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H2O + S + Na2Cr2O7 = NaOH + SO2 + Cr2O3

Input interpretation

H_2O water + S mixed sulfur + Na_2Cr_2O_7 sodium bichromate ⟶ NaOH sodium hydroxide + SO_2 sulfur dioxide + Cr_2O_3 chromium(III) oxide
H_2O water + S mixed sulfur + Na_2Cr_2O_7 sodium bichromate ⟶ NaOH sodium hydroxide + SO_2 sulfur dioxide + Cr_2O_3 chromium(III) oxide

Balanced equation

Balance the chemical equation algebraically: H_2O + S + Na_2Cr_2O_7 ⟶ NaOH + SO_2 + Cr_2O_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 S + c_3 Na_2Cr_2O_7 ⟶ c_4 NaOH + c_5 SO_2 + c_6 Cr_2O_3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, Cr and Na: H: | 2 c_1 = c_4 O: | c_1 + 7 c_3 = c_4 + 2 c_5 + 3 c_6 S: | c_2 = c_5 Cr: | 2 c_3 = 2 c_6 Na: | 2 c_3 = 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 = 3/2 c_3 = 1 c_4 = 2 c_5 = 3/2 c_6 = 1 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 2 c_2 = 3 c_3 = 2 c_4 = 4 c_5 = 3 c_6 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 H_2O + 3 S + 2 Na_2Cr_2O_7 ⟶ 4 NaOH + 3 SO_2 + 2 Cr_2O_3
Balance the chemical equation algebraically: H_2O + S + Na_2Cr_2O_7 ⟶ NaOH + SO_2 + Cr_2O_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 S + c_3 Na_2Cr_2O_7 ⟶ c_4 NaOH + c_5 SO_2 + c_6 Cr_2O_3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S, Cr and Na: H: | 2 c_1 = c_4 O: | c_1 + 7 c_3 = c_4 + 2 c_5 + 3 c_6 S: | c_2 = c_5 Cr: | 2 c_3 = 2 c_6 Na: | 2 c_3 = 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 = 3/2 c_3 = 1 c_4 = 2 c_5 = 3/2 c_6 = 1 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 2 c_2 = 3 c_3 = 2 c_4 = 4 c_5 = 3 c_6 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 H_2O + 3 S + 2 Na_2Cr_2O_7 ⟶ 4 NaOH + 3 SO_2 + 2 Cr_2O_3

Structures

+ + ⟶ + +
+ + ⟶ + +

Names

water + mixed sulfur + sodium bichromate ⟶ sodium hydroxide + sulfur dioxide + chromium(III) oxide
water + mixed sulfur + sodium bichromate ⟶ sodium hydroxide + sulfur dioxide + chromium(III) oxide

Equilibrium constant

Construct the equilibrium constant, K, expression for: H_2O + S + Na_2Cr_2O_7 ⟶ NaOH + SO_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: 2 H_2O + 3 S + 2 Na_2Cr_2O_7 ⟶ 4 NaOH + 3 SO_2 + 2 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 H_2O | 2 | -2 S | 3 | -3 Na_2Cr_2O_7 | 2 | -2 NaOH | 4 | 4 SO_2 | 3 | 3 Cr_2O_3 | 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 | 2 | -2 | ([H2O])^(-2) S | 3 | -3 | ([S])^(-3) Na_2Cr_2O_7 | 2 | -2 | ([Na2Cr2O7])^(-2) NaOH | 4 | 4 | ([NaOH])^4 SO_2 | 3 | 3 | ([SO2])^3 Cr_2O_3 | 2 | 2 | ([Cr2O3])^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])^(-2) ([S])^(-3) ([Na2Cr2O7])^(-2) ([NaOH])^4 ([SO2])^3 ([Cr2O3])^2 = (([NaOH])^4 ([SO2])^3 ([Cr2O3])^2)/(([H2O])^2 ([S])^3 ([Na2Cr2O7])^2)
Construct the equilibrium constant, K, expression for: H_2O + S + Na_2Cr_2O_7 ⟶ NaOH + SO_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: 2 H_2O + 3 S + 2 Na_2Cr_2O_7 ⟶ 4 NaOH + 3 SO_2 + 2 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 H_2O | 2 | -2 S | 3 | -3 Na_2Cr_2O_7 | 2 | -2 NaOH | 4 | 4 SO_2 | 3 | 3 Cr_2O_3 | 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 | 2 | -2 | ([H2O])^(-2) S | 3 | -3 | ([S])^(-3) Na_2Cr_2O_7 | 2 | -2 | ([Na2Cr2O7])^(-2) NaOH | 4 | 4 | ([NaOH])^4 SO_2 | 3 | 3 | ([SO2])^3 Cr_2O_3 | 2 | 2 | ([Cr2O3])^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])^(-2) ([S])^(-3) ([Na2Cr2O7])^(-2) ([NaOH])^4 ([SO2])^3 ([Cr2O3])^2 = (([NaOH])^4 ([SO2])^3 ([Cr2O3])^2)/(([H2O])^2 ([S])^3 ([Na2Cr2O7])^2)

Rate of reaction

Construct the rate of reaction expression for: H_2O + S + Na_2Cr_2O_7 ⟶ NaOH + SO_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: 2 H_2O + 3 S + 2 Na_2Cr_2O_7 ⟶ 4 NaOH + 3 SO_2 + 2 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 H_2O | 2 | -2 S | 3 | -3 Na_2Cr_2O_7 | 2 | -2 NaOH | 4 | 4 SO_2 | 3 | 3 Cr_2O_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 H_2O | 2 | -2 | -1/2 (Δ[H2O])/(Δt) S | 3 | -3 | -1/3 (Δ[S])/(Δt) Na_2Cr_2O_7 | 2 | -2 | -1/2 (Δ[Na2Cr2O7])/(Δt) NaOH | 4 | 4 | 1/4 (Δ[NaOH])/(Δt) SO_2 | 3 | 3 | 1/3 (Δ[SO2])/(Δt) Cr_2O_3 | 2 | 2 | 1/2 (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 = -1/2 (Δ[H2O])/(Δt) = -1/3 (Δ[S])/(Δt) = -1/2 (Δ[Na2Cr2O7])/(Δt) = 1/4 (Δ[NaOH])/(Δt) = 1/3 (Δ[SO2])/(Δt) = 1/2 (Δ[Cr2O3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Construct the rate of reaction expression for: H_2O + S + Na_2Cr_2O_7 ⟶ NaOH + SO_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: 2 H_2O + 3 S + 2 Na_2Cr_2O_7 ⟶ 4 NaOH + 3 SO_2 + 2 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 H_2O | 2 | -2 S | 3 | -3 Na_2Cr_2O_7 | 2 | -2 NaOH | 4 | 4 SO_2 | 3 | 3 Cr_2O_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 H_2O | 2 | -2 | -1/2 (Δ[H2O])/(Δt) S | 3 | -3 | -1/3 (Δ[S])/(Δt) Na_2Cr_2O_7 | 2 | -2 | -1/2 (Δ[Na2Cr2O7])/(Δt) NaOH | 4 | 4 | 1/4 (Δ[NaOH])/(Δt) SO_2 | 3 | 3 | 1/3 (Δ[SO2])/(Δt) Cr_2O_3 | 2 | 2 | 1/2 (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 = -1/2 (Δ[H2O])/(Δt) = -1/3 (Δ[S])/(Δt) = -1/2 (Δ[Na2Cr2O7])/(Δt) = 1/4 (Δ[NaOH])/(Δt) = 1/3 (Δ[SO2])/(Δt) = 1/2 (Δ[Cr2O3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

Chemical names and formulas

| water | mixed sulfur | sodium bichromate | sodium hydroxide | sulfur dioxide | chromium(III) oxide formula | H_2O | S | Na_2Cr_2O_7 | NaOH | SO_2 | Cr_2O_3 Hill formula | H_2O | S | Cr_2Na_2O_7 | HNaO | O_2S | Cr_2O_3 name | water | mixed sulfur | sodium bichromate | sodium hydroxide | sulfur dioxide | chromium(III) oxide IUPAC name | water | sulfur | disodium oxido-(oxido-dioxo-chromio)oxy-dioxo-chromium | sodium hydroxide | sulfur dioxide |
| water | mixed sulfur | sodium bichromate | sodium hydroxide | sulfur dioxide | chromium(III) oxide formula | H_2O | S | Na_2Cr_2O_7 | NaOH | SO_2 | Cr_2O_3 Hill formula | H_2O | S | Cr_2Na_2O_7 | HNaO | O_2S | Cr_2O_3 name | water | mixed sulfur | sodium bichromate | sodium hydroxide | sulfur dioxide | chromium(III) oxide IUPAC name | water | sulfur | disodium oxido-(oxido-dioxo-chromio)oxy-dioxo-chromium | sodium hydroxide | sulfur dioxide |

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