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H2SO4 + H2S + K2Cr7 = H2O + K2SO4 + S + Cr2(SO4)3

Input interpretation

H_2SO_4 sulfuric acid + H_2S hydrogen sulfide + K2Cr7 ⟶ H_2O water + K_2SO_4 potassium sulfate + S mixed sulfur + Cr_2(SO_4)_3 chromium sulfate
H_2SO_4 sulfuric acid + H_2S hydrogen sulfide + K2Cr7 ⟶ H_2O water + K_2SO_4 potassium sulfate + S mixed sulfur + Cr_2(SO_4)_3 chromium sulfate

Balanced equation

Balance the chemical equation algebraically: H_2SO_4 + H_2S + K2Cr7 ⟶ H_2O + K_2SO_4 + S + Cr_2(SO_4)_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 H_2S + c_3 K2Cr7 ⟶ c_4 H_2O + c_5 K_2SO_4 + c_6 S + c_7 Cr_2(SO_4)_3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, K and Cr: H: | 2 c_1 + 2 c_2 = 2 c_4 O: | 4 c_1 = c_4 + 4 c_5 + 12 c_7 S: | c_1 + c_2 = c_5 + c_6 + 3 c_7 K: | 2 c_3 = 2 c_5 Cr: | 7 c_3 = 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_2 = 1 and solve the system of equations for the remaining coefficients: c_2 = 1 c_3 = (3 c_1)/46 - 1/46 c_4 = c_1 + 1 c_5 = (3 c_1)/46 - 1/46 c_6 = c_1/4 + 5/4 c_7 = (21 c_1)/92 - 7/92 The resulting system of equations is still underdetermined, so an additional coefficient must be set arbitrarily. Set c_1 = 123 and solve for the remaining coefficients: c_1 = 123 c_2 = 1 c_3 = 8 c_4 = 124 c_5 = 8 c_6 = 32 c_7 = 28 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 123 H_2SO_4 + H_2S + 8 K2Cr7 ⟶ 124 H_2O + 8 K_2SO_4 + 32 S + 28 Cr_2(SO_4)_3
Balance the chemical equation algebraically: H_2SO_4 + H_2S + K2Cr7 ⟶ H_2O + K_2SO_4 + S + Cr_2(SO_4)_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 H_2S + c_3 K2Cr7 ⟶ c_4 H_2O + c_5 K_2SO_4 + c_6 S + c_7 Cr_2(SO_4)_3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, K and Cr: H: | 2 c_1 + 2 c_2 = 2 c_4 O: | 4 c_1 = c_4 + 4 c_5 + 12 c_7 S: | c_1 + c_2 = c_5 + c_6 + 3 c_7 K: | 2 c_3 = 2 c_5 Cr: | 7 c_3 = 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_2 = 1 and solve the system of equations for the remaining coefficients: c_2 = 1 c_3 = (3 c_1)/46 - 1/46 c_4 = c_1 + 1 c_5 = (3 c_1)/46 - 1/46 c_6 = c_1/4 + 5/4 c_7 = (21 c_1)/92 - 7/92 The resulting system of equations is still underdetermined, so an additional coefficient must be set arbitrarily. Set c_1 = 123 and solve for the remaining coefficients: c_1 = 123 c_2 = 1 c_3 = 8 c_4 = 124 c_5 = 8 c_6 = 32 c_7 = 28 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 123 H_2SO_4 + H_2S + 8 K2Cr7 ⟶ 124 H_2O + 8 K_2SO_4 + 32 S + 28 Cr_2(SO_4)_3

Structures

+ + K2Cr7 ⟶ + + +
+ + K2Cr7 ⟶ + + +

Names

sulfuric acid + hydrogen sulfide + K2Cr7 ⟶ water + potassium sulfate + mixed sulfur + chromium sulfate
sulfuric acid + hydrogen sulfide + K2Cr7 ⟶ water + potassium sulfate + mixed sulfur + chromium sulfate

Equilibrium constant

Construct the equilibrium constant, K, expression for: H_2SO_4 + H_2S + K2Cr7 ⟶ H_2O + K_2SO_4 + S + Cr_2(SO_4)_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: 123 H_2SO_4 + H_2S + 8 K2Cr7 ⟶ 124 H_2O + 8 K_2SO_4 + 32 S + 28 Cr_2(SO_4)_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 | 123 | -123 H_2S | 1 | -1 K2Cr7 | 8 | -8 H_2O | 124 | 124 K_2SO_4 | 8 | 8 S | 32 | 32 Cr_2(SO_4)_3 | 28 | 28 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 123 | -123 | ([H2SO4])^(-123) H_2S | 1 | -1 | ([H2S])^(-1) K2Cr7 | 8 | -8 | ([K2Cr7])^(-8) H_2O | 124 | 124 | ([H2O])^124 K_2SO_4 | 8 | 8 | ([K2SO4])^8 S | 32 | 32 | ([S])^32 Cr_2(SO_4)_3 | 28 | 28 | ([Cr2(SO4)3])^28 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])^(-123) ([H2S])^(-1) ([K2Cr7])^(-8) ([H2O])^124 ([K2SO4])^8 ([S])^32 ([Cr2(SO4)3])^28 = (([H2O])^124 ([K2SO4])^8 ([S])^32 ([Cr2(SO4)3])^28)/(([H2SO4])^123 [H2S] ([K2Cr7])^8)
Construct the equilibrium constant, K, expression for: H_2SO_4 + H_2S + K2Cr7 ⟶ H_2O + K_2SO_4 + S + Cr_2(SO_4)_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: 123 H_2SO_4 + H_2S + 8 K2Cr7 ⟶ 124 H_2O + 8 K_2SO_4 + 32 S + 28 Cr_2(SO_4)_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 | 123 | -123 H_2S | 1 | -1 K2Cr7 | 8 | -8 H_2O | 124 | 124 K_2SO_4 | 8 | 8 S | 32 | 32 Cr_2(SO_4)_3 | 28 | 28 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 123 | -123 | ([H2SO4])^(-123) H_2S | 1 | -1 | ([H2S])^(-1) K2Cr7 | 8 | -8 | ([K2Cr7])^(-8) H_2O | 124 | 124 | ([H2O])^124 K_2SO_4 | 8 | 8 | ([K2SO4])^8 S | 32 | 32 | ([S])^32 Cr_2(SO_4)_3 | 28 | 28 | ([Cr2(SO4)3])^28 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])^(-123) ([H2S])^(-1) ([K2Cr7])^(-8) ([H2O])^124 ([K2SO4])^8 ([S])^32 ([Cr2(SO4)3])^28 = (([H2O])^124 ([K2SO4])^8 ([S])^32 ([Cr2(SO4)3])^28)/(([H2SO4])^123 [H2S] ([K2Cr7])^8)

Rate of reaction

Construct the rate of reaction expression for: H_2SO_4 + H_2S + K2Cr7 ⟶ H_2O + K_2SO_4 + S + Cr_2(SO_4)_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: 123 H_2SO_4 + H_2S + 8 K2Cr7 ⟶ 124 H_2O + 8 K_2SO_4 + 32 S + 28 Cr_2(SO_4)_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 | 123 | -123 H_2S | 1 | -1 K2Cr7 | 8 | -8 H_2O | 124 | 124 K_2SO_4 | 8 | 8 S | 32 | 32 Cr_2(SO_4)_3 | 28 | 28 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 | 123 | -123 | -1/123 (Δ[H2SO4])/(Δt) H_2S | 1 | -1 | -(Δ[H2S])/(Δt) K2Cr7 | 8 | -8 | -1/8 (Δ[K2Cr7])/(Δt) H_2O | 124 | 124 | 1/124 (Δ[H2O])/(Δt) K_2SO_4 | 8 | 8 | 1/8 (Δ[K2SO4])/(Δt) S | 32 | 32 | 1/32 (Δ[S])/(Δt) Cr_2(SO_4)_3 | 28 | 28 | 1/28 (Δ[Cr2(SO4)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 = -1/123 (Δ[H2SO4])/(Δt) = -(Δ[H2S])/(Δt) = -1/8 (Δ[K2Cr7])/(Δt) = 1/124 (Δ[H2O])/(Δt) = 1/8 (Δ[K2SO4])/(Δt) = 1/32 (Δ[S])/(Δt) = 1/28 (Δ[Cr2(SO4)3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: H_2SO_4 + H_2S + K2Cr7 ⟶ H_2O + K_2SO_4 + S + Cr_2(SO_4)_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: 123 H_2SO_4 + H_2S + 8 K2Cr7 ⟶ 124 H_2O + 8 K_2SO_4 + 32 S + 28 Cr_2(SO_4)_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 | 123 | -123 H_2S | 1 | -1 K2Cr7 | 8 | -8 H_2O | 124 | 124 K_2SO_4 | 8 | 8 S | 32 | 32 Cr_2(SO_4)_3 | 28 | 28 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 | 123 | -123 | -1/123 (Δ[H2SO4])/(Δt) H_2S | 1 | -1 | -(Δ[H2S])/(Δt) K2Cr7 | 8 | -8 | -1/8 (Δ[K2Cr7])/(Δt) H_2O | 124 | 124 | 1/124 (Δ[H2O])/(Δt) K_2SO_4 | 8 | 8 | 1/8 (Δ[K2SO4])/(Δt) S | 32 | 32 | 1/32 (Δ[S])/(Δt) Cr_2(SO_4)_3 | 28 | 28 | 1/28 (Δ[Cr2(SO4)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 = -1/123 (Δ[H2SO4])/(Δt) = -(Δ[H2S])/(Δt) = -1/8 (Δ[K2Cr7])/(Δt) = 1/124 (Δ[H2O])/(Δt) = 1/8 (Δ[K2SO4])/(Δt) = 1/32 (Δ[S])/(Δt) = 1/28 (Δ[Cr2(SO4)3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| sulfuric acid | hydrogen sulfide | K2Cr7 | water | potassium sulfate | mixed sulfur | chromium sulfate formula | H_2SO_4 | H_2S | K2Cr7 | H_2O | K_2SO_4 | S | Cr_2(SO_4)_3 Hill formula | H_2O_4S | H_2S | Cr7K2 | H_2O | K_2O_4S | S | Cr_2O_12S_3 name | sulfuric acid | hydrogen sulfide | | water | potassium sulfate | mixed sulfur | chromium sulfate IUPAC name | sulfuric acid | hydrogen sulfide | | water | dipotassium sulfate | sulfur | chromium(+3) cation trisulfate
| sulfuric acid | hydrogen sulfide | K2Cr7 | water | potassium sulfate | mixed sulfur | chromium sulfate formula | H_2SO_4 | H_2S | K2Cr7 | H_2O | K_2SO_4 | S | Cr_2(SO_4)_3 Hill formula | H_2O_4S | H_2S | Cr7K2 | H_2O | K_2O_4S | S | Cr_2O_12S_3 name | sulfuric acid | hydrogen sulfide | | water | potassium sulfate | mixed sulfur | chromium sulfate IUPAC name | sulfuric acid | hydrogen sulfide | | water | dipotassium sulfate | sulfur | chromium(+3) cation trisulfate

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