HCl + Na2SO4 = H2SO4 + NaCl

HCl hydrogen chloride + Na_2SO_4 sodium sulfate ⟶ H_2SO_4 sulfuric acid + NaCl sodium chloride

Balance the chemical equation algebraically: HCl + Na_2SO_4 ⟶ H_2SO_4 + NaCl Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HCl + c_2 Na_2SO_4 ⟶ c_3 H_2SO_4 + c_4 NaCl Set the number of atoms in the reactants equal to the number of atoms in the products for Cl, H, Na, O and S: Cl: | c_1 = c_4 H: | c_1 = 2 c_3 Na: | 2 c_2 = c_4 O: | 4 c_2 = 4 c_3 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 HCl + Na_2SO_4 ⟶ H_2SO_4 + 2 NaCl

+ ⟶ +

hydrogen chloride + sodium sulfate ⟶ sulfuric acid + sodium chloride

| hydrogen chloride | sodium sulfate | sulfuric acid | sodium chloride molecular enthalpy | -92.3 kJ/mol | -1387 kJ/mol | -814 kJ/mol | -411.2 kJ/mol total enthalpy | -184.6 kJ/mol | -1387 kJ/mol | -814 kJ/mol | -822.4 kJ/mol | H_initial = -1572 kJ/mol | | H_final = -1636 kJ/mol | ΔH_rxn^0 | -1636 kJ/mol - -1572 kJ/mol = -64.7 kJ/mol (exothermic) | | |

| hydrogen chloride | sodium sulfate | sulfuric acid | sodium chloride molecular free energy | -95.3 kJ/mol | -1270 kJ/mol | -690 kJ/mol | -384.1 kJ/mol total free energy | -190.6 kJ/mol | -1270 kJ/mol | -690 kJ/mol | -768.2 kJ/mol | G_initial = -1461 kJ/mol | | G_final = -1458 kJ/mol | ΔG_rxn^0 | -1458 kJ/mol - -1461 kJ/mol = 2.6 kJ/mol (endergonic) | | |

Construct the equilibrium constant, K, expression for: HCl + Na_2SO_4 ⟶ H_2SO_4 + NaCl 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 HCl + Na_2SO_4 ⟶ H_2SO_4 + 2 NaCl 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 HCl | 2 | -2 Na_2SO_4 | 1 | -1 H_2SO_4 | 1 | 1 NaCl | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HCl | 2 | -2 | ([HCl])^(-2) Na_2SO_4 | 1 | -1 | ([Na2SO4])^(-1) H_2SO_4 | 1 | 1 | [H2SO4] NaCl | 2 | 2 | ([NaCl])^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 = ([HCl])^(-2) ([Na2SO4])^(-1) [H2SO4] ([NaCl])^2 = ([H2SO4] ([NaCl])^2)/(([HCl])^2 [Na2SO4])

Construct the rate of reaction expression for: HCl + Na_2SO_4 ⟶ H_2SO_4 + NaCl 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 HCl + Na_2SO_4 ⟶ H_2SO_4 + 2 NaCl 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 HCl | 2 | -2 Na_2SO_4 | 1 | -1 H_2SO_4 | 1 | 1 NaCl | 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 HCl | 2 | -2 | -1/2 (Δ[HCl])/(Δt) Na_2SO_4 | 1 | -1 | -(Δ[Na2SO4])/(Δt) H_2SO_4 | 1 | 1 | (Δ[H2SO4])/(Δt) NaCl | 2 | 2 | 1/2 (Δ[NaCl])/(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[HCl])/(Δt) = -(Δ[Na2SO4])/(Δt) = (Δ[H2SO4])/(Δt) = 1/2 (Δ[NaCl])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| hydrogen chloride | sodium sulfate | sulfuric acid | sodium chloride formula | HCl | Na_2SO_4 | H_2SO_4 | NaCl Hill formula | ClH | Na_2O_4S | H_2O_4S | ClNa name | hydrogen chloride | sodium sulfate | sulfuric acid | sodium chloride IUPAC name | hydrogen chloride | disodium sulfate | sulfuric acid | sodium chloride

| hydrogen chloride | sodium sulfate | sulfuric acid | sodium chloride molar mass | 36.46 g/mol | 142.04 g/mol | 98.07 g/mol | 58.44 g/mol phase | gas (at STP) | solid (at STP) | liquid (at STP) | solid (at STP) melting point | -114.17 °C | 884 °C | 10.371 °C | 801 °C boiling point | -85 °C | 1429 °C | 279.6 °C | 1413 °C density | 0.00149 g/cm^3 (at 25 °C) | 2.68 g/cm^3 | 1.8305 g/cm^3 | 2.16 g/cm^3 solubility in water | miscible | soluble | very soluble | soluble surface tension | | | 0.0735 N/m | dynamic viscosity | | | 0.021 Pa s (at 25 °C) | odor | | | odorless | odorless