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CH3CH2OH + H2Cr2O7 = H2O + Cr2O3 + CH3CHO

Input interpretation

CH_3CH_2OH ethanol + H_2Cr_2O_7 dichromic acid ⟶ H_2O water + Cr_2O_3 chromium(III) oxide + CH_3CHO acetaldehyde
CH_3CH_2OH ethanol + H_2Cr_2O_7 dichromic acid ⟶ H_2O water + Cr_2O_3 chromium(III) oxide + CH_3CHO acetaldehyde

Balanced equation

Balance the chemical equation algebraically: CH_3CH_2OH + H_2Cr_2O_7 ⟶ H_2O + Cr_2O_3 + CH_3CHO Add stoichiometric coefficients, c_i, to the reactants and products: c_1 CH_3CH_2OH + c_2 H_2Cr_2O_7 ⟶ c_3 H_2O + c_4 Cr_2O_3 + c_5 CH_3CHO Set the number of atoms in the reactants equal to the number of atoms in the products for C, H, O and Cr: C: | 2 c_1 = 2 c_5 H: | 6 c_1 + 2 c_2 = 2 c_3 + 4 c_5 O: | c_1 + 7 c_2 = c_3 + 3 c_4 + c_5 Cr: | 2 c_2 = 2 c_4 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 = 3 c_2 = 1 c_3 = 4 c_4 = 1 c_5 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 CH_3CH_2OH + H_2Cr_2O_7 ⟶ 4 H_2O + Cr_2O_3 + 3 CH_3CHO
Balance the chemical equation algebraically: CH_3CH_2OH + H_2Cr_2O_7 ⟶ H_2O + Cr_2O_3 + CH_3CHO Add stoichiometric coefficients, c_i, to the reactants and products: c_1 CH_3CH_2OH + c_2 H_2Cr_2O_7 ⟶ c_3 H_2O + c_4 Cr_2O_3 + c_5 CH_3CHO Set the number of atoms in the reactants equal to the number of atoms in the products for C, H, O and Cr: C: | 2 c_1 = 2 c_5 H: | 6 c_1 + 2 c_2 = 2 c_3 + 4 c_5 O: | c_1 + 7 c_2 = c_3 + 3 c_4 + c_5 Cr: | 2 c_2 = 2 c_4 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 = 3 c_2 = 1 c_3 = 4 c_4 = 1 c_5 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 CH_3CH_2OH + H_2Cr_2O_7 ⟶ 4 H_2O + Cr_2O_3 + 3 CH_3CHO

Structures

+ ⟶ + +
+ ⟶ + +

Names

ethanol + dichromic acid ⟶ water + chromium(III) oxide + acetaldehyde
ethanol + dichromic acid ⟶ water + chromium(III) oxide + acetaldehyde

Equilibrium constant

Construct the equilibrium constant, K, expression for: CH_3CH_2OH + H_2Cr_2O_7 ⟶ H_2O + Cr_2O_3 + CH_3CHO 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: 3 CH_3CH_2OH + H_2Cr_2O_7 ⟶ 4 H_2O + Cr_2O_3 + 3 CH_3CHO 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 CH_3CH_2OH | 3 | -3 H_2Cr_2O_7 | 1 | -1 H_2O | 4 | 4 Cr_2O_3 | 1 | 1 CH_3CHO | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression CH_3CH_2OH | 3 | -3 | ([CH3CH2OH])^(-3) H_2Cr_2O_7 | 1 | -1 | ([H2Cr2O7])^(-1) H_2O | 4 | 4 | ([H2O])^4 Cr_2O_3 | 1 | 1 | [Cr2O3] CH_3CHO | 3 | 3 | ([CH3CHO])^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 = ([CH3CH2OH])^(-3) ([H2Cr2O7])^(-1) ([H2O])^4 [Cr2O3] ([CH3CHO])^3 = (([H2O])^4 [Cr2O3] ([CH3CHO])^3)/(([CH3CH2OH])^3 [H2Cr2O7])
Construct the equilibrium constant, K, expression for: CH_3CH_2OH + H_2Cr_2O_7 ⟶ H_2O + Cr_2O_3 + CH_3CHO 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: 3 CH_3CH_2OH + H_2Cr_2O_7 ⟶ 4 H_2O + Cr_2O_3 + 3 CH_3CHO 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 CH_3CH_2OH | 3 | -3 H_2Cr_2O_7 | 1 | -1 H_2O | 4 | 4 Cr_2O_3 | 1 | 1 CH_3CHO | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression CH_3CH_2OH | 3 | -3 | ([CH3CH2OH])^(-3) H_2Cr_2O_7 | 1 | -1 | ([H2Cr2O7])^(-1) H_2O | 4 | 4 | ([H2O])^4 Cr_2O_3 | 1 | 1 | [Cr2O3] CH_3CHO | 3 | 3 | ([CH3CHO])^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 = ([CH3CH2OH])^(-3) ([H2Cr2O7])^(-1) ([H2O])^4 [Cr2O3] ([CH3CHO])^3 = (([H2O])^4 [Cr2O3] ([CH3CHO])^3)/(([CH3CH2OH])^3 [H2Cr2O7])

Rate of reaction

Construct the rate of reaction expression for: CH_3CH_2OH + H_2Cr_2O_7 ⟶ H_2O + Cr_2O_3 + CH_3CHO 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: 3 CH_3CH_2OH + H_2Cr_2O_7 ⟶ 4 H_2O + Cr_2O_3 + 3 CH_3CHO 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 CH_3CH_2OH | 3 | -3 H_2Cr_2O_7 | 1 | -1 H_2O | 4 | 4 Cr_2O_3 | 1 | 1 CH_3CHO | 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 CH_3CH_2OH | 3 | -3 | -1/3 (Δ[CH3CH2OH])/(Δt) H_2Cr_2O_7 | 1 | -1 | -(Δ[H2Cr2O7])/(Δt) H_2O | 4 | 4 | 1/4 (Δ[H2O])/(Δt) Cr_2O_3 | 1 | 1 | (Δ[Cr2O3])/(Δt) CH_3CHO | 3 | 3 | 1/3 (Δ[CH3CHO])/(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 = -1/3 (Δ[CH3CH2OH])/(Δt) = -(Δ[H2Cr2O7])/(Δt) = 1/4 (Δ[H2O])/(Δt) = (Δ[Cr2O3])/(Δt) = 1/3 (Δ[CH3CHO])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: CH_3CH_2OH + H_2Cr_2O_7 ⟶ H_2O + Cr_2O_3 + CH_3CHO 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: 3 CH_3CH_2OH + H_2Cr_2O_7 ⟶ 4 H_2O + Cr_2O_3 + 3 CH_3CHO 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 CH_3CH_2OH | 3 | -3 H_2Cr_2O_7 | 1 | -1 H_2O | 4 | 4 Cr_2O_3 | 1 | 1 CH_3CHO | 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 CH_3CH_2OH | 3 | -3 | -1/3 (Δ[CH3CH2OH])/(Δt) H_2Cr_2O_7 | 1 | -1 | -(Δ[H2Cr2O7])/(Δt) H_2O | 4 | 4 | 1/4 (Δ[H2O])/(Δt) Cr_2O_3 | 1 | 1 | (Δ[Cr2O3])/(Δt) CH_3CHO | 3 | 3 | 1/3 (Δ[CH3CHO])/(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 = -1/3 (Δ[CH3CH2OH])/(Δt) = -(Δ[H2Cr2O7])/(Δt) = 1/4 (Δ[H2O])/(Δt) = (Δ[Cr2O3])/(Δt) = 1/3 (Δ[CH3CHO])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| ethanol | dichromic acid | water | chromium(III) oxide | acetaldehyde formula | CH_3CH_2OH | H_2Cr_2O_7 | H_2O | Cr_2O_3 | CH_3CHO Hill formula | C_2H_6O | Cr_2H_2O_7 | H_2O | Cr_2O_3 | C_2H_4O name | ethanol | dichromic acid | water | chromium(III) oxide | acetaldehyde IUPAC name | ethanol | hydroxy-(hydroxy-dioxo-chromio)oxy-dioxo-chromium | water | | acetaldehyde
| ethanol | dichromic acid | water | chromium(III) oxide | acetaldehyde formula | CH_3CH_2OH | H_2Cr_2O_7 | H_2O | Cr_2O_3 | CH_3CHO Hill formula | C_2H_6O | Cr_2H_2O_7 | H_2O | Cr_2O_3 | C_2H_4O name | ethanol | dichromic acid | water | chromium(III) oxide | acetaldehyde IUPAC name | ethanol | hydroxy-(hydroxy-dioxo-chromio)oxy-dioxo-chromium | water | | acetaldehyde

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