HNO3 + Na2S = H2S + NaNO3

HNO_3 nitric acid + Na_2S sodium sulfide ⟶ H_2S hydrogen sulfide + NaNO_3 sodium nitrate

Balance the chemical equation algebraically: HNO_3 + Na_2S ⟶ H_2S + NaNO_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HNO_3 + c_2 Na_2S ⟶ c_3 H_2S + c_4 NaNO_3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, N, O, Na and S: H: | c_1 = 2 c_3 N: | c_1 = c_4 O: | 3 c_1 = 3 c_4 Na: | 2 c_2 = c_4 S: | c_2 = c_3 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 = 1 c_4 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 HNO_3 + Na_2S ⟶ H_2S + 2 NaNO_3

+ ⟶ +

nitric acid + sodium sulfide ⟶ hydrogen sulfide + sodium nitrate

| nitric acid | sodium sulfide | hydrogen sulfide | sodium nitrate molecular free energy | -80.7 kJ/mol | -349.8 kJ/mol | -33.4 kJ/mol | -366 kJ/mol total free energy | -161.4 kJ/mol | -349.8 kJ/mol | -33.4 kJ/mol | -732 kJ/mol | G_initial = -511.2 kJ/mol | | G_final = -765.4 kJ/mol | ΔG_rxn^0 | -765.4 kJ/mol - -511.2 kJ/mol = -254.2 kJ/mol (exergonic) | | |

Construct the equilibrium constant, K, expression for: HNO_3 + Na_2S ⟶ H_2S + NaNO_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 HNO_3 + Na_2S ⟶ H_2S + 2 NaNO_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 HNO_3 | 2 | -2 Na_2S | 1 | -1 H_2S | 1 | 1 NaNO_3 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HNO_3 | 2 | -2 | ([HNO3])^(-2) Na_2S | 1 | -1 | ([Na2S])^(-1) H_2S | 1 | 1 | [H2S] NaNO_3 | 2 | 2 | ([NaNO3])^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 = ([HNO3])^(-2) ([Na2S])^(-1) [H2S] ([NaNO3])^2 = ([H2S] ([NaNO3])^2)/(([HNO3])^2 [Na2S])

Construct the rate of reaction expression for: HNO_3 + Na_2S ⟶ H_2S + NaNO_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 HNO_3 + Na_2S ⟶ H_2S + 2 NaNO_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 HNO_3 | 2 | -2 Na_2S | 1 | -1 H_2S | 1 | 1 NaNO_3 | 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 HNO_3 | 2 | -2 | -1/2 (Δ[HNO3])/(Δt) Na_2S | 1 | -1 | -(Δ[Na2S])/(Δt) H_2S | 1 | 1 | (Δ[H2S])/(Δt) NaNO_3 | 2 | 2 | 1/2 (Δ[NaNO3])/(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[HNO3])/(Δt) = -(Δ[Na2S])/(Δt) = (Δ[H2S])/(Δt) = 1/2 (Δ[NaNO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| nitric acid | sodium sulfide | hydrogen sulfide | sodium nitrate formula | HNO_3 | Na_2S | H_2S | NaNO_3 Hill formula | HNO_3 | Na_2S_1 | H_2S | NNaO_3 name | nitric acid | sodium sulfide | hydrogen sulfide | sodium nitrate

| nitric acid | sodium sulfide | hydrogen sulfide | sodium nitrate molar mass | 63.012 g/mol | 78.04 g/mol | 34.08 g/mol | 84.994 g/mol phase | liquid (at STP) | solid (at STP) | gas (at STP) | solid (at STP) melting point | -41.6 °C | 1172 °C | -85 °C | 306 °C boiling point | 83 °C | | -60 °C | density | 1.5129 g/cm^3 | 1.856 g/cm^3 | 0.001393 g/cm^3 (at 25 °C) | 2.26 g/cm^3 solubility in water | miscible | | | soluble dynamic viscosity | 7.6×10^-4 Pa s (at 25 °C) | | 1.239×10^-5 Pa s (at 25 °C) | 0.003 Pa s (at 250 °C)