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H2SO4 + Fe + K2Cr2O7 = H2O + K2SO4 + Cr2(SO4)3 + Fe2(SO4)3

Input interpretation

H_2SO_4 sulfuric acid + Fe iron + K_2Cr_2O_7 potassium dichromate ⟶ H_2O water + K_2SO_4 potassium sulfate + Cr_2(SO_4)_3 chromium sulfate + Fe_2(SO_4)_3·xH_2O iron(III) sulfate hydrate
H_2SO_4 sulfuric acid + Fe iron + K_2Cr_2O_7 potassium dichromate ⟶ H_2O water + K_2SO_4 potassium sulfate + Cr_2(SO_4)_3 chromium sulfate + Fe_2(SO_4)_3·xH_2O iron(III) sulfate hydrate

Balanced equation

Balance the chemical equation algebraically: H_2SO_4 + Fe + K_2Cr_2O_7 ⟶ H_2O + K_2SO_4 + Cr_2(SO_4)_3 + Fe_2(SO_4)_3·xH_2O Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 Fe + c_3 K_2Cr_2O_7 ⟶ c_4 H_2O + c_5 K_2SO_4 + c_6 Cr_2(SO_4)_3 + c_7 Fe_2(SO_4)_3·xH_2O Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, Fe, 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 Fe: | 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 H_2SO_4 + 2 Fe + K_2Cr_2O_7 ⟶ 7 H_2O + K_2SO_4 + Cr_2(SO_4)_3 + Fe_2(SO_4)_3·xH_2O
Balance the chemical equation algebraically: H_2SO_4 + Fe + K_2Cr_2O_7 ⟶ H_2O + K_2SO_4 + Cr_2(SO_4)_3 + Fe_2(SO_4)_3·xH_2O Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 Fe + c_3 K_2Cr_2O_7 ⟶ c_4 H_2O + c_5 K_2SO_4 + c_6 Cr_2(SO_4)_3 + c_7 Fe_2(SO_4)_3·xH_2O Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, Fe, 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 Fe: | 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 H_2SO_4 + 2 Fe + K_2Cr_2O_7 ⟶ 7 H_2O + K_2SO_4 + Cr_2(SO_4)_3 + Fe_2(SO_4)_3·xH_2O

Structures

+ + ⟶ + + +
+ + ⟶ + + +

Names

sulfuric acid + iron + potassium dichromate ⟶ water + potassium sulfate + chromium sulfate + iron(III) sulfate hydrate
sulfuric acid + iron + potassium dichromate ⟶ water + potassium sulfate + chromium sulfate + iron(III) sulfate hydrate

Equilibrium constant

Construct the equilibrium constant, K, expression for: H_2SO_4 + Fe + K_2Cr_2O_7 ⟶ H_2O + K_2SO_4 + Cr_2(SO_4)_3 + Fe_2(SO_4)_3·xH_2O 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 H_2SO_4 + 2 Fe + K_2Cr_2O_7 ⟶ 7 H_2O + K_2SO_4 + Cr_2(SO_4)_3 + Fe_2(SO_4)_3·xH_2O 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 | 7 | -7 Fe | 2 | -2 K_2Cr_2O_7 | 1 | -1 H_2O | 7 | 7 K_2SO_4 | 1 | 1 Cr_2(SO_4)_3 | 1 | 1 Fe_2(SO_4)_3·xH_2O | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 7 | -7 | ([H2SO4])^(-7) Fe | 2 | -2 | ([Fe])^(-2) K_2Cr_2O_7 | 1 | -1 | ([K2Cr2O7])^(-1) H_2O | 7 | 7 | ([H2O])^7 K_2SO_4 | 1 | 1 | [K2SO4] Cr_2(SO_4)_3 | 1 | 1 | [Cr2(SO4)3] Fe_2(SO_4)_3·xH_2O | 1 | 1 | [Fe2(SO4)3·xH2O] 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) ([Fe])^(-2) ([K2Cr2O7])^(-1) ([H2O])^7 [K2SO4] [Cr2(SO4)3] [Fe2(SO4)3·xH2O] = (([H2O])^7 [K2SO4] [Cr2(SO4)3] [Fe2(SO4)3·xH2O])/(([H2SO4])^7 ([Fe])^2 [K2Cr2O7])
Construct the equilibrium constant, K, expression for: H_2SO_4 + Fe + K_2Cr_2O_7 ⟶ H_2O + K_2SO_4 + Cr_2(SO_4)_3 + Fe_2(SO_4)_3·xH_2O 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 H_2SO_4 + 2 Fe + K_2Cr_2O_7 ⟶ 7 H_2O + K_2SO_4 + Cr_2(SO_4)_3 + Fe_2(SO_4)_3·xH_2O 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 | 7 | -7 Fe | 2 | -2 K_2Cr_2O_7 | 1 | -1 H_2O | 7 | 7 K_2SO_4 | 1 | 1 Cr_2(SO_4)_3 | 1 | 1 Fe_2(SO_4)_3·xH_2O | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 7 | -7 | ([H2SO4])^(-7) Fe | 2 | -2 | ([Fe])^(-2) K_2Cr_2O_7 | 1 | -1 | ([K2Cr2O7])^(-1) H_2O | 7 | 7 | ([H2O])^7 K_2SO_4 | 1 | 1 | [K2SO4] Cr_2(SO_4)_3 | 1 | 1 | [Cr2(SO4)3] Fe_2(SO_4)_3·xH_2O | 1 | 1 | [Fe2(SO4)3·xH2O] 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) ([Fe])^(-2) ([K2Cr2O7])^(-1) ([H2O])^7 [K2SO4] [Cr2(SO4)3] [Fe2(SO4)3·xH2O] = (([H2O])^7 [K2SO4] [Cr2(SO4)3] [Fe2(SO4)3·xH2O])/(([H2SO4])^7 ([Fe])^2 [K2Cr2O7])

Rate of reaction

Construct the rate of reaction expression for: H_2SO_4 + Fe + K_2Cr_2O_7 ⟶ H_2O + K_2SO_4 + Cr_2(SO_4)_3 + Fe_2(SO_4)_3·xH_2O 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 H_2SO_4 + 2 Fe + K_2Cr_2O_7 ⟶ 7 H_2O + K_2SO_4 + Cr_2(SO_4)_3 + Fe_2(SO_4)_3·xH_2O 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 | 7 | -7 Fe | 2 | -2 K_2Cr_2O_7 | 1 | -1 H_2O | 7 | 7 K_2SO_4 | 1 | 1 Cr_2(SO_4)_3 | 1 | 1 Fe_2(SO_4)_3·xH_2O | 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 H_2SO_4 | 7 | -7 | -1/7 (Δ[H2SO4])/(Δt) Fe | 2 | -2 | -1/2 (Δ[Fe])/(Δt) K_2Cr_2O_7 | 1 | -1 | -(Δ[K2Cr2O7])/(Δt) H_2O | 7 | 7 | 1/7 (Δ[H2O])/(Δt) K_2SO_4 | 1 | 1 | (Δ[K2SO4])/(Δt) Cr_2(SO_4)_3 | 1 | 1 | (Δ[Cr2(SO4)3])/(Δt) Fe_2(SO_4)_3·xH_2O | 1 | 1 | (Δ[Fe2(SO4)3·xH2O])/(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[Fe])/(Δt) = -(Δ[K2Cr2O7])/(Δt) = 1/7 (Δ[H2O])/(Δt) = (Δ[K2SO4])/(Δt) = (Δ[Cr2(SO4)3])/(Δt) = (Δ[Fe2(SO4)3·xH2O])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: H_2SO_4 + Fe + K_2Cr_2O_7 ⟶ H_2O + K_2SO_4 + Cr_2(SO_4)_3 + Fe_2(SO_4)_3·xH_2O 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 H_2SO_4 + 2 Fe + K_2Cr_2O_7 ⟶ 7 H_2O + K_2SO_4 + Cr_2(SO_4)_3 + Fe_2(SO_4)_3·xH_2O 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 | 7 | -7 Fe | 2 | -2 K_2Cr_2O_7 | 1 | -1 H_2O | 7 | 7 K_2SO_4 | 1 | 1 Cr_2(SO_4)_3 | 1 | 1 Fe_2(SO_4)_3·xH_2O | 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 H_2SO_4 | 7 | -7 | -1/7 (Δ[H2SO4])/(Δt) Fe | 2 | -2 | -1/2 (Δ[Fe])/(Δt) K_2Cr_2O_7 | 1 | -1 | -(Δ[K2Cr2O7])/(Δt) H_2O | 7 | 7 | 1/7 (Δ[H2O])/(Δt) K_2SO_4 | 1 | 1 | (Δ[K2SO4])/(Δt) Cr_2(SO_4)_3 | 1 | 1 | (Δ[Cr2(SO4)3])/(Δt) Fe_2(SO_4)_3·xH_2O | 1 | 1 | (Δ[Fe2(SO4)3·xH2O])/(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[Fe])/(Δt) = -(Δ[K2Cr2O7])/(Δt) = 1/7 (Δ[H2O])/(Δt) = (Δ[K2SO4])/(Δt) = (Δ[Cr2(SO4)3])/(Δt) = (Δ[Fe2(SO4)3·xH2O])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| sulfuric acid | iron | potassium dichromate | water | potassium sulfate | chromium sulfate | iron(III) sulfate hydrate formula | H_2SO_4 | Fe | K_2Cr_2O_7 | H_2O | K_2SO_4 | Cr_2(SO_4)_3 | Fe_2(SO_4)_3·xH_2O Hill formula | H_2O_4S | Fe | Cr_2K_2O_7 | H_2O | K_2O_4S | Cr_2O_12S_3 | Fe_2O_12S_3 name | sulfuric acid | iron | potassium dichromate | water | potassium sulfate | chromium sulfate | iron(III) sulfate hydrate IUPAC name | sulfuric acid | iron | dipotassium oxido-(oxido-dioxochromio)oxy-dioxochromium | water | dipotassium sulfate | chromium(+3) cation trisulfate | diferric trisulfate
| sulfuric acid | iron | potassium dichromate | water | potassium sulfate | chromium sulfate | iron(III) sulfate hydrate formula | H_2SO_4 | Fe | K_2Cr_2O_7 | H_2O | K_2SO_4 | Cr_2(SO_4)_3 | Fe_2(SO_4)_3·xH_2O Hill formula | H_2O_4S | Fe | Cr_2K_2O_7 | H_2O | K_2O_4S | Cr_2O_12S_3 | Fe_2O_12S_3 name | sulfuric acid | iron | potassium dichromate | water | potassium sulfate | chromium sulfate | iron(III) sulfate hydrate IUPAC name | sulfuric acid | iron | dipotassium oxido-(oxido-dioxochromio)oxy-dioxochromium | water | dipotassium sulfate | chromium(+3) cation trisulfate | diferric trisulfate

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