Input interpretation
sulfuric acid + potassium dichromate + duretter ⟶ water + chromium sulfate + iron(III) sulfate hydrate + potassium bisulfate
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, Cr, K and Fe: H: | 2 c_1 = 2 c_4 + c_7 O: | 4 c_1 + 7 c_2 + 4 c_3 = c_4 + 12 c_5 + 12 c_6 + 4 c_7 S: | c_1 + c_3 = 3 c_5 + 3 c_6 + c_7 Cr: | 2 c_2 = 2 c_5 K: | 2 c_2 = c_7 Fe: | c_3 = 2 c_6 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_1 = 8 c_2 = 1 c_3 = 6 c_4 = 7 c_5 = 1 c_6 = 3 c_7 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 8 + + 6 ⟶ 7 + + 3 + 2
Structures
+ + ⟶ + + +
Names
sulfuric acid + potassium dichromate + duretter ⟶ water + chromium sulfate + iron(III) sulfate hydrate + potassium bisulfate
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: 8 + + 6 ⟶ 7 + + 3 + 2 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 | 8 | -8 | 1 | -1 | 6 | -6 | 7 | 7 | 1 | 1 | 3 | 3 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression | 8 | -8 | ([H2SO4])^(-8) | 1 | -1 | ([K2Cr2O7])^(-1) | 6 | -6 | ([FeSO4])^(-6) | 7 | 7 | ([H2O])^7 | 1 | 1 | [Cr2(SO4)3] | 3 | 3 | ([Fe2(SO4)3·xH2O])^3 | 2 | 2 | ([KHSO4])^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])^(-8) ([K2Cr2O7])^(-1) ([FeSO4])^(-6) ([H2O])^7 [Cr2(SO4)3] ([Fe2(SO4)3·xH2O])^3 ([KHSO4])^2 = (([H2O])^7 [Cr2(SO4)3] ([Fe2(SO4)3·xH2O])^3 ([KHSO4])^2)/(([H2SO4])^8 [K2Cr2O7] ([FeSO4])^6)](../image_source/850f84a809f64d0833af16a46335524c.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: 8 + + 6 ⟶ 7 + + 3 + 2 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 | 8 | -8 | 1 | -1 | 6 | -6 | 7 | 7 | 1 | 1 | 3 | 3 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression | 8 | -8 | ([H2SO4])^(-8) | 1 | -1 | ([K2Cr2O7])^(-1) | 6 | -6 | ([FeSO4])^(-6) | 7 | 7 | ([H2O])^7 | 1 | 1 | [Cr2(SO4)3] | 3 | 3 | ([Fe2(SO4)3·xH2O])^3 | 2 | 2 | ([KHSO4])^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])^(-8) ([K2Cr2O7])^(-1) ([FeSO4])^(-6) ([H2O])^7 [Cr2(SO4)3] ([Fe2(SO4)3·xH2O])^3 ([KHSO4])^2 = (([H2O])^7 [Cr2(SO4)3] ([Fe2(SO4)3·xH2O])^3 ([KHSO4])^2)/(([H2SO4])^8 [K2Cr2O7] ([FeSO4])^6)
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: 8 + + 6 ⟶ 7 + + 3 + 2 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 | 8 | -8 | 1 | -1 | 6 | -6 | 7 | 7 | 1 | 1 | 3 | 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 | 8 | -8 | -1/8 (Δ[H2SO4])/(Δt) | 1 | -1 | -(Δ[K2Cr2O7])/(Δt) | 6 | -6 | -1/6 (Δ[FeSO4])/(Δt) | 7 | 7 | 1/7 (Δ[H2O])/(Δt) | 1 | 1 | (Δ[Cr2(SO4)3])/(Δt) | 3 | 3 | 1/3 (Δ[Fe2(SO4)3·xH2O])/(Δt) | 2 | 2 | 1/2 (Δ[KHSO4])/(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 = -1/8 (Δ[H2SO4])/(Δt) = -(Δ[K2Cr2O7])/(Δt) = -1/6 (Δ[FeSO4])/(Δt) = 1/7 (Δ[H2O])/(Δt) = (Δ[Cr2(SO4)3])/(Δt) = 1/3 (Δ[Fe2(SO4)3·xH2O])/(Δt) = 1/2 (Δ[KHSO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)](../image_source/fc49a6fed1fc57acc7b76e5f4928a397.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: 8 + + 6 ⟶ 7 + + 3 + 2 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 | 8 | -8 | 1 | -1 | 6 | -6 | 7 | 7 | 1 | 1 | 3 | 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 | 8 | -8 | -1/8 (Δ[H2SO4])/(Δt) | 1 | -1 | -(Δ[K2Cr2O7])/(Δt) | 6 | -6 | -1/6 (Δ[FeSO4])/(Δt) | 7 | 7 | 1/7 (Δ[H2O])/(Δt) | 1 | 1 | (Δ[Cr2(SO4)3])/(Δt) | 3 | 3 | 1/3 (Δ[Fe2(SO4)3·xH2O])/(Δt) | 2 | 2 | 1/2 (Δ[KHSO4])/(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 = -1/8 (Δ[H2SO4])/(Δt) = -(Δ[K2Cr2O7])/(Δt) = -1/6 (Δ[FeSO4])/(Δt) = 1/7 (Δ[H2O])/(Δt) = (Δ[Cr2(SO4)3])/(Δt) = 1/3 (Δ[Fe2(SO4)3·xH2O])/(Δt) = 1/2 (Δ[KHSO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Chemical names and formulas
| sulfuric acid | potassium dichromate | duretter | water | chromium sulfate | iron(III) sulfate hydrate | potassium bisulfate Hill formula | H_2O_4S | Cr_2K_2O_7 | FeO_4S | H_2O | Cr_2O_12S_3 | Fe_2O_12S_3 | HKO_4S name | sulfuric acid | potassium dichromate | duretter | water | chromium sulfate | iron(III) sulfate hydrate | potassium bisulfate IUPAC name | sulfuric acid | dipotassium oxido-(oxido-dioxochromio)oxy-dioxochromium | iron(+2) cation sulfate | water | chromium(+3) cation trisulfate | diferric trisulfate | potassium hydrogen sulfate