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H2O + SO2 + K2Cr2O7 = K2SO4 + CrOHSO4

Input interpretation

H_2O water + SO_2 sulfur dioxide + K_2Cr_2O_7 potassium dichromate ⟶ K_2SO_4 potassium sulfate + HO_5SCr chromium(III) hydroxide sulfate
H_2O water + SO_2 sulfur dioxide + K_2Cr_2O_7 potassium dichromate ⟶ K_2SO_4 potassium sulfate + HO_5SCr chromium(III) hydroxide sulfate

Balanced equation

Balance the chemical equation algebraically: H_2O + SO_2 + K_2Cr_2O_7 ⟶ K_2SO_4 + HO_5SCr Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 SO_2 + c_3 K_2Cr_2O_7 ⟶ c_4 K_2SO_4 + c_5 HO_5SCr Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, Cr and K: H: | 2 c_1 = c_5 O: | c_1 + 2 c_2 + 7 c_3 = 4 c_4 + 5 c_5 S: | c_2 = c_4 + c_5 Cr: | 2 c_3 = c_5 K: | 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 = 3 c_3 = 1 c_4 = 1 c_5 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | H_2O + 3 SO_2 + K_2Cr_2O_7 ⟶ K_2SO_4 + 2 HO_5SCr
Balance the chemical equation algebraically: H_2O + SO_2 + K_2Cr_2O_7 ⟶ K_2SO_4 + HO_5SCr Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 SO_2 + c_3 K_2Cr_2O_7 ⟶ c_4 K_2SO_4 + c_5 HO_5SCr Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, Cr and K: H: | 2 c_1 = c_5 O: | c_1 + 2 c_2 + 7 c_3 = 4 c_4 + 5 c_5 S: | c_2 = c_4 + c_5 Cr: | 2 c_3 = c_5 K: | 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 = 3 c_3 = 1 c_4 = 1 c_5 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | H_2O + 3 SO_2 + K_2Cr_2O_7 ⟶ K_2SO_4 + 2 HO_5SCr

Structures

+ + ⟶ +
+ + ⟶ +

Names

water + sulfur dioxide + potassium dichromate ⟶ potassium sulfate + chromium(III) hydroxide sulfate
water + sulfur dioxide + potassium dichromate ⟶ potassium sulfate + chromium(III) hydroxide sulfate

Equilibrium constant

Construct the equilibrium constant, K, expression for: H_2O + SO_2 + K_2Cr_2O_7 ⟶ K_2SO_4 + HO_5SCr 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: H_2O + 3 SO_2 + K_2Cr_2O_7 ⟶ K_2SO_4 + 2 HO_5SCr 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_2O | 1 | -1 SO_2 | 3 | -3 K_2Cr_2O_7 | 1 | -1 K_2SO_4 | 1 | 1 HO_5SCr | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 1 | -1 | ([H2O])^(-1) SO_2 | 3 | -3 | ([SO2])^(-3) K_2Cr_2O_7 | 1 | -1 | ([K2Cr2O7])^(-1) K_2SO_4 | 1 | 1 | [K2SO4] HO_5SCr | 2 | 2 | ([H1O5S1Cr1])^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 = ([H2O])^(-1) ([SO2])^(-3) ([K2Cr2O7])^(-1) [K2SO4] ([H1O5S1Cr1])^2 = ([K2SO4] ([H1O5S1Cr1])^2)/([H2O] ([SO2])^3 [K2Cr2O7])
Construct the equilibrium constant, K, expression for: H_2O + SO_2 + K_2Cr_2O_7 ⟶ K_2SO_4 + HO_5SCr 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: H_2O + 3 SO_2 + K_2Cr_2O_7 ⟶ K_2SO_4 + 2 HO_5SCr 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_2O | 1 | -1 SO_2 | 3 | -3 K_2Cr_2O_7 | 1 | -1 K_2SO_4 | 1 | 1 HO_5SCr | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 1 | -1 | ([H2O])^(-1) SO_2 | 3 | -3 | ([SO2])^(-3) K_2Cr_2O_7 | 1 | -1 | ([K2Cr2O7])^(-1) K_2SO_4 | 1 | 1 | [K2SO4] HO_5SCr | 2 | 2 | ([H1O5S1Cr1])^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 = ([H2O])^(-1) ([SO2])^(-3) ([K2Cr2O7])^(-1) [K2SO4] ([H1O5S1Cr1])^2 = ([K2SO4] ([H1O5S1Cr1])^2)/([H2O] ([SO2])^3 [K2Cr2O7])

Rate of reaction

Construct the rate of reaction expression for: H_2O + SO_2 + K_2Cr_2O_7 ⟶ K_2SO_4 + HO_5SCr 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: H_2O + 3 SO_2 + K_2Cr_2O_7 ⟶ K_2SO_4 + 2 HO_5SCr 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_2O | 1 | -1 SO_2 | 3 | -3 K_2Cr_2O_7 | 1 | -1 K_2SO_4 | 1 | 1 HO_5SCr | 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 H_2O | 1 | -1 | -(Δ[H2O])/(Δt) SO_2 | 3 | -3 | -1/3 (Δ[SO2])/(Δt) K_2Cr_2O_7 | 1 | -1 | -(Δ[K2Cr2O7])/(Δt) K_2SO_4 | 1 | 1 | (Δ[K2SO4])/(Δt) HO_5SCr | 2 | 2 | 1/2 (Δ[H1O5S1Cr1])/(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[H2O])/(Δt) = -1/3 (Δ[SO2])/(Δt) = -(Δ[K2Cr2O7])/(Δt) = (Δ[K2SO4])/(Δt) = 1/2 (Δ[H1O5S1Cr1])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: H_2O + SO_2 + K_2Cr_2O_7 ⟶ K_2SO_4 + HO_5SCr 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: H_2O + 3 SO_2 + K_2Cr_2O_7 ⟶ K_2SO_4 + 2 HO_5SCr 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_2O | 1 | -1 SO_2 | 3 | -3 K_2Cr_2O_7 | 1 | -1 K_2SO_4 | 1 | 1 HO_5SCr | 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 H_2O | 1 | -1 | -(Δ[H2O])/(Δt) SO_2 | 3 | -3 | -1/3 (Δ[SO2])/(Δt) K_2Cr_2O_7 | 1 | -1 | -(Δ[K2Cr2O7])/(Δt) K_2SO_4 | 1 | 1 | (Δ[K2SO4])/(Δt) HO_5SCr | 2 | 2 | 1/2 (Δ[H1O5S1Cr1])/(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[H2O])/(Δt) = -1/3 (Δ[SO2])/(Δt) = -(Δ[K2Cr2O7])/(Δt) = (Δ[K2SO4])/(Δt) = 1/2 (Δ[H1O5S1Cr1])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| water | sulfur dioxide | potassium dichromate | potassium sulfate | chromium(III) hydroxide sulfate formula | H_2O | SO_2 | K_2Cr_2O_7 | K_2SO_4 | HO_5SCr Hill formula | H_2O | O_2S | Cr_2K_2O_7 | K_2O_4S | CrHO_5S name | water | sulfur dioxide | potassium dichromate | potassium sulfate | chromium(III) hydroxide sulfate IUPAC name | water | sulfur dioxide | dipotassium oxido-(oxido-dioxochromio)oxy-dioxochromium | dipotassium sulfate | chromium(3+) hydroxide sulfate
| water | sulfur dioxide | potassium dichromate | potassium sulfate | chromium(III) hydroxide sulfate formula | H_2O | SO_2 | K_2Cr_2O_7 | K_2SO_4 | HO_5SCr Hill formula | H_2O | O_2S | Cr_2K_2O_7 | K_2O_4S | CrHO_5S name | water | sulfur dioxide | potassium dichromate | potassium sulfate | chromium(III) hydroxide sulfate IUPAC name | water | sulfur dioxide | dipotassium oxido-(oxido-dioxochromio)oxy-dioxochromium | dipotassium sulfate | chromium(3+) hydroxide sulfate

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