NaOH + H2O2 + CrCl3 = H2O + O2 + NaCl + Na2CrO4

NaOH sodium hydroxide + H_2O_2 hydrogen peroxide + CrCl_3 chromic chloride ⟶ H_2O water + O_2 oxygen + NaCl sodium chloride + Na_2CrO_4 sodium chromate

Balance the chemical equation algebraically: NaOH + H_2O_2 + CrCl_3 ⟶ H_2O + O_2 + NaCl + Na_2CrO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 NaOH + c_2 H_2O_2 + c_3 CrCl_3 ⟶ c_4 H_2O + c_5 O_2 + c_6 NaCl + c_7 Na_2CrO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, Na, O, Cl and Cr: H: | c_1 + 2 c_2 = 2 c_4 Na: | c_1 = c_6 + 2 c_7 O: | c_1 + 2 c_2 = c_4 + 2 c_5 + 4 c_7 Cl: | 3 c_3 = c_6 Cr: | c_3 = c_7 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_5 = 1 and solve the system of equations for the remaining coefficients: c_2 = (3 c_1)/10 + 2 c_3 = c_1/5 c_4 = (4 c_1)/5 + 2 c_5 = 1 c_6 = (3 c_1)/5 c_7 = c_1/5 The resulting system of equations is still underdetermined, so an additional coefficient must be set arbitrarily. Set c_1 = 10 and solve for the remaining coefficients: c_1 = 10 c_2 = 5 c_3 = 2 c_4 = 10 c_5 = 1 c_6 = 6 c_7 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 10 NaOH + 5 H_2O_2 + 2 CrCl_3 ⟶ 10 H_2O + O_2 + 6 NaCl + 2 Na_2CrO_4

+ + ⟶ + + +

sodium hydroxide + hydrogen peroxide + chromic chloride ⟶ water + oxygen + sodium chloride + sodium chromate

Construct the equilibrium constant, K, expression for: NaOH + H_2O_2 + CrCl_3 ⟶ H_2O + O_2 + NaCl + 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: 10 NaOH + 5 H_2O_2 + 2 CrCl_3 ⟶ 10 H_2O + O_2 + 6 NaCl + 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 NaOH | 10 | -10 H_2O_2 | 5 | -5 CrCl_3 | 2 | -2 H_2O | 10 | 10 O_2 | 1 | 1 NaCl | 6 | 6 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 NaOH | 10 | -10 | ([NaOH])^(-10) H_2O_2 | 5 | -5 | ([H2O2])^(-5) CrCl_3 | 2 | -2 | ([CrCl3])^(-2) H_2O | 10 | 10 | ([H2O])^10 O_2 | 1 | 1 | [O2] NaCl | 6 | 6 | ([NaCl])^6 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 = ([NaOH])^(-10) ([H2O2])^(-5) ([CrCl3])^(-2) ([H2O])^10 [O2] ([NaCl])^6 ([Na2CrO4])^2 = (([H2O])^10 [O2] ([NaCl])^6 ([Na2CrO4])^2)/(([NaOH])^10 ([H2O2])^5 ([CrCl3])^2)

Construct the rate of reaction expression for: NaOH + H_2O_2 + CrCl_3 ⟶ H_2O + O_2 + NaCl + 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: 10 NaOH + 5 H_2O_2 + 2 CrCl_3 ⟶ 10 H_2O + O_2 + 6 NaCl + 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 NaOH | 10 | -10 H_2O_2 | 5 | -5 CrCl_3 | 2 | -2 H_2O | 10 | 10 O_2 | 1 | 1 NaCl | 6 | 6 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 NaOH | 10 | -10 | -1/10 (Δ[NaOH])/(Δt) H_2O_2 | 5 | -5 | -1/5 (Δ[H2O2])/(Δt) CrCl_3 | 2 | -2 | -1/2 (Δ[CrCl3])/(Δt) H_2O | 10 | 10 | 1/10 (Δ[H2O])/(Δt) O_2 | 1 | 1 | (Δ[O2])/(Δt) NaCl | 6 | 6 | 1/6 (Δ[NaCl])/(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 = -1/10 (Δ[NaOH])/(Δt) = -1/5 (Δ[H2O2])/(Δt) = -1/2 (Δ[CrCl3])/(Δt) = 1/10 (Δ[H2O])/(Δt) = (Δ[O2])/(Δt) = 1/6 (Δ[NaCl])/(Δt) = 1/2 (Δ[Na2CrO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sodium hydroxide | hydrogen peroxide | chromic chloride | water | oxygen | sodium chloride | sodium chromate formula | NaOH | H_2O_2 | CrCl_3 | H_2O | O_2 | NaCl | Na_2CrO_4 Hill formula | HNaO | H_2O_2 | Cl_3Cr | H_2O | O_2 | ClNa | CrNa_2O_4 name | sodium hydroxide | hydrogen peroxide | chromic chloride | water | oxygen | sodium chloride | sodium chromate IUPAC name | sodium hydroxide | hydrogen peroxide | trichlorochromium | water | molecular oxygen | sodium chloride | disodium dioxido(dioxo)chromium

| sodium hydroxide | hydrogen peroxide | chromic chloride | water | oxygen | sodium chloride | sodium chromate molar mass | 39.997 g/mol | 34.014 g/mol | 158.3 g/mol | 18.015 g/mol | 31.998 g/mol | 58.44 g/mol | 161.97 g/mol phase | solid (at STP) | liquid (at STP) | solid (at STP) | liquid (at STP) | gas (at STP) | solid (at STP) | solid (at STP) melting point | 323 °C | -0.43 °C | 1152 °C | 0 °C | -218 °C | 801 °C | 780 °C boiling point | 1390 °C | 150.2 °C | | 99.9839 °C | -183 °C | 1413 °C | density | 2.13 g/cm^3 | 1.44 g/cm^3 | 2.87 g/cm^3 | 1 g/cm^3 | 0.001429 g/cm^3 (at 0 °C) | 2.16 g/cm^3 | 2.698 g/cm^3 solubility in water | soluble | miscible | slightly soluble | | | soluble | surface tension | 0.07435 N/m | 0.0804 N/m | | 0.0728 N/m | 0.01347 N/m | | dynamic viscosity | 0.004 Pa s (at 350 °C) | 0.001249 Pa s (at 20 °C) | | 8.9×10^-4 Pa s (at 25 °C) | 2.055×10^-5 Pa s (at 25 °C) | | odor | | | | odorless | odorless | odorless |