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H2SO4 + KMnO4 + KBr = H2O + K2SO4 + Br2 + MnS4

Input interpretation

H_2SO_4 sulfuric acid + KMnO_4 potassium permanganate + KBr potassium bromide ⟶ H_2O water + K_2SO_4 potassium sulfate + Br_2 bromine + MnS4
H_2SO_4 sulfuric acid + KMnO_4 potassium permanganate + KBr potassium bromide ⟶ H_2O water + K_2SO_4 potassium sulfate + Br_2 bromine + MnS4

Balanced equation

Balance the chemical equation algebraically: H_2SO_4 + KMnO_4 + KBr ⟶ H_2O + K_2SO_4 + Br_2 + MnS4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 KMnO_4 + c_3 KBr ⟶ c_4 H_2O + c_5 K_2SO_4 + c_6 Br_2 + c_7 MnS4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, K, Mn and Br: H: | 2 c_1 = 2 c_4 O: | 4 c_1 + 4 c_2 = c_4 + 4 c_5 S: | c_1 = c_5 + 4 c_7 K: | c_2 + c_3 = 2 c_5 Mn: | c_2 = c_7 Br: | c_3 = 2 c_6 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 = 20 c_2 = 1 c_3 = 31 c_4 = 20 c_5 = 16 c_6 = 31/2 c_7 = 1 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 40 c_2 = 2 c_3 = 62 c_4 = 40 c_5 = 32 c_6 = 31 c_7 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 40 H_2SO_4 + 2 KMnO_4 + 62 KBr ⟶ 40 H_2O + 32 K_2SO_4 + 31 Br_2 + 2 MnS4
Balance the chemical equation algebraically: H_2SO_4 + KMnO_4 + KBr ⟶ H_2O + K_2SO_4 + Br_2 + MnS4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 KMnO_4 + c_3 KBr ⟶ c_4 H_2O + c_5 K_2SO_4 + c_6 Br_2 + c_7 MnS4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, K, Mn and Br: H: | 2 c_1 = 2 c_4 O: | 4 c_1 + 4 c_2 = c_4 + 4 c_5 S: | c_1 = c_5 + 4 c_7 K: | c_2 + c_3 = 2 c_5 Mn: | c_2 = c_7 Br: | c_3 = 2 c_6 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 = 20 c_2 = 1 c_3 = 31 c_4 = 20 c_5 = 16 c_6 = 31/2 c_7 = 1 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 40 c_2 = 2 c_3 = 62 c_4 = 40 c_5 = 32 c_6 = 31 c_7 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 40 H_2SO_4 + 2 KMnO_4 + 62 KBr ⟶ 40 H_2O + 32 K_2SO_4 + 31 Br_2 + 2 MnS4

Structures

+ + ⟶ + + + MnS4
+ + ⟶ + + + MnS4

Names

sulfuric acid + potassium permanganate + potassium bromide ⟶ water + potassium sulfate + bromine + MnS4
sulfuric acid + potassium permanganate + potassium bromide ⟶ water + potassium sulfate + bromine + MnS4

Equilibrium constant

Construct the equilibrium constant, K, expression for: H_2SO_4 + KMnO_4 + KBr ⟶ H_2O + K_2SO_4 + Br_2 + MnS4 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: 40 H_2SO_4 + 2 KMnO_4 + 62 KBr ⟶ 40 H_2O + 32 K_2SO_4 + 31 Br_2 + 2 MnS4 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 | 40 | -40 KMnO_4 | 2 | -2 KBr | 62 | -62 H_2O | 40 | 40 K_2SO_4 | 32 | 32 Br_2 | 31 | 31 MnS4 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 40 | -40 | ([H2SO4])^(-40) KMnO_4 | 2 | -2 | ([KMnO4])^(-2) KBr | 62 | -62 | ([KBr])^(-62) H_2O | 40 | 40 | ([H2O])^40 K_2SO_4 | 32 | 32 | ([K2SO4])^32 Br_2 | 31 | 31 | ([Br2])^31 MnS4 | 2 | 2 | ([MnS4])^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 = ([H2SO4])^(-40) ([KMnO4])^(-2) ([KBr])^(-62) ([H2O])^40 ([K2SO4])^32 ([Br2])^31 ([MnS4])^2 = (([H2O])^40 ([K2SO4])^32 ([Br2])^31 ([MnS4])^2)/(([H2SO4])^40 ([KMnO4])^2 ([KBr])^62)
Construct the equilibrium constant, K, expression for: H_2SO_4 + KMnO_4 + KBr ⟶ H_2O + K_2SO_4 + Br_2 + MnS4 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: 40 H_2SO_4 + 2 KMnO_4 + 62 KBr ⟶ 40 H_2O + 32 K_2SO_4 + 31 Br_2 + 2 MnS4 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 | 40 | -40 KMnO_4 | 2 | -2 KBr | 62 | -62 H_2O | 40 | 40 K_2SO_4 | 32 | 32 Br_2 | 31 | 31 MnS4 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 40 | -40 | ([H2SO4])^(-40) KMnO_4 | 2 | -2 | ([KMnO4])^(-2) KBr | 62 | -62 | ([KBr])^(-62) H_2O | 40 | 40 | ([H2O])^40 K_2SO_4 | 32 | 32 | ([K2SO4])^32 Br_2 | 31 | 31 | ([Br2])^31 MnS4 | 2 | 2 | ([MnS4])^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 = ([H2SO4])^(-40) ([KMnO4])^(-2) ([KBr])^(-62) ([H2O])^40 ([K2SO4])^32 ([Br2])^31 ([MnS4])^2 = (([H2O])^40 ([K2SO4])^32 ([Br2])^31 ([MnS4])^2)/(([H2SO4])^40 ([KMnO4])^2 ([KBr])^62)

Rate of reaction

Construct the rate of reaction expression for: H_2SO_4 + KMnO_4 + KBr ⟶ H_2O + K_2SO_4 + Br_2 + MnS4 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: 40 H_2SO_4 + 2 KMnO_4 + 62 KBr ⟶ 40 H_2O + 32 K_2SO_4 + 31 Br_2 + 2 MnS4 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 | 40 | -40 KMnO_4 | 2 | -2 KBr | 62 | -62 H_2O | 40 | 40 K_2SO_4 | 32 | 32 Br_2 | 31 | 31 MnS4 | 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 H_2SO_4 | 40 | -40 | -1/40 (Δ[H2SO4])/(Δt) KMnO_4 | 2 | -2 | -1/2 (Δ[KMnO4])/(Δt) KBr | 62 | -62 | -1/62 (Δ[KBr])/(Δt) H_2O | 40 | 40 | 1/40 (Δ[H2O])/(Δt) K_2SO_4 | 32 | 32 | 1/32 (Δ[K2SO4])/(Δt) Br_2 | 31 | 31 | 1/31 (Δ[Br2])/(Δt) MnS4 | 2 | 2 | 1/2 (Δ[MnS4])/(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 = -1/40 (Δ[H2SO4])/(Δt) = -1/2 (Δ[KMnO4])/(Δt) = -1/62 (Δ[KBr])/(Δt) = 1/40 (Δ[H2O])/(Δt) = 1/32 (Δ[K2SO4])/(Δt) = 1/31 (Δ[Br2])/(Δt) = 1/2 (Δ[MnS4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: H_2SO_4 + KMnO_4 + KBr ⟶ H_2O + K_2SO_4 + Br_2 + MnS4 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: 40 H_2SO_4 + 2 KMnO_4 + 62 KBr ⟶ 40 H_2O + 32 K_2SO_4 + 31 Br_2 + 2 MnS4 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 | 40 | -40 KMnO_4 | 2 | -2 KBr | 62 | -62 H_2O | 40 | 40 K_2SO_4 | 32 | 32 Br_2 | 31 | 31 MnS4 | 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 H_2SO_4 | 40 | -40 | -1/40 (Δ[H2SO4])/(Δt) KMnO_4 | 2 | -2 | -1/2 (Δ[KMnO4])/(Δt) KBr | 62 | -62 | -1/62 (Δ[KBr])/(Δt) H_2O | 40 | 40 | 1/40 (Δ[H2O])/(Δt) K_2SO_4 | 32 | 32 | 1/32 (Δ[K2SO4])/(Δt) Br_2 | 31 | 31 | 1/31 (Δ[Br2])/(Δt) MnS4 | 2 | 2 | 1/2 (Δ[MnS4])/(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 = -1/40 (Δ[H2SO4])/(Δt) = -1/2 (Δ[KMnO4])/(Δt) = -1/62 (Δ[KBr])/(Δt) = 1/40 (Δ[H2O])/(Δt) = 1/32 (Δ[K2SO4])/(Δt) = 1/31 (Δ[Br2])/(Δt) = 1/2 (Δ[MnS4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| sulfuric acid | potassium permanganate | potassium bromide | water | potassium sulfate | bromine | MnS4 formula | H_2SO_4 | KMnO_4 | KBr | H_2O | K_2SO_4 | Br_2 | MnS4 Hill formula | H_2O_4S | KMnO_4 | BrK | H_2O | K_2O_4S | Br_2 | MnS4 name | sulfuric acid | potassium permanganate | potassium bromide | water | potassium sulfate | bromine | IUPAC name | sulfuric acid | potassium permanganate | potassium bromide | water | dipotassium sulfate | molecular bromine |
| sulfuric acid | potassium permanganate | potassium bromide | water | potassium sulfate | bromine | MnS4 formula | H_2SO_4 | KMnO_4 | KBr | H_2O | K_2SO_4 | Br_2 | MnS4 Hill formula | H_2O_4S | KMnO_4 | BrK | H_2O | K_2O_4S | Br_2 | MnS4 name | sulfuric acid | potassium permanganate | potassium bromide | water | potassium sulfate | bromine | IUPAC name | sulfuric acid | potassium permanganate | potassium bromide | water | dipotassium sulfate | molecular bromine |

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