H2O + O2 + Cr(OH)2 = Cr(OH)3

H_2O water + O_2 oxygen + Cr(OH)2 ⟶ Cr(OH)3

Balance the chemical equation algebraically: H_2O + O_2 + Cr(OH)2 ⟶ Cr(OH)3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 O_2 + c_3 Cr(OH)2 ⟶ c_4 Cr(OH)3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O and Cr: H: | 2 c_1 + 2 c_3 = 3 c_4 O: | c_1 + 2 c_2 + 2 c_3 = 3 c_4 Cr: | 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 1 c_3 = 4 c_4 = 4 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 H_2O + O_2 + 4 Cr(OH)2 ⟶ 4 Cr(OH)3

+ + Cr(OH)2 ⟶ Cr(OH)3

water + oxygen + Cr(OH)2 ⟶ Cr(OH)3

Construct the equilibrium constant, K, expression for: H_2O + O_2 + Cr(OH)2 ⟶ Cr(OH)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 + O_2 + 4 Cr(OH)2 ⟶ 4 Cr(OH)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 O_2 | 1 | -1 Cr(OH)2 | 4 | -4 Cr(OH)3 | 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 | 2 | -2 | ([H2O])^(-2) O_2 | 1 | -1 | ([O2])^(-1) Cr(OH)2 | 4 | -4 | ([Cr(OH)2])^(-4) Cr(OH)3 | 4 | 4 | ([Cr(OH)3])^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])^(-2) ([O2])^(-1) ([Cr(OH)2])^(-4) ([Cr(OH)3])^4 = ([Cr(OH)3])^4/(([H2O])^2 [O2] ([Cr(OH)2])^4)

Construct the rate of reaction expression for: H_2O + O_2 + Cr(OH)2 ⟶ Cr(OH)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 + O_2 + 4 Cr(OH)2 ⟶ 4 Cr(OH)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 O_2 | 1 | -1 Cr(OH)2 | 4 | -4 Cr(OH)3 | 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 | 2 | -2 | -1/2 (Δ[H2O])/(Δt) O_2 | 1 | -1 | -(Δ[O2])/(Δt) Cr(OH)2 | 4 | -4 | -1/4 (Δ[Cr(OH)2])/(Δt) Cr(OH)3 | 4 | 4 | 1/4 (Δ[Cr(OH)3])/(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) = -(Δ[O2])/(Δt) = -1/4 (Δ[Cr(OH)2])/(Δt) = 1/4 (Δ[Cr(OH)3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | oxygen | Cr(OH)2 | Cr(OH)3 formula | H_2O | O_2 | Cr(OH)2 | Cr(OH)3 Hill formula | H_2O | O_2 | H2CrO2 | H3CrO3 name | water | oxygen | | IUPAC name | water | molecular oxygen | |

| water | oxygen | Cr(OH)2 | Cr(OH)3 molar mass | 18.015 g/mol | 31.998 g/mol | 86.01 g/mol | 103.02 g/mol phase | liquid (at STP) | gas (at STP) | | melting point | 0 °C | -218 °C | | boiling point | 99.9839 °C | -183 °C | | density | 1 g/cm^3 | 0.001429 g/cm^3 (at 0 °C) | | surface tension | 0.0728 N/m | 0.01347 N/m | | dynamic viscosity | 8.9×10^-4 Pa s (at 25 °C) | 2.055×10^-5 Pa s (at 25 °C) | | odor | odorless | odorless | |