NaOH + H2O2 + Hg(NO3)2 = H2O + O2 + NaNO3 + Hg

NaOH (sodium hydroxide) + H_2O_2 (hydrogen peroxide) + Hg(NO_3)_2 (mercury(II) nitrate) ⟶ H_2O (water) + O_2 (oxygen) + NaNO_3 (sodium nitrate) + Hg (mercury)

Balance the chemical equation algebraically: NaOH + H_2O_2 + Hg(NO_3)_2 ⟶ H_2O + O_2 + NaNO_3 + Hg Add stoichiometric coefficients, c_i, to the reactants and products: c_1 NaOH + c_2 H_2O_2 + c_3 Hg(NO_3)_2 ⟶ c_4 H_2O + c_5 O_2 + c_6 NaNO_3 + c_7 Hg Set the number of atoms in the reactants equal to the number of atoms in the products for H, Na, O, Hg and N: H: | c_1 + 2 c_2 = 2 c_4 Na: | c_1 = c_6 O: | c_1 + 2 c_2 + 6 c_3 = c_4 + 2 c_5 + 3 c_6 Hg: | c_3 = c_7 N: | 2 c_3 = c_6 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_2 = 1 c_3 = c_1/2 c_4 = c_1/2 + 1 c_5 = c_1/4 + 1/2 c_6 = c_1 c_7 = c_1/2 The resulting system of equations is still underdetermined, so an additional coefficient must be set arbitrarily. Set c_1 = 2 and solve for the remaining coefficients: c_1 = 2 c_2 = 1 c_3 = 1 c_4 = 2 c_5 = 1 c_6 = 2 c_7 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 NaOH + H_2O_2 + Hg(NO_3)_2 ⟶ 2 H_2O + O_2 + 2 NaNO_3 + Hg

+ + ⟶ + + +

sodium hydroxide + hydrogen peroxide + mercury(II) nitrate ⟶ water + oxygen + sodium nitrate + mercury

Construct the equilibrium constant, K, expression for: NaOH + H_2O_2 + Hg(NO_3)_2 ⟶ H_2O + O_2 + NaNO_3 + Hg 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 NaOH + H_2O_2 + Hg(NO_3)_2 ⟶ 2 H_2O + O_2 + 2 NaNO_3 + Hg 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 | 2 | -2 H_2O_2 | 1 | -1 Hg(NO_3)_2 | 1 | -1 H_2O | 2 | 2 O_2 | 1 | 1 NaNO_3 | 2 | 2 Hg | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression NaOH | 2 | -2 | ([NaOH])^(-2) H_2O_2 | 1 | -1 | ([H2O2])^(-1) Hg(NO_3)_2 | 1 | -1 | ([Hg(NO3)2])^(-1) H_2O | 2 | 2 | ([H2O])^2 O_2 | 1 | 1 | [O2] NaNO_3 | 2 | 2 | ([NaNO3])^2 Hg | 1 | 1 | [Hg] 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])^(-2) ([H2O2])^(-1) ([Hg(NO3)2])^(-1) ([H2O])^2 [O2] ([NaNO3])^2 [Hg] = (([H2O])^2 [O2] ([NaNO3])^2 [Hg])/(([NaOH])^2 [H2O2] [Hg(NO3)2])

Construct the rate of reaction expression for: NaOH + H_2O_2 + Hg(NO_3)_2 ⟶ H_2O + O_2 + NaNO_3 + Hg 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 NaOH + H_2O_2 + Hg(NO_3)_2 ⟶ 2 H_2O + O_2 + 2 NaNO_3 + Hg 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 | 2 | -2 H_2O_2 | 1 | -1 Hg(NO_3)_2 | 1 | -1 H_2O | 2 | 2 O_2 | 1 | 1 NaNO_3 | 2 | 2 Hg | 1 | 1 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 | 2 | -2 | -1/2 (Δ[NaOH])/(Δt) H_2O_2 | 1 | -1 | -(Δ[H2O2])/(Δt) Hg(NO_3)_2 | 1 | -1 | -(Δ[Hg(NO3)2])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(Δt) O_2 | 1 | 1 | (Δ[O2])/(Δt) NaNO_3 | 2 | 2 | 1/2 (Δ[NaNO3])/(Δt) Hg | 1 | 1 | (Δ[Hg])/(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[NaOH])/(Δt) = -(Δ[H2O2])/(Δt) = -(Δ[Hg(NO3)2])/(Δt) = 1/2 (Δ[H2O])/(Δt) = (Δ[O2])/(Δt) = 1/2 (Δ[NaNO3])/(Δt) = (Δ[Hg])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sodium hydroxide | hydrogen peroxide | mercury(II) nitrate | water | oxygen | sodium nitrate | mercury formula | NaOH | H_2O_2 | Hg(NO_3)_2 | H_2O | O_2 | NaNO_3 | Hg Hill formula | HNaO | H_2O_2 | HgN_2O_6 | H_2O | O_2 | NNaO_3 | Hg name | sodium hydroxide | hydrogen peroxide | mercury(II) nitrate | water | oxygen | sodium nitrate | mercury IUPAC name | sodium hydroxide | hydrogen peroxide | mercury(+2) cation dinitrate | water | molecular oxygen | sodium nitrate | mercury