Ba(NO3)2 + Na2(SO4) = Ba(SO4) + Na(NO3)

Ba(NO_3)_2 barium nitrate + Na_2SO_4 sodium sulfate ⟶ BaSO_4 barium sulfate + NaNO_3 sodium nitrate

Balance the chemical equation algebraically: Ba(NO_3)_2 + Na_2SO_4 ⟶ BaSO_4 + NaNO_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Ba(NO_3)_2 + c_2 Na_2SO_4 ⟶ c_3 BaSO_4 + c_4 NaNO_3 Set the number of atoms in the reactants equal to the number of atoms in the products for Ba, N, O, Na and S: Ba: | c_1 = c_3 N: | 2 c_1 = c_4 O: | 6 c_1 + 4 c_2 = 4 c_3 + 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 1 c_3 = 1 c_4 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | Ba(NO_3)_2 + Na_2SO_4 ⟶ BaSO_4 + 2 NaNO_3

+ ⟶ +

barium nitrate + sodium sulfate ⟶ barium sulfate + sodium nitrate

| barium nitrate | sodium sulfate | barium sulfate | sodium nitrate molecular enthalpy | -988 kJ/mol | -1387 kJ/mol | -1473 kJ/mol | -467.9 kJ/mol total enthalpy | -988 kJ/mol | -1387 kJ/mol | -1473 kJ/mol | -935.8 kJ/mol | H_initial = -2375 kJ/mol | | H_final = -2409 kJ/mol | ΔH_rxn^0 | -2409 kJ/mol - -2375 kJ/mol = -33.9 kJ/mol (exothermic) | | |

| barium nitrate | sodium sulfate | barium sulfate | sodium nitrate molecular free energy | -7926 kJ/mol | -1270 kJ/mol | -1362 kJ/mol | -366 kJ/mol total free energy | -7926 kJ/mol | -1270 kJ/mol | -1362 kJ/mol | -732 kJ/mol | G_initial = -9196 kJ/mol | | G_final = -2094 kJ/mol | ΔG_rxn^0 | -2094 kJ/mol - -9196 kJ/mol = 7102 kJ/mol (endergonic) | | |

Construct the equilibrium constant, K, expression for: Ba(NO_3)_2 + Na_2SO_4 ⟶ BaSO_4 + 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: Ba(NO_3)_2 + Na_2SO_4 ⟶ BaSO_4 + 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 Ba(NO_3)_2 | 1 | -1 Na_2SO_4 | 1 | -1 BaSO_4 | 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 Ba(NO_3)_2 | 1 | -1 | ([Ba(NO3)2])^(-1) Na_2SO_4 | 1 | -1 | ([Na2SO4])^(-1) BaSO_4 | 1 | 1 | [BaSO4] 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 = ([Ba(NO3)2])^(-1) ([Na2SO4])^(-1) [BaSO4] ([NaNO3])^2 = ([BaSO4] ([NaNO3])^2)/([Ba(NO3)2] [Na2SO4])

Construct the rate of reaction expression for: Ba(NO_3)_2 + Na_2SO_4 ⟶ BaSO_4 + 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: Ba(NO_3)_2 + Na_2SO_4 ⟶ BaSO_4 + 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 Ba(NO_3)_2 | 1 | -1 Na_2SO_4 | 1 | -1 BaSO_4 | 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 Ba(NO_3)_2 | 1 | -1 | -(Δ[Ba(NO3)2])/(Δt) Na_2SO_4 | 1 | -1 | -(Δ[Na2SO4])/(Δt) BaSO_4 | 1 | 1 | (Δ[BaSO4])/(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 = -(Δ[Ba(NO3)2])/(Δt) = -(Δ[Na2SO4])/(Δt) = (Δ[BaSO4])/(Δt) = 1/2 (Δ[NaNO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| barium nitrate | sodium sulfate | barium sulfate | sodium nitrate formula | Ba(NO_3)_2 | Na_2SO_4 | BaSO_4 | NaNO_3 Hill formula | BaN_2O_6 | Na_2O_4S | BaO_4S | NNaO_3 name | barium nitrate | sodium sulfate | barium sulfate | sodium nitrate IUPAC name | barium(+2) cation dinitrate | disodium sulfate | barium(+2) cation sulfate | sodium nitrate

| barium nitrate | sodium sulfate | barium sulfate | sodium nitrate molar mass | 261.34 g/mol | 142.04 g/mol | 233.38 g/mol | 84.994 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | solid (at STP) melting point | 592 °C | 884 °C | 1345 °C | 306 °C boiling point | | 1429 °C | | density | 3.23 g/cm^3 | 2.68 g/cm^3 | 4.5 g/cm^3 | 2.26 g/cm^3 solubility in water | | soluble | insoluble | soluble dynamic viscosity | | | | 0.003 Pa s (at 250 °C)