KOH + Hg2(NO3)2 = H2O + KNO3 + Hg + HgO

Input interpretation

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KOH potassium hydroxide + Hg_2(NO_3)_2 mercury(I) nitrate ⟶ H_2O water + KNO_3 potassium nitrate + Hg mercury + HgO mercuric oxide

Balanced equation

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Balance the chemical equation algebraically: KOH + Hg_2(NO_3)_2 ⟶ H_2O + KNO_3 + Hg + HgO Add stoichiometric coefficients, c_i, to the reactants and products: c_1 KOH + c_2 Hg_2(NO_3)_2 ⟶ c_3 H_2O + c_4 KNO_3 + c_5 Hg + c_6 HgO Set the number of atoms in the reactants equal to the number of atoms in the products for H, K, O, Hg and N: H: | c_1 = 2 c_3 K: | c_1 = c_4 O: | c_1 + 3 c_2 = c_3 + 3 c_4 + c_6 Hg: | c_2 = c_5 + c_6 N: | c_2 = 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 2 c_3 = 1 c_4 = 2 c_5 = 1 c_6 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 KOH + 2 Hg_2(NO_3)_2 ⟶ H_2O + 2 KNO_3 + Hg + HgO

+ ⟶ + + +

Names

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potassium hydroxide + mercury(I) nitrate ⟶ water + potassium nitrate + mercury + mercuric oxide

Equilibrium constant

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Construct the equilibrium constant, K, expression for: KOH + Hg_2(NO_3)_2 ⟶ H_2O + KNO_3 + Hg + HgO 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 KOH + 2 Hg_2(NO_3)_2 ⟶ H_2O + 2 KNO_3 + Hg + HgO 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 KOH | 2 | -2 Hg_2(NO_3)_2 | 2 | -2 H_2O | 1 | 1 KNO_3 | 2 | 2 Hg | 1 | 1 HgO | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression KOH | 2 | -2 | ([KOH])^(-2) Hg_2(NO_3)_2 | 2 | -2 | ([Hg2(NO3)2])^(-2) H_2O | 1 | 1 | [H2O] KNO_3 | 2 | 2 | ([KNO3])^2 Hg | 1 | 1 | [Hg] HgO | 1 | 1 | [HgO] 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 = ([KOH])^(-2) ([Hg2(NO3)2])^(-2) [H2O] ([KNO3])^2 [Hg] [HgO] = ([H2O] ([KNO3])^2 [Hg] [HgO])/(([KOH])^2 ([Hg2(NO3)2])^2)

Rate of reaction

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Construct the rate of reaction expression for: KOH + Hg_2(NO_3)_2 ⟶ H_2O + KNO_3 + Hg + HgO 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 KOH + 2 Hg_2(NO_3)_2 ⟶ H_2O + 2 KNO_3 + Hg + HgO 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 KOH | 2 | -2 Hg_2(NO_3)_2 | 2 | -2 H_2O | 1 | 1 KNO_3 | 2 | 2 Hg | 1 | 1 HgO | 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 KOH | 2 | -2 | -1/2 (Δ[KOH])/(Δt) Hg_2(NO_3)_2 | 2 | -2 | -1/2 (Δ[Hg2(NO3)2])/(Δt) H_2O | 1 | 1 | (Δ[H2O])/(Δt) KNO_3 | 2 | 2 | 1/2 (Δ[KNO3])/(Δt) Hg | 1 | 1 | (Δ[Hg])/(Δt) HgO | 1 | 1 | (Δ[HgO])/(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[KOH])/(Δt) = -1/2 (Δ[Hg2(NO3)2])/(Δt) = (Δ[H2O])/(Δt) = 1/2 (Δ[KNO3])/(Δt) = (Δ[Hg])/(Δt) = (Δ[HgO])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)