Input interpretation
![H_2SO_4 sulfuric acid + H_2S hydrogen sulfide + K2Cr2O3 ⟶ H_2O water + K_2SO_4 potassium sulfate + S mixed sulfur + Cr_2(SO_4)_3 chromium sulfate](../image_source/c256d851e94c911cba039fc40b93b8e4.png)
H_2SO_4 sulfuric acid + H_2S hydrogen sulfide + K2Cr2O3 ⟶ 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 + K2Cr2O3 ⟶ 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 K2Cr2O3 ⟶ 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 + 3 c_3 = 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: | 2 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)/13 - 1/13 c_4 = c_1 + 1 c_5 = (3 c_1)/13 - 1/13 c_6 = c_1/13 + 17/13 c_7 = (3 c_1)/13 - 1/13 The resulting system of equations is still underdetermined, so an additional coefficient must be set arbitrarily. Set c_1 = 9 and solve for the remaining coefficients: c_1 = 9 c_2 = 1 c_3 = 2 c_4 = 10 c_5 = 2 c_6 = 2 c_7 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 9 H_2SO_4 + H_2S + 2 K2Cr2O3 ⟶ 10 H_2O + 2 K_2SO_4 + 2 S + 2 Cr_2(SO_4)_3](../image_source/b5013e45aa57472a7995042527148125.png)
Balance the chemical equation algebraically: H_2SO_4 + H_2S + K2Cr2O3 ⟶ 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 K2Cr2O3 ⟶ 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 + 3 c_3 = 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: | 2 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)/13 - 1/13 c_4 = c_1 + 1 c_5 = (3 c_1)/13 - 1/13 c_6 = c_1/13 + 17/13 c_7 = (3 c_1)/13 - 1/13 The resulting system of equations is still underdetermined, so an additional coefficient must be set arbitrarily. Set c_1 = 9 and solve for the remaining coefficients: c_1 = 9 c_2 = 1 c_3 = 2 c_4 = 10 c_5 = 2 c_6 = 2 c_7 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 9 H_2SO_4 + H_2S + 2 K2Cr2O3 ⟶ 10 H_2O + 2 K_2SO_4 + 2 S + 2 Cr_2(SO_4)_3
Structures
![+ + K2Cr2O3 ⟶ + + +](../image_source/d8c3542c05446b045acdecc208768634.png)
+ + K2Cr2O3 ⟶ + + +
Names
![sulfuric acid + hydrogen sulfide + K2Cr2O3 ⟶ water + potassium sulfate + mixed sulfur + chromium sulfate](../image_source/74f883e646978d50d320097793820a10.png)
sulfuric acid + hydrogen sulfide + K2Cr2O3 ⟶ water + potassium sulfate + mixed sulfur + chromium sulfate
Equilibrium constant
![Construct the equilibrium constant, K, expression for: H_2SO_4 + H_2S + K2Cr2O3 ⟶ 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: 9 H_2SO_4 + H_2S + 2 K2Cr2O3 ⟶ 10 H_2O + 2 K_2SO_4 + 2 S + 2 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 | 9 | -9 H_2S | 1 | -1 K2Cr2O3 | 2 | -2 H_2O | 10 | 10 K_2SO_4 | 2 | 2 S | 2 | 2 Cr_2(SO_4)_3 | 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 | 9 | -9 | ([H2SO4])^(-9) H_2S | 1 | -1 | ([H2S])^(-1) K2Cr2O3 | 2 | -2 | ([K2Cr2O3])^(-2) H_2O | 10 | 10 | ([H2O])^10 K_2SO_4 | 2 | 2 | ([K2SO4])^2 S | 2 | 2 | ([S])^2 Cr_2(SO_4)_3 | 2 | 2 | ([Cr2(SO4)3])^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])^(-9) ([H2S])^(-1) ([K2Cr2O3])^(-2) ([H2O])^10 ([K2SO4])^2 ([S])^2 ([Cr2(SO4)3])^2 = (([H2O])^10 ([K2SO4])^2 ([S])^2 ([Cr2(SO4)3])^2)/(([H2SO4])^9 [H2S] ([K2Cr2O3])^2)](../image_source/0f85f0200d25a4d11b0548fb7afd7528.png)
Construct the equilibrium constant, K, expression for: H_2SO_4 + H_2S + K2Cr2O3 ⟶ 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: 9 H_2SO_4 + H_2S + 2 K2Cr2O3 ⟶ 10 H_2O + 2 K_2SO_4 + 2 S + 2 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 | 9 | -9 H_2S | 1 | -1 K2Cr2O3 | 2 | -2 H_2O | 10 | 10 K_2SO_4 | 2 | 2 S | 2 | 2 Cr_2(SO_4)_3 | 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 | 9 | -9 | ([H2SO4])^(-9) H_2S | 1 | -1 | ([H2S])^(-1) K2Cr2O3 | 2 | -2 | ([K2Cr2O3])^(-2) H_2O | 10 | 10 | ([H2O])^10 K_2SO_4 | 2 | 2 | ([K2SO4])^2 S | 2 | 2 | ([S])^2 Cr_2(SO_4)_3 | 2 | 2 | ([Cr2(SO4)3])^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])^(-9) ([H2S])^(-1) ([K2Cr2O3])^(-2) ([H2O])^10 ([K2SO4])^2 ([S])^2 ([Cr2(SO4)3])^2 = (([H2O])^10 ([K2SO4])^2 ([S])^2 ([Cr2(SO4)3])^2)/(([H2SO4])^9 [H2S] ([K2Cr2O3])^2)
Rate of reaction
![Construct the rate of reaction expression for: H_2SO_4 + H_2S + K2Cr2O3 ⟶ 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: 9 H_2SO_4 + H_2S + 2 K2Cr2O3 ⟶ 10 H_2O + 2 K_2SO_4 + 2 S + 2 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 | 9 | -9 H_2S | 1 | -1 K2Cr2O3 | 2 | -2 H_2O | 10 | 10 K_2SO_4 | 2 | 2 S | 2 | 2 Cr_2(SO_4)_3 | 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 | 9 | -9 | -1/9 (Δ[H2SO4])/(Δt) H_2S | 1 | -1 | -(Δ[H2S])/(Δt) K2Cr2O3 | 2 | -2 | -1/2 (Δ[K2Cr2O3])/(Δt) H_2O | 10 | 10 | 1/10 (Δ[H2O])/(Δt) K_2SO_4 | 2 | 2 | 1/2 (Δ[K2SO4])/(Δt) S | 2 | 2 | 1/2 (Δ[S])/(Δt) Cr_2(SO_4)_3 | 2 | 2 | 1/2 (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 = -1/9 (Δ[H2SO4])/(Δt) = -(Δ[H2S])/(Δt) = -1/2 (Δ[K2Cr2O3])/(Δt) = 1/10 (Δ[H2O])/(Δt) = 1/2 (Δ[K2SO4])/(Δt) = 1/2 (Δ[S])/(Δt) = 1/2 (Δ[Cr2(SO4)3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)](../image_source/7a2d5b012e74ad89047facb6d400b74a.png)
Construct the rate of reaction expression for: H_2SO_4 + H_2S + K2Cr2O3 ⟶ 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: 9 H_2SO_4 + H_2S + 2 K2Cr2O3 ⟶ 10 H_2O + 2 K_2SO_4 + 2 S + 2 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 | 9 | -9 H_2S | 1 | -1 K2Cr2O3 | 2 | -2 H_2O | 10 | 10 K_2SO_4 | 2 | 2 S | 2 | 2 Cr_2(SO_4)_3 | 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 | 9 | -9 | -1/9 (Δ[H2SO4])/(Δt) H_2S | 1 | -1 | -(Δ[H2S])/(Δt) K2Cr2O3 | 2 | -2 | -1/2 (Δ[K2Cr2O3])/(Δt) H_2O | 10 | 10 | 1/10 (Δ[H2O])/(Δt) K_2SO_4 | 2 | 2 | 1/2 (Δ[K2SO4])/(Δt) S | 2 | 2 | 1/2 (Δ[S])/(Δt) Cr_2(SO_4)_3 | 2 | 2 | 1/2 (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 = -1/9 (Δ[H2SO4])/(Δt) = -(Δ[H2S])/(Δt) = -1/2 (Δ[K2Cr2O3])/(Δt) = 1/10 (Δ[H2O])/(Δt) = 1/2 (Δ[K2SO4])/(Δt) = 1/2 (Δ[S])/(Δt) = 1/2 (Δ[Cr2(SO4)3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Chemical names and formulas
![| sulfuric acid | hydrogen sulfide | K2Cr2O3 | water | potassium sulfate | mixed sulfur | chromium sulfate formula | H_2SO_4 | H_2S | K2Cr2O3 | H_2O | K_2SO_4 | S | Cr_2(SO_4)_3 Hill formula | H_2O_4S | H_2S | Cr2K2O3 | 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](../image_source/654d7ee840bbae732856d36c0e158d12.png)
| sulfuric acid | hydrogen sulfide | K2Cr2O3 | water | potassium sulfate | mixed sulfur | chromium sulfate formula | H_2SO_4 | H_2S | K2Cr2O3 | H_2O | K_2SO_4 | S | Cr_2(SO_4)_3 Hill formula | H_2O_4S | H_2S | Cr2K2O3 | 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
Substance properties
![| sulfuric acid | hydrogen sulfide | K2Cr2O3 | water | potassium sulfate | mixed sulfur | chromium sulfate molar mass | 98.07 g/mol | 34.08 g/mol | 230.186 g/mol | 18.015 g/mol | 174.25 g/mol | 32.06 g/mol | 392.2 g/mol phase | liquid (at STP) | gas (at STP) | | liquid (at STP) | | solid (at STP) | liquid (at STP) melting point | 10.371 °C | -85 °C | | 0 °C | | 112.8 °C | boiling point | 279.6 °C | -60 °C | | 99.9839 °C | | 444.7 °C | 330 °C density | 1.8305 g/cm^3 | 0.001393 g/cm^3 (at 25 °C) | | 1 g/cm^3 | | 2.07 g/cm^3 | 1.84 g/cm^3 solubility in water | very soluble | | | | soluble | | surface tension | 0.0735 N/m | | | 0.0728 N/m | | | dynamic viscosity | 0.021 Pa s (at 25 °C) | 1.239×10^-5 Pa s (at 25 °C) | | 8.9×10^-4 Pa s (at 25 °C) | | | odor | odorless | | | odorless | | | odorless](../image_source/9616f846fbdd26517ffd4e6be93d31bd.png)
| sulfuric acid | hydrogen sulfide | K2Cr2O3 | water | potassium sulfate | mixed sulfur | chromium sulfate molar mass | 98.07 g/mol | 34.08 g/mol | 230.186 g/mol | 18.015 g/mol | 174.25 g/mol | 32.06 g/mol | 392.2 g/mol phase | liquid (at STP) | gas (at STP) | | liquid (at STP) | | solid (at STP) | liquid (at STP) melting point | 10.371 °C | -85 °C | | 0 °C | | 112.8 °C | boiling point | 279.6 °C | -60 °C | | 99.9839 °C | | 444.7 °C | 330 °C density | 1.8305 g/cm^3 | 0.001393 g/cm^3 (at 25 °C) | | 1 g/cm^3 | | 2.07 g/cm^3 | 1.84 g/cm^3 solubility in water | very soluble | | | | soluble | | surface tension | 0.0735 N/m | | | 0.0728 N/m | | | dynamic viscosity | 0.021 Pa s (at 25 °C) | 1.239×10^-5 Pa s (at 25 °C) | | 8.9×10^-4 Pa s (at 25 °C) | | | odor | odorless | | | odorless | | | odorless
Units