H2O2 + Na3CrO3 = H2O + NaOH + Na2CrO4

H_2O_2 hydrogen peroxide + Na3CrO3 ⟶ H_2O water + NaOH sodium hydroxide + Na_2CrO_4 sodium chromate

Balance the chemical equation algebraically: H_2O_2 + Na3CrO3 ⟶ H_2O + NaOH + Na_2CrO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O_2 + c_2 Na3CrO3 ⟶ c_3 H_2O + c_4 NaOH + c_5 Na_2CrO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, Na and Cr: H: | 2 c_1 = 2 c_3 + c_4 O: | 2 c_1 + 3 c_2 = c_3 + c_4 + 4 c_5 Na: | 3 c_2 = c_4 + 2 c_5 Cr: | c_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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3/2 c_2 = 1 c_3 = 1 c_4 = 1 c_5 = 1 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 3 c_2 = 2 c_3 = 2 c_4 = 2 c_5 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 3 H_2O_2 + 2 Na3CrO3 ⟶ 2 H_2O + 2 NaOH + 2 Na_2CrO_4

+ Na3CrO3 ⟶ + +

hydrogen peroxide + Na3CrO3 ⟶ water + sodium hydroxide + sodium chromate

Construct the equilibrium constant, K, expression for: H_2O_2 + Na3CrO3 ⟶ H_2O + NaOH + Na_2CrO_4 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 H_2O_2 + 2 Na3CrO3 ⟶ 2 H_2O + 2 NaOH + 2 Na_2CrO_4 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 | 3 | -3 Na3CrO3 | 2 | -2 H_2O | 2 | 2 NaOH | 2 | 2 Na_2CrO_4 | 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 | 3 | -3 | ([H2O2])^(-3) Na3CrO3 | 2 | -2 | ([Na3CrO3])^(-2) H_2O | 2 | 2 | ([H2O])^2 NaOH | 2 | 2 | ([NaOH])^2 Na_2CrO_4 | 2 | 2 | ([Na2CrO4])^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 = ([H2O2])^(-3) ([Na3CrO3])^(-2) ([H2O])^2 ([NaOH])^2 ([Na2CrO4])^2 = (([H2O])^2 ([NaOH])^2 ([Na2CrO4])^2)/(([H2O2])^3 ([Na3CrO3])^2)

Construct the rate of reaction expression for: H_2O_2 + Na3CrO3 ⟶ H_2O + NaOH + Na_2CrO_4 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 H_2O_2 + 2 Na3CrO3 ⟶ 2 H_2O + 2 NaOH + 2 Na_2CrO_4 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 | 3 | -3 Na3CrO3 | 2 | -2 H_2O | 2 | 2 NaOH | 2 | 2 Na_2CrO_4 | 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 | 3 | -3 | -1/3 (Δ[H2O2])/(Δt) Na3CrO3 | 2 | -2 | -1/2 (Δ[Na3CrO3])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(Δt) NaOH | 2 | 2 | 1/2 (Δ[NaOH])/(Δt) Na_2CrO_4 | 2 | 2 | 1/2 (Δ[Na2CrO4])/(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[H2O2])/(Δt) = -1/2 (Δ[Na3CrO3])/(Δt) = 1/2 (Δ[H2O])/(Δt) = 1/2 (Δ[NaOH])/(Δt) = 1/2 (Δ[Na2CrO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| hydrogen peroxide | Na3CrO3 | water | sodium hydroxide | sodium chromate formula | H_2O_2 | Na3CrO3 | H_2O | NaOH | Na_2CrO_4 Hill formula | H_2O_2 | CrNa3O3 | H_2O | HNaO | CrNa_2O_4 name | hydrogen peroxide | | water | sodium hydroxide | sodium chromate IUPAC name | hydrogen peroxide | | water | sodium hydroxide | disodium dioxido(dioxo)chromium

| hydrogen peroxide | Na3CrO3 | water | sodium hydroxide | sodium chromate molar mass | 34.014 g/mol | 168.962 g/mol | 18.015 g/mol | 39.997 g/mol | 161.97 g/mol phase | liquid (at STP) | | liquid (at STP) | solid (at STP) | solid (at STP) melting point | -0.43 °C | | 0 °C | 323 °C | 780 °C boiling point | 150.2 °C | | 99.9839 °C | 1390 °C | density | 1.44 g/cm^3 | | 1 g/cm^3 | 2.13 g/cm^3 | 2.698 g/cm^3 solubility in water | miscible | | | soluble | surface tension | 0.0804 N/m | | 0.0728 N/m | 0.07435 N/m | dynamic viscosity | 0.001249 Pa s (at 20 °C) | | 8.9×10^-4 Pa s (at 25 °C) | 0.004 Pa s (at 350 °C) | odor | | | odorless | |