH3)2])^(-5) ([H2O])^42 ([K2SO4])^9 ([MnSO4])^18 ([C6H3(CO2H)3])^5 = (([H2O])^42 ([K2SO4])^9 ([MnSO4])^18 ([C6H3(CO2H)3])^5)/(([H2SO4])^27 ([KMnO4])^18 ([C6H5CH(CH3)2])^5)

Rate of reaction

Construct the rate of reaction expression for: H_2SO_4 + KMnO_4 + C_6H_5CH(CH_3)_2 ⟶ H_2O + K_2SO_4 + MnSO_4 + C_6H_3(CO_2H)_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: 27 H_2SO_4 + 18 KMnO_4 + 5 C_6H_5CH(CH_3)_2 ⟶ 42 H_2O + 9 K_2SO_4 + 18 MnSO_4 + 5 C_6H_3(CO_2H)_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 H_2SO_4 | 27 | -27 KMnO_4 | 18 | -18 C_6H_5CH(CH_3)_2 | 5 | -5 H_2O | 42 | 42 K_2SO_4 | 9 | 9 MnSO_4 | 18 | 18 C_6H_3(CO_2H)_3 | 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 | 27 | -27 | -1/27 (Δ[H2SO4])/(Δt) KMnO_4 | 18 | -18 | -1/18 (Δ[KMnO4])/(Δt) C_6H_5CH(CH_3)_2 | 5 | -5 | -1/5 (Δ[C6H5CH(CH3)2])/(Δt) H_2O | 42 | 42 | 1/42 (Δ[H2O])/(Δt) K_2SO_4 | 9 | 9 | 1/9 (Δ[K2SO4])/(Δt) MnSO_4 | 18 | 18 | 1/18 (Δ[MnSO4])/(Δt) C_6H_3(CO_2H)_3 | 5 | 5 | 1/5 (Δ[C6H3(CO2H)3])/(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 = -1/27 (Δ[H2SO4])/(Δt) = -1/18 (Δ[KMnO4])/(Δt) = -1/5 (Δ[C6H5CH(CH3)2])/(Δt) = 1/42 (Δ[H2O])/(Δt) = 1/9 (Δ[K2SO4])/(Δt) = 1/18 (Δ[MnSO4])/(Δt) = 1/5 (Δ[C6H3(CO2H)3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: H_2SO_4 + KMnO_4 + C_6H_5CH(CH_3)_2 ⟶ H_2O + K_2SO_4 + MnSO_4 + C_6H_3(CO_2H)_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: 27 H_2SO_4 + 18 KMnO_4 + 5 C_6H_5CH(CH_3)_2 ⟶ 42 H_2O + 9 K_2SO_4 + 18 MnSO_4 + 5 C_6H_3(CO_2H)_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 H_2SO_4 | 27 | -27 KMnO_4 | 18 | -18 C_6H_5CH(CH_3)_2 | 5 | -5 H_2O | 42 | 42 K_2SO_4 | 9 | 9 MnSO_4 | 18 | 18 C_6H_3(CO_2H)_3 | 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 | 27 | -27 | -1/27 (Δ[H2SO4])/(Δt) KMnO_4 | 18 | -18 | -1/18 (Δ[KMnO4])/(Δt) C_6H_5CH(CH_3)_2 | 5 | -5 | -1/5 (Δ[C6H5CH(CH3)2])/(Δt) H_2O | 42 | 42 | 1/42 (Δ[H2O])/(Δt) K_2SO_4 | 9 | 9 | 1/9 (Δ[K2SO4])/(Δt) MnSO_4 | 18 | 18 | 1/18 (Δ[MnSO4])/(Δt) C_6H_3(CO_2H)_3 | 5 | 5 | 1/5 (Δ[C6H3(CO2H)3])/(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 = -1/27 (Δ[H2SO4])/(Δt) = -1/18 (Δ[KMnO4])/(Δt) = -1/5 (Δ[C6H5CH(CH3)2])/(Δt) = 1/42 (Δ[H2O])/(Δt) = 1/9 (Δ[K2SO4])/(Δt) = 1/18 (Δ[MnSO4])/(Δt) = 1/5 (Δ[C6H3(CO2H)3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| sulfuric acid | potassium permanganate | cumene | water | potassium sulfate | manganese(II) sulfate | trimellitic acid formula | H_2SO_4 | KMnO_4 | C_6H_5CH(CH_3)_2 | H_2O | K_2SO_4 | MnSO_4 | C_6H_3(CO_2H)_3 Hill formula | H_2O_4S | KMnO_4 | C_9H_12 | H_2O | K_2O_4S | MnSO_4 | C_9H_6O_6 name | sulfuric acid | potassium permanganate | cumene | water | potassium sulfate | manganese(II) sulfate | trimellitic acid IUPAC name | sulfuric acid | potassium permanganate | isopropylbenzene | water | dipotassium sulfate | manganese(+2) cation sulfate | benzene-1, 2, 4-tricarboxylic acid
| sulfuric acid | potassium permanganate | cumene | water | potassium sulfate | manganese(II) sulfate | trimellitic acid formula | H_2SO_4 | KMnO_4 | C_6H_5CH(CH_3)_2 | H_2O | K_2SO_4 | MnSO_4 | C_6H_3(CO_2H)_3 Hill formula | H_2O_4S | KMnO_4 | C_9H_12 | H_2O | K_2O_4S | MnSO_4 | C_9H_6O_6 name | sulfuric acid | potassium permanganate | cumene | water | potassium sulfate | manganese(II) sulfate | trimellitic acid IUPAC name | sulfuric acid | potassium permanganate | isopropylbenzene | water | dipotassium sulfate | manganese(+2) cation sulfate | benzene-1, 2, 4-tricarboxylic acid

Substance properties

| sulfuric acid | potassium permanganate | cumene | water | potassium sulfate | manganese(II) sulfate | trimellitic acid molar mass | 98.07 g/mol | 158.03 g/mol | 120.19 g/mol | 18.015 g/mol | 174.25 g/mol | 150.99 g/mol | 210.14 g/mol phase | liquid (at STP) | solid (at STP) | liquid (at STP) | liquid (at STP) | | solid (at STP) | solid (at STP) melting point | 10.371 °C | 240 °C | -96 °C | 0 °C | | 710 °C | 230 °C boiling point | 279.6 °C | | 153 °C | 99.9839 °C | | | density | 1.8305 g/cm^3 | 1 g/cm^3 | 0.864 g/cm^3 | 1 g/cm^3 | | 3.25 g/cm^3 | solubility in water | very soluble | | insoluble | | soluble | soluble | very soluble surface tension | 0.0735 N/m | | 0.02769 N/m | 0.0728 N/m | | | dynamic viscosity | 0.021 Pa s (at 25 °C) | | 7.37×10^-4 Pa s (at 25 °C) | 8.9×10^-4 Pa s (at 25 °C) | | | odor | odorless | odorless | | odorless | | |
| sulfuric acid | potassium permanganate | cumene | water | potassium sulfate | manganese(II) sulfate | trimellitic acid molar mass | 98.07 g/mol | 158.03 g/mol | 120.19 g/mol | 18.015 g/mol | 174.25 g/mol | 150.99 g/mol | 210.14 g/mol phase | liquid (at STP) | solid (at STP) | liquid (at STP) | liquid (at STP) | | solid (at STP) | solid (at STP) melting point | 10.371 °C | 240 °C | -96 °C | 0 °C | | 710 °C | 230 °C boiling point | 279.6 °C | | 153 °C | 99.9839 °C | | | density | 1.8305 g/cm^3 | 1 g/cm^3 | 0.864 g/cm^3 | 1 g/cm^3 | | 3.25 g/cm^3 | solubility in water | very soluble | | insoluble | | soluble | soluble | very soluble surface tension | 0.0735 N/m | | 0.02769 N/m | 0.0728 N/m | | | dynamic viscosity | 0.021 Pa s (at 25 °C) | | 7.37×10^-4 Pa s (at 25 °C) | 8.9×10^-4 Pa s (at 25 °C) | | | odor | odorless | odorless | | odorless | | |

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