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H2O + Cr2(SO4)3 = H2SO4 + O2 + H2 + Cr

Input interpretation

H_2O water + Cr_2(SO_4)_3 chromium sulfate ⟶ H_2SO_4 sulfuric acid + O_2 oxygen + H_2 hydrogen + Cr chromium
H_2O water + Cr_2(SO_4)_3 chromium sulfate ⟶ H_2SO_4 sulfuric acid + O_2 oxygen + H_2 hydrogen + Cr chromium

Balanced equation

Balance the chemical equation algebraically: H_2O + Cr_2(SO_4)_3 ⟶ H_2SO_4 + O_2 + H_2 + Cr Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 Cr_2(SO_4)_3 ⟶ c_3 H_2SO_4 + c_4 O_2 + c_5 H_2 + c_6 Cr Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, Cr and S: H: | 2 c_1 = 2 c_3 + 2 c_5 O: | c_1 + 12 c_2 = 4 c_3 + 2 c_4 Cr: | 2 c_2 = c_6 S: | 3 c_2 = c_3 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_4 = c_1/2 c_5 = c_1 - 3 c_6 = 2 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 = 1 c_3 = 3 c_4 = 2 c_5 = 1 c_6 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 H_2O + Cr_2(SO_4)_3 ⟶ 3 H_2SO_4 + 2 O_2 + H_2 + 2 Cr
Balance the chemical equation algebraically: H_2O + Cr_2(SO_4)_3 ⟶ H_2SO_4 + O_2 + H_2 + Cr Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 Cr_2(SO_4)_3 ⟶ c_3 H_2SO_4 + c_4 O_2 + c_5 H_2 + c_6 Cr Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, Cr and S: H: | 2 c_1 = 2 c_3 + 2 c_5 O: | c_1 + 12 c_2 = 4 c_3 + 2 c_4 Cr: | 2 c_2 = c_6 S: | 3 c_2 = c_3 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_4 = c_1/2 c_5 = c_1 - 3 c_6 = 2 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 = 1 c_3 = 3 c_4 = 2 c_5 = 1 c_6 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 H_2O + Cr_2(SO_4)_3 ⟶ 3 H_2SO_4 + 2 O_2 + H_2 + 2 Cr

Structures

+ ⟶ + + +
+ ⟶ + + +

Names

water + chromium sulfate ⟶ sulfuric acid + oxygen + hydrogen + chromium
water + chromium sulfate ⟶ sulfuric acid + oxygen + hydrogen + chromium

Equilibrium constant

Construct the equilibrium constant, K, expression for: H_2O + Cr_2(SO_4)_3 ⟶ H_2SO_4 + O_2 + H_2 + Cr 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_2O + Cr_2(SO_4)_3 ⟶ 3 H_2SO_4 + 2 O_2 + H_2 + 2 Cr 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_2O | 4 | -4 Cr_2(SO_4)_3 | 1 | -1 H_2SO_4 | 3 | 3 O_2 | 2 | 2 H_2 | 1 | 1 Cr | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 4 | -4 | ([H2O])^(-4) Cr_2(SO_4)_3 | 1 | -1 | ([Cr2(SO4)3])^(-1) H_2SO_4 | 3 | 3 | ([H2SO4])^3 O_2 | 2 | 2 | ([O2])^2 H_2 | 1 | 1 | [H2] Cr | 2 | 2 | ([Cr])^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 = ([H2O])^(-4) ([Cr2(SO4)3])^(-1) ([H2SO4])^3 ([O2])^2 [H2] ([Cr])^2 = (([H2SO4])^3 ([O2])^2 [H2] ([Cr])^2)/(([H2O])^4 [Cr2(SO4)3])
Construct the equilibrium constant, K, expression for: H_2O + Cr_2(SO_4)_3 ⟶ H_2SO_4 + O_2 + H_2 + Cr 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_2O + Cr_2(SO_4)_3 ⟶ 3 H_2SO_4 + 2 O_2 + H_2 + 2 Cr 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_2O | 4 | -4 Cr_2(SO_4)_3 | 1 | -1 H_2SO_4 | 3 | 3 O_2 | 2 | 2 H_2 | 1 | 1 Cr | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 4 | -4 | ([H2O])^(-4) Cr_2(SO_4)_3 | 1 | -1 | ([Cr2(SO4)3])^(-1) H_2SO_4 | 3 | 3 | ([H2SO4])^3 O_2 | 2 | 2 | ([O2])^2 H_2 | 1 | 1 | [H2] Cr | 2 | 2 | ([Cr])^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 = ([H2O])^(-4) ([Cr2(SO4)3])^(-1) ([H2SO4])^3 ([O2])^2 [H2] ([Cr])^2 = (([H2SO4])^3 ([O2])^2 [H2] ([Cr])^2)/(([H2O])^4 [Cr2(SO4)3])

Rate of reaction

Construct the rate of reaction expression for: H_2O + Cr_2(SO_4)_3 ⟶ H_2SO_4 + O_2 + H_2 + Cr 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_2O + Cr_2(SO_4)_3 ⟶ 3 H_2SO_4 + 2 O_2 + H_2 + 2 Cr 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_2O | 4 | -4 Cr_2(SO_4)_3 | 1 | -1 H_2SO_4 | 3 | 3 O_2 | 2 | 2 H_2 | 1 | 1 Cr | 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_2O | 4 | -4 | -1/4 (Δ[H2O])/(Δt) Cr_2(SO_4)_3 | 1 | -1 | -(Δ[Cr2(SO4)3])/(Δt) H_2SO_4 | 3 | 3 | 1/3 (Δ[H2SO4])/(Δt) O_2 | 2 | 2 | 1/2 (Δ[O2])/(Δt) H_2 | 1 | 1 | (Δ[H2])/(Δt) Cr | 2 | 2 | 1/2 (Δ[Cr])/(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[H2O])/(Δt) = -(Δ[Cr2(SO4)3])/(Δt) = 1/3 (Δ[H2SO4])/(Δt) = 1/2 (Δ[O2])/(Δt) = (Δ[H2])/(Δt) = 1/2 (Δ[Cr])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: H_2O + Cr_2(SO_4)_3 ⟶ H_2SO_4 + O_2 + H_2 + Cr 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_2O + Cr_2(SO_4)_3 ⟶ 3 H_2SO_4 + 2 O_2 + H_2 + 2 Cr 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_2O | 4 | -4 Cr_2(SO_4)_3 | 1 | -1 H_2SO_4 | 3 | 3 O_2 | 2 | 2 H_2 | 1 | 1 Cr | 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_2O | 4 | -4 | -1/4 (Δ[H2O])/(Δt) Cr_2(SO_4)_3 | 1 | -1 | -(Δ[Cr2(SO4)3])/(Δt) H_2SO_4 | 3 | 3 | 1/3 (Δ[H2SO4])/(Δt) O_2 | 2 | 2 | 1/2 (Δ[O2])/(Δt) H_2 | 1 | 1 | (Δ[H2])/(Δt) Cr | 2 | 2 | 1/2 (Δ[Cr])/(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[H2O])/(Δt) = -(Δ[Cr2(SO4)3])/(Δt) = 1/3 (Δ[H2SO4])/(Δt) = 1/2 (Δ[O2])/(Δt) = (Δ[H2])/(Δt) = 1/2 (Δ[Cr])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| water | chromium sulfate | sulfuric acid | oxygen | hydrogen | chromium formula | H_2O | Cr_2(SO_4)_3 | H_2SO_4 | O_2 | H_2 | Cr Hill formula | H_2O | Cr_2O_12S_3 | H_2O_4S | O_2 | H_2 | Cr name | water | chromium sulfate | sulfuric acid | oxygen | hydrogen | chromium IUPAC name | water | chromium(+3) cation trisulfate | sulfuric acid | molecular oxygen | molecular hydrogen | chromium
| water | chromium sulfate | sulfuric acid | oxygen | hydrogen | chromium formula | H_2O | Cr_2(SO_4)_3 | H_2SO_4 | O_2 | H_2 | Cr Hill formula | H_2O | Cr_2O_12S_3 | H_2O_4S | O_2 | H_2 | Cr name | water | chromium sulfate | sulfuric acid | oxygen | hydrogen | chromium IUPAC name | water | chromium(+3) cation trisulfate | sulfuric acid | molecular oxygen | molecular hydrogen | chromium

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