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K2Cr2O7 + KSCN + H2Cr2O7 = H2O + CO2 + K2SO4 + NO2 + Cr2O3

Input interpretation

K_2Cr_2O_7 potassium dichromate + KSCN potassium thiocyanate + H_2Cr_2O_7 dichromic acid ⟶ H_2O water + CO_2 carbon dioxide + K_2SO_4 potassium sulfate + NO_2 nitrogen dioxide + Cr_2O_3 chromium(III) oxide
K_2Cr_2O_7 potassium dichromate + KSCN potassium thiocyanate + H_2Cr_2O_7 dichromic acid ⟶ H_2O water + CO_2 carbon dioxide + K_2SO_4 potassium sulfate + NO_2 nitrogen dioxide + Cr_2O_3 chromium(III) oxide

Balanced equation

Balance the chemical equation algebraically: K_2Cr_2O_7 + KSCN + H_2Cr_2O_7 ⟶ H_2O + CO_2 + K_2SO_4 + NO_2 + Cr_2O_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 K_2Cr_2O_7 + c_2 KSCN + c_3 H_2Cr_2O_7 ⟶ c_4 H_2O + c_5 CO_2 + c_6 K_2SO_4 + c_7 NO_2 + c_8 Cr_2O_3 Set the number of atoms in the reactants equal to the number of atoms in the products for Cr, K, O, C, N, S and H: Cr: | 2 c_1 + 2 c_3 = 2 c_8 K: | 2 c_1 + c_2 = 2 c_6 O: | 7 c_1 + 7 c_3 = c_4 + 2 c_5 + 4 c_6 + 2 c_7 + 3 c_8 C: | c_2 = c_5 N: | c_2 = c_7 S: | c_2 = c_6 H: | 2 c_3 = 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 2 c_3 = 4 c_4 = 4 c_5 = 2 c_6 = 2 c_7 = 2 c_8 = 5 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | K_2Cr_2O_7 + 2 KSCN + 4 H_2Cr_2O_7 ⟶ 4 H_2O + 2 CO_2 + 2 K_2SO_4 + 2 NO_2 + 5 Cr_2O_3
Balance the chemical equation algebraically: K_2Cr_2O_7 + KSCN + H_2Cr_2O_7 ⟶ H_2O + CO_2 + K_2SO_4 + NO_2 + Cr_2O_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 K_2Cr_2O_7 + c_2 KSCN + c_3 H_2Cr_2O_7 ⟶ c_4 H_2O + c_5 CO_2 + c_6 K_2SO_4 + c_7 NO_2 + c_8 Cr_2O_3 Set the number of atoms in the reactants equal to the number of atoms in the products for Cr, K, O, C, N, S and H: Cr: | 2 c_1 + 2 c_3 = 2 c_8 K: | 2 c_1 + c_2 = 2 c_6 O: | 7 c_1 + 7 c_3 = c_4 + 2 c_5 + 4 c_6 + 2 c_7 + 3 c_8 C: | c_2 = c_5 N: | c_2 = c_7 S: | c_2 = c_6 H: | 2 c_3 = 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 2 c_3 = 4 c_4 = 4 c_5 = 2 c_6 = 2 c_7 = 2 c_8 = 5 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | K_2Cr_2O_7 + 2 KSCN + 4 H_2Cr_2O_7 ⟶ 4 H_2O + 2 CO_2 + 2 K_2SO_4 + 2 NO_2 + 5 Cr_2O_3

Structures

+ + ⟶ + + + +
+ + ⟶ + + + +

Names

potassium dichromate + potassium thiocyanate + dichromic acid ⟶ water + carbon dioxide + potassium sulfate + nitrogen dioxide + chromium(III) oxide
potassium dichromate + potassium thiocyanate + dichromic acid ⟶ water + carbon dioxide + potassium sulfate + nitrogen dioxide + chromium(III) oxide

Equilibrium constant

Construct the equilibrium constant, K, expression for: K_2Cr_2O_7 + KSCN + H_2Cr_2O_7 ⟶ H_2O + CO_2 + K_2SO_4 + NO_2 + Cr_2O_3 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: K_2Cr_2O_7 + 2 KSCN + 4 H_2Cr_2O_7 ⟶ 4 H_2O + 2 CO_2 + 2 K_2SO_4 + 2 NO_2 + 5 Cr_2O_3 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 K_2Cr_2O_7 | 1 | -1 KSCN | 2 | -2 H_2Cr_2O_7 | 4 | -4 H_2O | 4 | 4 CO_2 | 2 | 2 K_2SO_4 | 2 | 2 NO_2 | 2 | 2 Cr_2O_3 | 5 | 5 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression K_2Cr_2O_7 | 1 | -1 | ([K2Cr2O7])^(-1) KSCN | 2 | -2 | ([KSCN])^(-2) H_2Cr_2O_7 | 4 | -4 | ([H2Cr2O7])^(-4) H_2O | 4 | 4 | ([H2O])^4 CO_2 | 2 | 2 | ([CO2])^2 K_2SO_4 | 2 | 2 | ([K2SO4])^2 NO_2 | 2 | 2 | ([NO2])^2 Cr_2O_3 | 5 | 5 | ([Cr2O3])^5 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 = ([K2Cr2O7])^(-1) ([KSCN])^(-2) ([H2Cr2O7])^(-4) ([H2O])^4 ([CO2])^2 ([K2SO4])^2 ([NO2])^2 ([Cr2O3])^5 = (([H2O])^4 ([CO2])^2 ([K2SO4])^2 ([NO2])^2 ([Cr2O3])^5)/([K2Cr2O7] ([KSCN])^2 ([H2Cr2O7])^4)
Construct the equilibrium constant, K, expression for: K_2Cr_2O_7 + KSCN + H_2Cr_2O_7 ⟶ H_2O + CO_2 + K_2SO_4 + NO_2 + Cr_2O_3 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: K_2Cr_2O_7 + 2 KSCN + 4 H_2Cr_2O_7 ⟶ 4 H_2O + 2 CO_2 + 2 K_2SO_4 + 2 NO_2 + 5 Cr_2O_3 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 K_2Cr_2O_7 | 1 | -1 KSCN | 2 | -2 H_2Cr_2O_7 | 4 | -4 H_2O | 4 | 4 CO_2 | 2 | 2 K_2SO_4 | 2 | 2 NO_2 | 2 | 2 Cr_2O_3 | 5 | 5 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression K_2Cr_2O_7 | 1 | -1 | ([K2Cr2O7])^(-1) KSCN | 2 | -2 | ([KSCN])^(-2) H_2Cr_2O_7 | 4 | -4 | ([H2Cr2O7])^(-4) H_2O | 4 | 4 | ([H2O])^4 CO_2 | 2 | 2 | ([CO2])^2 K_2SO_4 | 2 | 2 | ([K2SO4])^2 NO_2 | 2 | 2 | ([NO2])^2 Cr_2O_3 | 5 | 5 | ([Cr2O3])^5 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 = ([K2Cr2O7])^(-1) ([KSCN])^(-2) ([H2Cr2O7])^(-4) ([H2O])^4 ([CO2])^2 ([K2SO4])^2 ([NO2])^2 ([Cr2O3])^5 = (([H2O])^4 ([CO2])^2 ([K2SO4])^2 ([NO2])^2 ([Cr2O3])^5)/([K2Cr2O7] ([KSCN])^2 ([H2Cr2O7])^4)

Rate of reaction

Construct the rate of reaction expression for: K_2Cr_2O_7 + KSCN + H_2Cr_2O_7 ⟶ H_2O + CO_2 + K_2SO_4 + NO_2 + Cr_2O_3 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: K_2Cr_2O_7 + 2 KSCN + 4 H_2Cr_2O_7 ⟶ 4 H_2O + 2 CO_2 + 2 K_2SO_4 + 2 NO_2 + 5 Cr_2O_3 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 K_2Cr_2O_7 | 1 | -1 KSCN | 2 | -2 H_2Cr_2O_7 | 4 | -4 H_2O | 4 | 4 CO_2 | 2 | 2 K_2SO_4 | 2 | 2 NO_2 | 2 | 2 Cr_2O_3 | 5 | 5 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 K_2Cr_2O_7 | 1 | -1 | -(Δ[K2Cr2O7])/(Δt) KSCN | 2 | -2 | -1/2 (Δ[KSCN])/(Δt) H_2Cr_2O_7 | 4 | -4 | -1/4 (Δ[H2Cr2O7])/(Δt) H_2O | 4 | 4 | 1/4 (Δ[H2O])/(Δt) CO_2 | 2 | 2 | 1/2 (Δ[CO2])/(Δt) K_2SO_4 | 2 | 2 | 1/2 (Δ[K2SO4])/(Δt) NO_2 | 2 | 2 | 1/2 (Δ[NO2])/(Δt) Cr_2O_3 | 5 | 5 | 1/5 (Δ[Cr2O3])/(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 = -(Δ[K2Cr2O7])/(Δt) = -1/2 (Δ[KSCN])/(Δt) = -1/4 (Δ[H2Cr2O7])/(Δt) = 1/4 (Δ[H2O])/(Δt) = 1/2 (Δ[CO2])/(Δt) = 1/2 (Δ[K2SO4])/(Δt) = 1/2 (Δ[NO2])/(Δt) = 1/5 (Δ[Cr2O3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: K_2Cr_2O_7 + KSCN + H_2Cr_2O_7 ⟶ H_2O + CO_2 + K_2SO_4 + NO_2 + Cr_2O_3 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: K_2Cr_2O_7 + 2 KSCN + 4 H_2Cr_2O_7 ⟶ 4 H_2O + 2 CO_2 + 2 K_2SO_4 + 2 NO_2 + 5 Cr_2O_3 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 K_2Cr_2O_7 | 1 | -1 KSCN | 2 | -2 H_2Cr_2O_7 | 4 | -4 H_2O | 4 | 4 CO_2 | 2 | 2 K_2SO_4 | 2 | 2 NO_2 | 2 | 2 Cr_2O_3 | 5 | 5 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 K_2Cr_2O_7 | 1 | -1 | -(Δ[K2Cr2O7])/(Δt) KSCN | 2 | -2 | -1/2 (Δ[KSCN])/(Δt) H_2Cr_2O_7 | 4 | -4 | -1/4 (Δ[H2Cr2O7])/(Δt) H_2O | 4 | 4 | 1/4 (Δ[H2O])/(Δt) CO_2 | 2 | 2 | 1/2 (Δ[CO2])/(Δt) K_2SO_4 | 2 | 2 | 1/2 (Δ[K2SO4])/(Δt) NO_2 | 2 | 2 | 1/2 (Δ[NO2])/(Δt) Cr_2O_3 | 5 | 5 | 1/5 (Δ[Cr2O3])/(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 = -(Δ[K2Cr2O7])/(Δt) = -1/2 (Δ[KSCN])/(Δt) = -1/4 (Δ[H2Cr2O7])/(Δt) = 1/4 (Δ[H2O])/(Δt) = 1/2 (Δ[CO2])/(Δt) = 1/2 (Δ[K2SO4])/(Δt) = 1/2 (Δ[NO2])/(Δt) = 1/5 (Δ[Cr2O3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| potassium dichromate | potassium thiocyanate | dichromic acid | water | carbon dioxide | potassium sulfate | nitrogen dioxide | chromium(III) oxide formula | K_2Cr_2O_7 | KSCN | H_2Cr_2O_7 | H_2O | CO_2 | K_2SO_4 | NO_2 | Cr_2O_3 Hill formula | Cr_2K_2O_7 | CKNS | Cr_2H_2O_7 | H_2O | CO_2 | K_2O_4S | NO_2 | Cr_2O_3 name | potassium dichromate | potassium thiocyanate | dichromic acid | water | carbon dioxide | potassium sulfate | nitrogen dioxide | chromium(III) oxide IUPAC name | dipotassium oxido-(oxido-dioxochromio)oxy-dioxochromium | potassium isothiocyanate | hydroxy-(hydroxy-dioxo-chromio)oxy-dioxo-chromium | water | carbon dioxide | dipotassium sulfate | Nitrogen dioxide |
| potassium dichromate | potassium thiocyanate | dichromic acid | water | carbon dioxide | potassium sulfate | nitrogen dioxide | chromium(III) oxide formula | K_2Cr_2O_7 | KSCN | H_2Cr_2O_7 | H_2O | CO_2 | K_2SO_4 | NO_2 | Cr_2O_3 Hill formula | Cr_2K_2O_7 | CKNS | Cr_2H_2O_7 | H_2O | CO_2 | K_2O_4S | NO_2 | Cr_2O_3 name | potassium dichromate | potassium thiocyanate | dichromic acid | water | carbon dioxide | potassium sulfate | nitrogen dioxide | chromium(III) oxide IUPAC name | dipotassium oxido-(oxido-dioxochromio)oxy-dioxochromium | potassium isothiocyanate | hydroxy-(hydroxy-dioxo-chromio)oxy-dioxo-chromium | water | carbon dioxide | dipotassium sulfate | Nitrogen dioxide |

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