H2O + Na2SO3 + Na2CrO4 = Na2SO4 + Cr(OH)3 + Na(OH)

H_2O water + Na_2SO_3 sodium sulfite + Na_2CrO_4 sodium chromate ⟶ Na_2SO_4 sodium sulfate + Cr(OH)3 + NaOH sodium hydroxide

Balance the chemical equation algebraically: H_2O + Na_2SO_3 + Na_2CrO_4 ⟶ Na_2SO_4 + Cr(OH)3 + NaOH Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 Na_2SO_3 + c_3 Na_2CrO_4 ⟶ c_4 Na_2SO_4 + c_5 Cr(OH)3 + c_6 NaOH Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, Na, S and Cr: H: | 2 c_1 = 3 c_5 + c_6 O: | c_1 + 3 c_2 + 4 c_3 = 4 c_4 + 3 c_5 + c_6 Na: | 2 c_2 + 2 c_3 = 2 c_4 + c_6 S: | c_2 = c_4 Cr: | c_3 = 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 5/2 c_2 = 3/2 c_3 = 1 c_4 = 3/2 c_5 = 1 c_6 = 2 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 5 c_2 = 3 c_3 = 2 c_4 = 3 c_5 = 2 c_6 = 4 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 5 H_2O + 3 Na_2SO_3 + 2 Na_2CrO_4 ⟶ 3 Na_2SO_4 + 2 Cr(OH)3 + 4 NaOH

+ + ⟶ + Cr(OH)3 +

water + sodium sulfite + sodium chromate ⟶ sodium sulfate + Cr(OH)3 + sodium hydroxide

Construct the equilibrium constant, K, expression for: H_2O + Na_2SO_3 + Na_2CrO_4 ⟶ Na_2SO_4 + Cr(OH)3 + NaOH 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: 5 H_2O + 3 Na_2SO_3 + 2 Na_2CrO_4 ⟶ 3 Na_2SO_4 + 2 Cr(OH)3 + 4 NaOH 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 | 5 | -5 Na_2SO_3 | 3 | -3 Na_2CrO_4 | 2 | -2 Na_2SO_4 | 3 | 3 Cr(OH)3 | 2 | 2 NaOH | 4 | 4 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 5 | -5 | ([H2O])^(-5) Na_2SO_3 | 3 | -3 | ([Na2SO3])^(-3) Na_2CrO_4 | 2 | -2 | ([Na2CrO4])^(-2) Na_2SO_4 | 3 | 3 | ([Na2SO4])^3 Cr(OH)3 | 2 | 2 | ([Cr(OH)3])^2 NaOH | 4 | 4 | ([NaOH])^4 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])^(-5) ([Na2SO3])^(-3) ([Na2CrO4])^(-2) ([Na2SO4])^3 ([Cr(OH)3])^2 ([NaOH])^4 = (([Na2SO4])^3 ([Cr(OH)3])^2 ([NaOH])^4)/(([H2O])^5 ([Na2SO3])^3 ([Na2CrO4])^2)

Construct the rate of reaction expression for: H_2O + Na_2SO_3 + Na_2CrO_4 ⟶ Na_2SO_4 + Cr(OH)3 + NaOH 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: 5 H_2O + 3 Na_2SO_3 + 2 Na_2CrO_4 ⟶ 3 Na_2SO_4 + 2 Cr(OH)3 + 4 NaOH 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 | 5 | -5 Na_2SO_3 | 3 | -3 Na_2CrO_4 | 2 | -2 Na_2SO_4 | 3 | 3 Cr(OH)3 | 2 | 2 NaOH | 4 | 4 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 | 5 | -5 | -1/5 (Δ[H2O])/(Δt) Na_2SO_3 | 3 | -3 | -1/3 (Δ[Na2SO3])/(Δt) Na_2CrO_4 | 2 | -2 | -1/2 (Δ[Na2CrO4])/(Δt) Na_2SO_4 | 3 | 3 | 1/3 (Δ[Na2SO4])/(Δt) Cr(OH)3 | 2 | 2 | 1/2 (Δ[Cr(OH)3])/(Δt) NaOH | 4 | 4 | 1/4 (Δ[NaOH])/(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 = -1/5 (Δ[H2O])/(Δt) = -1/3 (Δ[Na2SO3])/(Δt) = -1/2 (Δ[Na2CrO4])/(Δt) = 1/3 (Δ[Na2SO4])/(Δt) = 1/2 (Δ[Cr(OH)3])/(Δt) = 1/4 (Δ[NaOH])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | sodium sulfite | sodium chromate | sodium sulfate | Cr(OH)3 | sodium hydroxide formula | H_2O | Na_2SO_3 | Na_2CrO_4 | Na_2SO_4 | Cr(OH)3 | NaOH Hill formula | H_2O | Na_2O_3S | CrNa_2O_4 | Na_2O_4S | H3CrO3 | HNaO name | water | sodium sulfite | sodium chromate | sodium sulfate | | sodium hydroxide IUPAC name | water | disodium sulfite | disodium dioxido(dioxo)chromium | disodium sulfate | | sodium hydroxide

| water | sodium sulfite | sodium chromate | sodium sulfate | Cr(OH)3 | sodium hydroxide molar mass | 18.015 g/mol | 126.04 g/mol | 161.97 g/mol | 142.04 g/mol | 103.02 g/mol | 39.997 g/mol phase | liquid (at STP) | solid (at STP) | solid (at STP) | solid (at STP) | | solid (at STP) melting point | 0 °C | 500 °C | 780 °C | 884 °C | | 323 °C boiling point | 99.9839 °C | | | 1429 °C | | 1390 °C density | 1 g/cm^3 | 2.63 g/cm^3 | 2.698 g/cm^3 | 2.68 g/cm^3 | | 2.13 g/cm^3 solubility in water | | | | soluble | | soluble surface tension | 0.0728 N/m | | | | | 0.07435 N/m dynamic viscosity | 8.9×10^-4 Pa s (at 25 °C) | | | | | 0.004 Pa s (at 350 °C) odor | odorless | | | | |