Input interpretation
sulfuric acid + aluminum + potassium dichromate ⟶ water + potassium sulfate + chromium sulfate + aluminum sulfate
Balanced equation
Balance the chemical equation algebraically: + + ⟶ + + + Add stoichiometric coefficients, c_i, to the reactants and products: c_1 + c_2 + c_3 ⟶ c_4 + c_5 + c_6 + c_7 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 + 12 c_7 S: | c_1 = c_5 + 3 c_6 + 3 c_7 Al: | c_2 = 2 c_7 Cr: | 2 c_3 = 2 c_6 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 = 2 c_3 = 1 c_4 = 7 c_5 = 1 c_6 = 1 c_7 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 7 + 2 + ⟶ 7 + + +
Structures
+ + ⟶ + + +
Names
sulfuric acid + aluminum + potassium dichromate ⟶ water + potassium sulfate + chromium sulfate + aluminum sulfate
Equilibrium constant
![Construct the equilibrium constant, K, expression for: + + ⟶ + + + 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: 7 + 2 + ⟶ 7 + + + 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 | 7 | -7 | 2 | -2 | 1 | -1 | 7 | 7 | 1 | 1 | 1 | 1 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression | 7 | -7 | ([H2SO4])^(-7) | 2 | -2 | ([Al])^(-2) | 1 | -1 | ([K2Cr2O7])^(-1) | 7 | 7 | ([H2O])^7 | 1 | 1 | [K2SO4] | 1 | 1 | [Cr2(SO4)3] | 1 | 1 | [Al2(SO4)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])^(-7) ([Al])^(-2) ([K2Cr2O7])^(-1) ([H2O])^7 [K2SO4] [Cr2(SO4)3] [Al2(SO4)3] = (([H2O])^7 [K2SO4] [Cr2(SO4)3] [Al2(SO4)3])/(([H2SO4])^7 ([Al])^2 [K2Cr2O7])](../image_source/c5bc932ad37bf2b9bf6bfda2850136eb.png)
Construct the equilibrium constant, K, expression for: + + ⟶ + + + 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: 7 + 2 + ⟶ 7 + + + 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 | 7 | -7 | 2 | -2 | 1 | -1 | 7 | 7 | 1 | 1 | 1 | 1 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression | 7 | -7 | ([H2SO4])^(-7) | 2 | -2 | ([Al])^(-2) | 1 | -1 | ([K2Cr2O7])^(-1) | 7 | 7 | ([H2O])^7 | 1 | 1 | [K2SO4] | 1 | 1 | [Cr2(SO4)3] | 1 | 1 | [Al2(SO4)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])^(-7) ([Al])^(-2) ([K2Cr2O7])^(-1) ([H2O])^7 [K2SO4] [Cr2(SO4)3] [Al2(SO4)3] = (([H2O])^7 [K2SO4] [Cr2(SO4)3] [Al2(SO4)3])/(([H2SO4])^7 ([Al])^2 [K2Cr2O7])
Rate of reaction
![Construct the rate of reaction expression for: + + ⟶ + + + 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: 7 + 2 + ⟶ 7 + + + 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 | 7 | -7 | 2 | -2 | 1 | -1 | 7 | 7 | 1 | 1 | 1 | 1 | 1 | 1 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 | 7 | -7 | -1/7 (Δ[H2SO4])/(Δt) | 2 | -2 | -1/2 (Δ[Al])/(Δt) | 1 | -1 | -(Δ[K2Cr2O7])/(Δt) | 7 | 7 | 1/7 (Δ[H2O])/(Δt) | 1 | 1 | (Δ[K2SO4])/(Δt) | 1 | 1 | (Δ[Cr2(SO4)3])/(Δt) | 1 | 1 | (Δ[Al2(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 = -1/7 (Δ[H2SO4])/(Δt) = -1/2 (Δ[Al])/(Δt) = -(Δ[K2Cr2O7])/(Δt) = 1/7 (Δ[H2O])/(Δt) = (Δ[K2SO4])/(Δt) = (Δ[Cr2(SO4)3])/(Δt) = (Δ[Al2(SO4)3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)](../image_source/af6683d0cd644d898510e5fdefd2d794.png)
Construct the rate of reaction expression for: + + ⟶ + + + 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: 7 + 2 + ⟶ 7 + + + 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 | 7 | -7 | 2 | -2 | 1 | -1 | 7 | 7 | 1 | 1 | 1 | 1 | 1 | 1 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 | 7 | -7 | -1/7 (Δ[H2SO4])/(Δt) | 2 | -2 | -1/2 (Δ[Al])/(Δt) | 1 | -1 | -(Δ[K2Cr2O7])/(Δt) | 7 | 7 | 1/7 (Δ[H2O])/(Δt) | 1 | 1 | (Δ[K2SO4])/(Δt) | 1 | 1 | (Δ[Cr2(SO4)3])/(Δt) | 1 | 1 | (Δ[Al2(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 = -1/7 (Δ[H2SO4])/(Δt) = -1/2 (Δ[Al])/(Δt) = -(Δ[K2Cr2O7])/(Δt) = 1/7 (Δ[H2O])/(Δt) = (Δ[K2SO4])/(Δt) = (Δ[Cr2(SO4)3])/(Δt) = (Δ[Al2(SO4)3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Chemical names and formulas
| sulfuric acid | aluminum | potassium dichromate | water | potassium sulfate | chromium sulfate | aluminum sulfate Hill formula | H_2O_4S | Al | Cr_2K_2O_7 | H_2O | K_2O_4S | Cr_2O_12S_3 | Al_2O_12S_3 name | sulfuric acid | aluminum | potassium dichromate | water | potassium sulfate | chromium sulfate | aluminum sulfate IUPAC name | sulfuric acid | aluminum | dipotassium oxido-(oxido-dioxochromio)oxy-dioxochromium | water | dipotassium sulfate | chromium(+3) cation trisulfate | dialuminum trisulfate