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H2SO4 + Al + K2Cr2O7 = H2O + K2SO4 + Al2(SO4)3 + Cr2SO4

Input interpretation

H_2SO_4 sulfuric acid + Al aluminum + K_2Cr_2O_7 potassium dichromate ⟶ H_2O water + K_2SO_4 potassium sulfate + Al_2(SO_4)_3 aluminum sulfate + Cr2SO4
H_2SO_4 sulfuric acid + Al aluminum + K_2Cr_2O_7 potassium dichromate ⟶ H_2O water + K_2SO_4 potassium sulfate + Al_2(SO_4)_3 aluminum sulfate + Cr2SO4

Balanced equation

Balance the chemical equation algebraically: H_2SO_4 + Al + K_2Cr_2O_7 ⟶ H_2O + K_2SO_4 + Al_2(SO_4)_3 + Cr2SO4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 Al + c_3 K_2Cr_2O_7 ⟶ c_4 H_2O + c_5 K_2SO_4 + c_6 Al_2(SO_4)_3 + c_7 Cr2SO4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, Al, Cr and K: H: | 2 c_1 = 2 c_4 O: | 4 c_1 + 7 c_3 = c_4 + 4 c_5 + 12 c_6 + 4 c_7 S: | c_1 = c_5 + 3 c_6 + c_7 Al: | c_2 = 2 c_6 Cr: | 2 c_3 = 2 c_7 K: | 2 c_3 = 2 c_5 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 7 c_2 = 10/3 c_3 = 1 c_4 = 7 c_5 = 1 c_6 = 5/3 c_7 = 1 Multiply by the least common denominator, 3, to eliminate fractional coefficients: c_1 = 21 c_2 = 10 c_3 = 3 c_4 = 21 c_5 = 3 c_6 = 5 c_7 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 21 H_2SO_4 + 10 Al + 3 K_2Cr_2O_7 ⟶ 21 H_2O + 3 K_2SO_4 + 5 Al_2(SO_4)_3 + 3 Cr2SO4
Balance the chemical equation algebraically: H_2SO_4 + Al + K_2Cr_2O_7 ⟶ H_2O + K_2SO_4 + Al_2(SO_4)_3 + Cr2SO4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 Al + c_3 K_2Cr_2O_7 ⟶ c_4 H_2O + c_5 K_2SO_4 + c_6 Al_2(SO_4)_3 + c_7 Cr2SO4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, Al, Cr and K: H: | 2 c_1 = 2 c_4 O: | 4 c_1 + 7 c_3 = c_4 + 4 c_5 + 12 c_6 + 4 c_7 S: | c_1 = c_5 + 3 c_6 + c_7 Al: | c_2 = 2 c_6 Cr: | 2 c_3 = 2 c_7 K: | 2 c_3 = 2 c_5 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 7 c_2 = 10/3 c_3 = 1 c_4 = 7 c_5 = 1 c_6 = 5/3 c_7 = 1 Multiply by the least common denominator, 3, to eliminate fractional coefficients: c_1 = 21 c_2 = 10 c_3 = 3 c_4 = 21 c_5 = 3 c_6 = 5 c_7 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 21 H_2SO_4 + 10 Al + 3 K_2Cr_2O_7 ⟶ 21 H_2O + 3 K_2SO_4 + 5 Al_2(SO_4)_3 + 3 Cr2SO4

Structures

+ + ⟶ + + + Cr2SO4
+ + ⟶ + + + Cr2SO4

Names

sulfuric acid + aluminum + potassium dichromate ⟶ water + potassium sulfate + aluminum sulfate + Cr2SO4
sulfuric acid + aluminum + potassium dichromate ⟶ water + potassium sulfate + aluminum sulfate + Cr2SO4

Equilibrium constant

Construct the equilibrium constant, K, expression for: H_2SO_4 + Al + K_2Cr_2O_7 ⟶ H_2O + K_2SO_4 + Al_2(SO_4)_3 + Cr2SO4 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: 21 H_2SO_4 + 10 Al + 3 K_2Cr_2O_7 ⟶ 21 H_2O + 3 K_2SO_4 + 5 Al_2(SO_4)_3 + 3 Cr2SO4 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 | 21 | -21 Al | 10 | -10 K_2Cr_2O_7 | 3 | -3 H_2O | 21 | 21 K_2SO_4 | 3 | 3 Al_2(SO_4)_3 | 5 | 5 Cr2SO4 | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 21 | -21 | ([H2SO4])^(-21) Al | 10 | -10 | ([Al])^(-10) K_2Cr_2O_7 | 3 | -3 | ([K2Cr2O7])^(-3) H_2O | 21 | 21 | ([H2O])^21 K_2SO_4 | 3 | 3 | ([K2SO4])^3 Al_2(SO_4)_3 | 5 | 5 | ([Al2(SO4)3])^5 Cr2SO4 | 3 | 3 | ([Cr2SO4])^3 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])^(-21) ([Al])^(-10) ([K2Cr2O7])^(-3) ([H2O])^21 ([K2SO4])^3 ([Al2(SO4)3])^5 ([Cr2SO4])^3 = (([H2O])^21 ([K2SO4])^3 ([Al2(SO4)3])^5 ([Cr2SO4])^3)/(([H2SO4])^21 ([Al])^10 ([K2Cr2O7])^3)
Construct the equilibrium constant, K, expression for: H_2SO_4 + Al + K_2Cr_2O_7 ⟶ H_2O + K_2SO_4 + Al_2(SO_4)_3 + Cr2SO4 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: 21 H_2SO_4 + 10 Al + 3 K_2Cr_2O_7 ⟶ 21 H_2O + 3 K_2SO_4 + 5 Al_2(SO_4)_3 + 3 Cr2SO4 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 | 21 | -21 Al | 10 | -10 K_2Cr_2O_7 | 3 | -3 H_2O | 21 | 21 K_2SO_4 | 3 | 3 Al_2(SO_4)_3 | 5 | 5 Cr2SO4 | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 21 | -21 | ([H2SO4])^(-21) Al | 10 | -10 | ([Al])^(-10) K_2Cr_2O_7 | 3 | -3 | ([K2Cr2O7])^(-3) H_2O | 21 | 21 | ([H2O])^21 K_2SO_4 | 3 | 3 | ([K2SO4])^3 Al_2(SO_4)_3 | 5 | 5 | ([Al2(SO4)3])^5 Cr2SO4 | 3 | 3 | ([Cr2SO4])^3 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])^(-21) ([Al])^(-10) ([K2Cr2O7])^(-3) ([H2O])^21 ([K2SO4])^3 ([Al2(SO4)3])^5 ([Cr2SO4])^3 = (([H2O])^21 ([K2SO4])^3 ([Al2(SO4)3])^5 ([Cr2SO4])^3)/(([H2SO4])^21 ([Al])^10 ([K2Cr2O7])^3)

Rate of reaction

Construct the rate of reaction expression for: H_2SO_4 + Al + K_2Cr_2O_7 ⟶ H_2O + K_2SO_4 + Al_2(SO_4)_3 + Cr2SO4 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: 21 H_2SO_4 + 10 Al + 3 K_2Cr_2O_7 ⟶ 21 H_2O + 3 K_2SO_4 + 5 Al_2(SO_4)_3 + 3 Cr2SO4 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 | 21 | -21 Al | 10 | -10 K_2Cr_2O_7 | 3 | -3 H_2O | 21 | 21 K_2SO_4 | 3 | 3 Al_2(SO_4)_3 | 5 | 5 Cr2SO4 | 3 | 3 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 | 21 | -21 | -1/21 (Δ[H2SO4])/(Δt) Al | 10 | -10 | -1/10 (Δ[Al])/(Δt) K_2Cr_2O_7 | 3 | -3 | -1/3 (Δ[K2Cr2O7])/(Δt) H_2O | 21 | 21 | 1/21 (Δ[H2O])/(Δt) K_2SO_4 | 3 | 3 | 1/3 (Δ[K2SO4])/(Δt) Al_2(SO_4)_3 | 5 | 5 | 1/5 (Δ[Al2(SO4)3])/(Δt) Cr2SO4 | 3 | 3 | 1/3 (Δ[Cr2SO4])/(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 = -1/21 (Δ[H2SO4])/(Δt) = -1/10 (Δ[Al])/(Δt) = -1/3 (Δ[K2Cr2O7])/(Δt) = 1/21 (Δ[H2O])/(Δt) = 1/3 (Δ[K2SO4])/(Δt) = 1/5 (Δ[Al2(SO4)3])/(Δt) = 1/3 (Δ[Cr2SO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: H_2SO_4 + Al + K_2Cr_2O_7 ⟶ H_2O + K_2SO_4 + Al_2(SO_4)_3 + Cr2SO4 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: 21 H_2SO_4 + 10 Al + 3 K_2Cr_2O_7 ⟶ 21 H_2O + 3 K_2SO_4 + 5 Al_2(SO_4)_3 + 3 Cr2SO4 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 | 21 | -21 Al | 10 | -10 K_2Cr_2O_7 | 3 | -3 H_2O | 21 | 21 K_2SO_4 | 3 | 3 Al_2(SO_4)_3 | 5 | 5 Cr2SO4 | 3 | 3 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 | 21 | -21 | -1/21 (Δ[H2SO4])/(Δt) Al | 10 | -10 | -1/10 (Δ[Al])/(Δt) K_2Cr_2O_7 | 3 | -3 | -1/3 (Δ[K2Cr2O7])/(Δt) H_2O | 21 | 21 | 1/21 (Δ[H2O])/(Δt) K_2SO_4 | 3 | 3 | 1/3 (Δ[K2SO4])/(Δt) Al_2(SO_4)_3 | 5 | 5 | 1/5 (Δ[Al2(SO4)3])/(Δt) Cr2SO4 | 3 | 3 | 1/3 (Δ[Cr2SO4])/(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 = -1/21 (Δ[H2SO4])/(Δt) = -1/10 (Δ[Al])/(Δt) = -1/3 (Δ[K2Cr2O7])/(Δt) = 1/21 (Δ[H2O])/(Δt) = 1/3 (Δ[K2SO4])/(Δt) = 1/5 (Δ[Al2(SO4)3])/(Δt) = 1/3 (Δ[Cr2SO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| sulfuric acid | aluminum | potassium dichromate | water | potassium sulfate | aluminum sulfate | Cr2SO4 formula | H_2SO_4 | Al | K_2Cr_2O_7 | H_2O | K_2SO_4 | Al_2(SO_4)_3 | Cr2SO4 Hill formula | H_2O_4S | Al | Cr_2K_2O_7 | H_2O | K_2O_4S | Al_2O_12S_3 | Cr2O4S name | sulfuric acid | aluminum | potassium dichromate | water | potassium sulfate | aluminum sulfate | IUPAC name | sulfuric acid | aluminum | dipotassium oxido-(oxido-dioxochromio)oxy-dioxochromium | water | dipotassium sulfate | dialuminum trisulfate |
| sulfuric acid | aluminum | potassium dichromate | water | potassium sulfate | aluminum sulfate | Cr2SO4 formula | H_2SO_4 | Al | K_2Cr_2O_7 | H_2O | K_2SO_4 | Al_2(SO_4)_3 | Cr2SO4 Hill formula | H_2O_4S | Al | Cr_2K_2O_7 | H_2O | K_2O_4S | Al_2O_12S_3 | Cr2O4S name | sulfuric acid | aluminum | potassium dichromate | water | potassium sulfate | aluminum sulfate | IUPAC name | sulfuric acid | aluminum | dipotassium oxido-(oxido-dioxochromio)oxy-dioxochromium | water | dipotassium sulfate | dialuminum trisulfate |

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