Na2SO4 + C + SiO2 = CO2 + SO2 + Na2SiO3

Na_2SO_4 sodium sulfate + C activated charcoal + SiO_2 silicon dioxide ⟶ CO_2 carbon dioxide + SO_2 sulfur dioxide + Na_2SiO_3 sodium metasilicate

Balance the chemical equation algebraically: Na_2SO_4 + C + SiO_2 ⟶ CO_2 + SO_2 + Na_2SiO_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Na_2SO_4 + c_2 C + c_3 SiO_2 ⟶ c_4 CO_2 + c_5 SO_2 + c_6 Na_2SiO_3 Set the number of atoms in the reactants equal to the number of atoms in the products for Na, O, S, C and Si: Na: | 2 c_1 = 2 c_6 O: | 4 c_1 + 2 c_3 = 2 c_4 + 2 c_5 + 3 c_6 S: | c_1 = c_5 C: | c_2 = c_4 Si: | c_3 = c_6 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 = 2 c_4 = 1 c_5 = 2 c_6 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 Na_2SO_4 + C + 2 SiO_2 ⟶ CO_2 + 2 SO_2 + 2 Na_2SiO_3

+ + ⟶ + +

sodium sulfate + activated charcoal + silicon dioxide ⟶ carbon dioxide + sulfur dioxide + sodium metasilicate

Construct the equilibrium constant, K, expression for: Na_2SO_4 + C + SiO_2 ⟶ CO_2 + SO_2 + Na_2SiO_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 Na_2SO_4 + C + 2 SiO_2 ⟶ CO_2 + 2 SO_2 + 2 Na_2SiO_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_2SO_4 | 2 | -2 C | 1 | -1 SiO_2 | 2 | -2 CO_2 | 1 | 1 SO_2 | 2 | 2 Na_2SiO_3 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Na_2SO_4 | 2 | -2 | ([Na2SO4])^(-2) C | 1 | -1 | ([C])^(-1) SiO_2 | 2 | -2 | ([SiO2])^(-2) CO_2 | 1 | 1 | [CO2] SO_2 | 2 | 2 | ([SO2])^2 Na_2SiO_3 | 2 | 2 | ([Na2SiO3])^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 = ([Na2SO4])^(-2) ([C])^(-1) ([SiO2])^(-2) [CO2] ([SO2])^2 ([Na2SiO3])^2 = ([CO2] ([SO2])^2 ([Na2SiO3])^2)/(([Na2SO4])^2 [C] ([SiO2])^2)

Construct the rate of reaction expression for: Na_2SO_4 + C + SiO_2 ⟶ CO_2 + SO_2 + Na_2SiO_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 Na_2SO_4 + C + 2 SiO_2 ⟶ CO_2 + 2 SO_2 + 2 Na_2SiO_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_2SO_4 | 2 | -2 C | 1 | -1 SiO_2 | 2 | -2 CO_2 | 1 | 1 SO_2 | 2 | 2 Na_2SiO_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 Na_2SO_4 | 2 | -2 | -1/2 (Δ[Na2SO4])/(Δt) C | 1 | -1 | -(Δ[C])/(Δt) SiO_2 | 2 | -2 | -1/2 (Δ[SiO2])/(Δt) CO_2 | 1 | 1 | (Δ[CO2])/(Δt) SO_2 | 2 | 2 | 1/2 (Δ[SO2])/(Δt) Na_2SiO_3 | 2 | 2 | 1/2 (Δ[Na2SiO3])/(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[Na2SO4])/(Δt) = -(Δ[C])/(Δt) = -1/2 (Δ[SiO2])/(Δt) = (Δ[CO2])/(Δt) = 1/2 (Δ[SO2])/(Δt) = 1/2 (Δ[Na2SiO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sodium sulfate | activated charcoal | silicon dioxide | carbon dioxide | sulfur dioxide | sodium metasilicate formula | Na_2SO_4 | C | SiO_2 | CO_2 | SO_2 | Na_2SiO_3 Hill formula | Na_2O_4S | C | O_2Si | CO_2 | O_2S | Na_2O_3Si name | sodium sulfate | activated charcoal | silicon dioxide | carbon dioxide | sulfur dioxide | sodium metasilicate IUPAC name | disodium sulfate | carbon | dioxosilane | carbon dioxide | sulfur dioxide | disodium dioxido-oxosilane

| sodium sulfate | activated charcoal | silicon dioxide | carbon dioxide | sulfur dioxide | sodium metasilicate molar mass | 142.04 g/mol | 12.011 g/mol | 60.083 g/mol | 44.009 g/mol | 64.06 g/mol | 122.06 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | gas (at STP) | gas (at STP) | solid (at STP) melting point | 884 °C | 3550 °C | 1713 °C | -56.56 °C (at triple point) | -73 °C | 72.2 °C boiling point | 1429 °C | 4027 °C | 2950 °C | -78.5 °C (at sublimation point) | -10 °C | density | 2.68 g/cm^3 | 2.26 g/cm^3 | 2.196 g/cm^3 | 0.00184212 g/cm^3 (at 20 °C) | 0.002619 g/cm^3 (at 25 °C) | 1.749 g/cm^3 solubility in water | soluble | insoluble | insoluble | | | soluble surface tension | | | | | 0.02859 N/m | dynamic viscosity | | | | 1.491×10^-5 Pa s (at 25 °C) | 1.282×10^-5 Pa s (at 25 °C) | 1 Pa s (at 1088 °C) odor | | | odorless | odorless | |