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H2SO4 + KMnO4 + K2S = H2O + K2SO4 + S + MnO2

Input interpretation

H_2SO_4 sulfuric acid + KMnO_4 potassium permanganate + K2S ⟶ H_2O water + K_2SO_4 potassium sulfate + S mixed sulfur + MnO_2 manganese dioxide
H_2SO_4 sulfuric acid + KMnO_4 potassium permanganate + K2S ⟶ H_2O water + K_2SO_4 potassium sulfate + S mixed sulfur + MnO_2 manganese dioxide

Balanced equation

Balance the chemical equation algebraically: H_2SO_4 + KMnO_4 + K2S ⟶ H_2O + K_2SO_4 + S + MnO_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 KMnO_4 + c_3 K2S ⟶ c_4 H_2O + c_5 K_2SO_4 + c_6 S + c_7 MnO_2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, K and Mn: H: | 2 c_1 = 2 c_4 O: | 4 c_1 + 4 c_2 = c_4 + 4 c_5 + 2 c_7 S: | c_1 + c_3 = c_5 + c_6 K: | c_2 + 2 c_3 = 2 c_5 Mn: | c_2 = 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_6 = 1 and solve the system of equations for the remaining coefficients: c_2 = 2 c_1 - 2 c_3 = (3 c_1)/4 c_4 = c_1 c_5 = (7 c_1)/4 - 1 c_6 = 1 c_7 = 2 c_1 - 2 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_2 = 2 c_1 - 4 c_3 = (3 c_1)/4 c_4 = c_1 c_5 = (7 c_1)/4 - 2 c_6 = 2 c_7 = 2 c_1 - 4 The resulting system of equations is still underdetermined, so an additional coefficient must be set arbitrarily. Set c_1 = 4 and solve for the remaining coefficients: c_1 = 4 c_2 = 4 c_3 = 3 c_4 = 4 c_5 = 5 c_6 = 2 c_7 = 4 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: |   | 4 H_2SO_4 + 4 KMnO_4 + 3 K2S ⟶ 4 H_2O + 5 K_2SO_4 + 2 S + 4 MnO_2
Balance the chemical equation algebraically: H_2SO_4 + KMnO_4 + K2S ⟶ H_2O + K_2SO_4 + S + MnO_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 KMnO_4 + c_3 K2S ⟶ c_4 H_2O + c_5 K_2SO_4 + c_6 S + c_7 MnO_2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, K and Mn: H: | 2 c_1 = 2 c_4 O: | 4 c_1 + 4 c_2 = c_4 + 4 c_5 + 2 c_7 S: | c_1 + c_3 = c_5 + c_6 K: | c_2 + 2 c_3 = 2 c_5 Mn: | c_2 = 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_6 = 1 and solve the system of equations for the remaining coefficients: c_2 = 2 c_1 - 2 c_3 = (3 c_1)/4 c_4 = c_1 c_5 = (7 c_1)/4 - 1 c_6 = 1 c_7 = 2 c_1 - 2 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_2 = 2 c_1 - 4 c_3 = (3 c_1)/4 c_4 = c_1 c_5 = (7 c_1)/4 - 2 c_6 = 2 c_7 = 2 c_1 - 4 The resulting system of equations is still underdetermined, so an additional coefficient must be set arbitrarily. Set c_1 = 4 and solve for the remaining coefficients: c_1 = 4 c_2 = 4 c_3 = 3 c_4 = 4 c_5 = 5 c_6 = 2 c_7 = 4 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 H_2SO_4 + 4 KMnO_4 + 3 K2S ⟶ 4 H_2O + 5 K_2SO_4 + 2 S + 4 MnO_2

Structures

 + + K2S ⟶ + + +
+ + K2S ⟶ + + +

Names

sulfuric acid + potassium permanganate + K2S ⟶ water + potassium sulfate + mixed sulfur + manganese dioxide
sulfuric acid + potassium permanganate + K2S ⟶ water + potassium sulfate + mixed sulfur + manganese dioxide

Equilibrium constant

Construct the equilibrium constant, K, expression for: H_2SO_4 + KMnO_4 + K2S ⟶ H_2O + K_2SO_4 + S + MnO_2 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: 4 H_2SO_4 + 4 KMnO_4 + 3 K2S ⟶ 4 H_2O + 5 K_2SO_4 + 2 S + 4 MnO_2 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 | 4 | -4 KMnO_4 | 4 | -4 K2S | 3 | -3 H_2O | 4 | 4 K_2SO_4 | 5 | 5 S | 2 | 2 MnO_2 | 4 | 4 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 4 | -4 | ([H2SO4])^(-4) KMnO_4 | 4 | -4 | ([KMnO4])^(-4) K2S | 3 | -3 | ([K2S])^(-3) H_2O | 4 | 4 | ([H2O])^4 K_2SO_4 | 5 | 5 | ([K2SO4])^5 S | 2 | 2 | ([S])^2 MnO_2 | 4 | 4 | ([MnO2])^4 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])^(-4) ([KMnO4])^(-4) ([K2S])^(-3) ([H2O])^4 ([K2SO4])^5 ([S])^2 ([MnO2])^4 = (([H2O])^4 ([K2SO4])^5 ([S])^2 ([MnO2])^4)/(([H2SO4])^4 ([KMnO4])^4 ([K2S])^3)
Construct the equilibrium constant, K, expression for: H_2SO_4 + KMnO_4 + K2S ⟶ H_2O + K_2SO_4 + S + MnO_2 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: 4 H_2SO_4 + 4 KMnO_4 + 3 K2S ⟶ 4 H_2O + 5 K_2SO_4 + 2 S + 4 MnO_2 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 | 4 | -4 KMnO_4 | 4 | -4 K2S | 3 | -3 H_2O | 4 | 4 K_2SO_4 | 5 | 5 S | 2 | 2 MnO_2 | 4 | 4 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 4 | -4 | ([H2SO4])^(-4) KMnO_4 | 4 | -4 | ([KMnO4])^(-4) K2S | 3 | -3 | ([K2S])^(-3) H_2O | 4 | 4 | ([H2O])^4 K_2SO_4 | 5 | 5 | ([K2SO4])^5 S | 2 | 2 | ([S])^2 MnO_2 | 4 | 4 | ([MnO2])^4 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])^(-4) ([KMnO4])^(-4) ([K2S])^(-3) ([H2O])^4 ([K2SO4])^5 ([S])^2 ([MnO2])^4 = (([H2O])^4 ([K2SO4])^5 ([S])^2 ([MnO2])^4)/(([H2SO4])^4 ([KMnO4])^4 ([K2S])^3)

Rate of reaction

Construct the rate of reaction expression for: H_2SO_4 + KMnO_4 + K2S ⟶ H_2O + K_2SO_4 + S + MnO_2 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: 4 H_2SO_4 + 4 KMnO_4 + 3 K2S ⟶ 4 H_2O + 5 K_2SO_4 + 2 S + 4 MnO_2 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 | 4 | -4 KMnO_4 | 4 | -4 K2S | 3 | -3 H_2O | 4 | 4 K_2SO_4 | 5 | 5 S | 2 | 2 MnO_2 | 4 | 4 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 | 4 | -4 | -1/4 (Δ[H2SO4])/(Δt) KMnO_4 | 4 | -4 | -1/4 (Δ[KMnO4])/(Δt) K2S | 3 | -3 | -1/3 (Δ[K2S])/(Δt) H_2O | 4 | 4 | 1/4 (Δ[H2O])/(Δt) K_2SO_4 | 5 | 5 | 1/5 (Δ[K2SO4])/(Δt) S | 2 | 2 | 1/2 (Δ[S])/(Δt) MnO_2 | 4 | 4 | 1/4 (Δ[MnO2])/(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 = -1/4 (Δ[H2SO4])/(Δt) = -1/4 (Δ[KMnO4])/(Δt) = -1/3 (Δ[K2S])/(Δt) = 1/4 (Δ[H2O])/(Δt) = 1/5 (Δ[K2SO4])/(Δt) = 1/2 (Δ[S])/(Δt) = 1/4 (Δ[MnO2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: H_2SO_4 + KMnO_4 + K2S ⟶ H_2O + K_2SO_4 + S + MnO_2 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: 4 H_2SO_4 + 4 KMnO_4 + 3 K2S ⟶ 4 H_2O + 5 K_2SO_4 + 2 S + 4 MnO_2 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 | 4 | -4 KMnO_4 | 4 | -4 K2S | 3 | -3 H_2O | 4 | 4 K_2SO_4 | 5 | 5 S | 2 | 2 MnO_2 | 4 | 4 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 | 4 | -4 | -1/4 (Δ[H2SO4])/(Δt) KMnO_4 | 4 | -4 | -1/4 (Δ[KMnO4])/(Δt) K2S | 3 | -3 | -1/3 (Δ[K2S])/(Δt) H_2O | 4 | 4 | 1/4 (Δ[H2O])/(Δt) K_2SO_4 | 5 | 5 | 1/5 (Δ[K2SO4])/(Δt) S | 2 | 2 | 1/2 (Δ[S])/(Δt) MnO_2 | 4 | 4 | 1/4 (Δ[MnO2])/(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 = -1/4 (Δ[H2SO4])/(Δt) = -1/4 (Δ[KMnO4])/(Δt) = -1/3 (Δ[K2S])/(Δt) = 1/4 (Δ[H2O])/(Δt) = 1/5 (Δ[K2SO4])/(Δt) = 1/2 (Δ[S])/(Δt) = 1/4 (Δ[MnO2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

 | sulfuric acid | potassium permanganate | K2S | water | potassium sulfate | mixed sulfur | manganese dioxide formula | H_2SO_4 | KMnO_4 | K2S | H_2O | K_2SO_4 | S | MnO_2 Hill formula | H_2O_4S | KMnO_4 | K2S | H_2O | K_2O_4S | S | MnO_2 name | sulfuric acid | potassium permanganate | | water | potassium sulfate | mixed sulfur | manganese dioxide IUPAC name | sulfuric acid | potassium permanganate | | water | dipotassium sulfate | sulfur | dioxomanganese
| sulfuric acid | potassium permanganate | K2S | water | potassium sulfate | mixed sulfur | manganese dioxide formula | H_2SO_4 | KMnO_4 | K2S | H_2O | K_2SO_4 | S | MnO_2 Hill formula | H_2O_4S | KMnO_4 | K2S | H_2O | K_2O_4S | S | MnO_2 name | sulfuric acid | potassium permanganate | | water | potassium sulfate | mixed sulfur | manganese dioxide IUPAC name | sulfuric acid | potassium permanganate | | water | dipotassium sulfate | sulfur | dioxomanganese

Substance properties

 | sulfuric acid | potassium permanganate | K2S | water | potassium sulfate | mixed sulfur | manganese dioxide molar mass | 98.07 g/mol | 158.03 g/mol | 110.26 g/mol | 18.015 g/mol | 174.25 g/mol | 32.06 g/mol | 86.936 g/mol phase | liquid (at STP) | solid (at STP) | | liquid (at STP) | | solid (at STP) | solid (at STP) melting point | 10.371 °C | 240 °C | | 0 °C | | 112.8 °C | 535 °C boiling point | 279.6 °C | | | 99.9839 °C | | 444.7 °C |  density | 1.8305 g/cm^3 | 1 g/cm^3 | | 1 g/cm^3 | | 2.07 g/cm^3 | 5.03 g/cm^3 solubility in water | very soluble | | | | soluble | | insoluble 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 | K2S | water | potassium sulfate | mixed sulfur | manganese dioxide molar mass | 98.07 g/mol | 158.03 g/mol | 110.26 g/mol | 18.015 g/mol | 174.25 g/mol | 32.06 g/mol | 86.936 g/mol phase | liquid (at STP) | solid (at STP) | | liquid (at STP) | | solid (at STP) | solid (at STP) melting point | 10.371 °C | 240 °C | | 0 °C | | 112.8 °C | 535 °C boiling point | 279.6 °C | | | 99.9839 °C | | 444.7 °C | density | 1.8305 g/cm^3 | 1 g/cm^3 | | 1 g/cm^3 | | 2.07 g/cm^3 | 5.03 g/cm^3 solubility in water | very soluble | | | | soluble | | insoluble 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