Na2CO3 + MgSO4 = Na2SO4 + MgCO3

Na_2CO_3 soda ash + MgSO_4 magnesium sulfate ⟶ Na_2SO_4 sodium sulfate + MgCO_3 magnesium carbonate

Balance the chemical equation algebraically: Na_2CO_3 + MgSO_4 ⟶ Na_2SO_4 + MgCO_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Na_2CO_3 + c_2 MgSO_4 ⟶ c_3 Na_2SO_4 + c_4 MgCO_3 Set the number of atoms in the reactants equal to the number of atoms in the products for C, Na, O, Mg and S: C: | c_1 = c_4 Na: | 2 c_1 = 2 c_3 O: | 3 c_1 + 4 c_2 = 4 c_3 + 3 c_4 Mg: | 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 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | Na_2CO_3 + MgSO_4 ⟶ Na_2SO_4 + MgCO_3

+ ⟶ +

soda ash + magnesium sulfate ⟶ sodium sulfate + magnesium carbonate

Construct the equilibrium constant, K, expression for: Na_2CO_3 + MgSO_4 ⟶ Na_2SO_4 + MgCO_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: Na_2CO_3 + MgSO_4 ⟶ Na_2SO_4 + MgCO_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 Na_2CO_3 | 1 | -1 MgSO_4 | 1 | -1 Na_2SO_4 | 1 | 1 MgCO_3 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Na_2CO_3 | 1 | -1 | ([Na2CO3])^(-1) MgSO_4 | 1 | -1 | ([MgSO4])^(-1) Na_2SO_4 | 1 | 1 | [Na2SO4] MgCO_3 | 1 | 1 | [MgCO3] 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 = ([Na2CO3])^(-1) ([MgSO4])^(-1) [Na2SO4] [MgCO3] = ([Na2SO4] [MgCO3])/([Na2CO3] [MgSO4])

Construct the rate of reaction expression for: Na_2CO_3 + MgSO_4 ⟶ Na_2SO_4 + MgCO_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: Na_2CO_3 + MgSO_4 ⟶ Na_2SO_4 + MgCO_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 Na_2CO_3 | 1 | -1 MgSO_4 | 1 | -1 Na_2SO_4 | 1 | 1 MgCO_3 | 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 Na_2CO_3 | 1 | -1 | -(Δ[Na2CO3])/(Δt) MgSO_4 | 1 | -1 | -(Δ[MgSO4])/(Δt) Na_2SO_4 | 1 | 1 | (Δ[Na2SO4])/(Δt) MgCO_3 | 1 | 1 | (Δ[MgCO3])/(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[Na2CO3])/(Δt) = -(Δ[MgSO4])/(Δt) = (Δ[Na2SO4])/(Δt) = (Δ[MgCO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| soda ash | magnesium sulfate | sodium sulfate | magnesium carbonate formula | Na_2CO_3 | MgSO_4 | Na_2SO_4 | MgCO_3 Hill formula | CNa_2O_3 | MgO_4S | Na_2O_4S | CMgO_3 name | soda ash | magnesium sulfate | sodium sulfate | magnesium carbonate IUPAC name | disodium carbonate | magnesium sulfate | disodium sulfate | magnesium carbonate

| soda ash | magnesium sulfate | sodium sulfate | magnesium carbonate molar mass | 105.99 g/mol | 120.4 g/mol | 142.04 g/mol | 84.313 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | melting point | 851 °C | | 884 °C | boiling point | 1600 °C | | 1429 °C | density | | | 2.68 g/cm^3 | solubility in water | soluble | soluble | soluble | dynamic viscosity | 0.00355 Pa s (at 900 °C) | | |