O2 + MnSO4 + Na2CO3 = CO2 + Na2SO4 + NaMnO4

O_2 oxygen + MnSO_4 manganese(II) sulfate + Na_2CO_3 soda ash ⟶ CO_2 carbon dioxide + Na_2SO_4 sodium sulfate + NaMnO_4 sodium permanganate

Balance the chemical equation algebraically: O_2 + MnSO_4 + Na_2CO_3 ⟶ CO_2 + Na_2SO_4 + NaMnO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 O_2 + c_2 MnSO_4 + c_3 Na_2CO_3 ⟶ c_4 CO_2 + c_5 Na_2SO_4 + c_6 NaMnO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for O, Mn, S, C and Na: O: | 2 c_1 + 4 c_2 + 3 c_3 = 2 c_4 + 4 c_5 + 4 c_6 Mn: | c_2 = c_6 S: | c_2 = c_5 C: | c_3 = c_4 Na: | 2 c_3 = 2 c_5 + 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 = 5/4 c_2 = 1 c_3 = 3/2 c_4 = 3/2 c_5 = 1 c_6 = 1 Multiply by the least common denominator, 4, to eliminate fractional coefficients: c_1 = 5 c_2 = 4 c_3 = 6 c_4 = 6 c_5 = 4 c_6 = 4 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 5 O_2 + 4 MnSO_4 + 6 Na_2CO_3 ⟶ 6 CO_2 + 4 Na_2SO_4 + 4 NaMnO_4

+ + ⟶ + +

oxygen + manganese(II) sulfate + soda ash ⟶ carbon dioxide + sodium sulfate + sodium permanganate

Construct the equilibrium constant, K, expression for: O_2 + MnSO_4 + Na_2CO_3 ⟶ CO_2 + Na_2SO_4 + NaMnO_4 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: 5 O_2 + 4 MnSO_4 + 6 Na_2CO_3 ⟶ 6 CO_2 + 4 Na_2SO_4 + 4 NaMnO_4 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 O_2 | 5 | -5 MnSO_4 | 4 | -4 Na_2CO_3 | 6 | -6 CO_2 | 6 | 6 Na_2SO_4 | 4 | 4 NaMnO_4 | 4 | 4 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression O_2 | 5 | -5 | ([O2])^(-5) MnSO_4 | 4 | -4 | ([MnSO4])^(-4) Na_2CO_3 | 6 | -6 | ([Na2CO3])^(-6) CO_2 | 6 | 6 | ([CO2])^6 Na_2SO_4 | 4 | 4 | ([Na2SO4])^4 NaMnO_4 | 4 | 4 | ([NaMnO4])^4 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 = ([O2])^(-5) ([MnSO4])^(-4) ([Na2CO3])^(-6) ([CO2])^6 ([Na2SO4])^4 ([NaMnO4])^4 = (([CO2])^6 ([Na2SO4])^4 ([NaMnO4])^4)/(([O2])^5 ([MnSO4])^4 ([Na2CO3])^6)

Construct the rate of reaction expression for: O_2 + MnSO_4 + Na_2CO_3 ⟶ CO_2 + Na_2SO_4 + NaMnO_4 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: 5 O_2 + 4 MnSO_4 + 6 Na_2CO_3 ⟶ 6 CO_2 + 4 Na_2SO_4 + 4 NaMnO_4 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 O_2 | 5 | -5 MnSO_4 | 4 | -4 Na_2CO_3 | 6 | -6 CO_2 | 6 | 6 Na_2SO_4 | 4 | 4 NaMnO_4 | 4 | 4 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 O_2 | 5 | -5 | -1/5 (Δ[O2])/(Δt) MnSO_4 | 4 | -4 | -1/4 (Δ[MnSO4])/(Δt) Na_2CO_3 | 6 | -6 | -1/6 (Δ[Na2CO3])/(Δt) CO_2 | 6 | 6 | 1/6 (Δ[CO2])/(Δt) Na_2SO_4 | 4 | 4 | 1/4 (Δ[Na2SO4])/(Δt) NaMnO_4 | 4 | 4 | 1/4 (Δ[NaMnO4])/(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 = -1/5 (Δ[O2])/(Δt) = -1/4 (Δ[MnSO4])/(Δt) = -1/6 (Δ[Na2CO3])/(Δt) = 1/6 (Δ[CO2])/(Δt) = 1/4 (Δ[Na2SO4])/(Δt) = 1/4 (Δ[NaMnO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| oxygen | manganese(II) sulfate | soda ash | carbon dioxide | sodium sulfate | sodium permanganate formula | O_2 | MnSO_4 | Na_2CO_3 | CO_2 | Na_2SO_4 | NaMnO_4 Hill formula | O_2 | MnSO_4 | CNa_2O_3 | CO_2 | Na_2O_4S | MnNaO_4 name | oxygen | manganese(II) sulfate | soda ash | carbon dioxide | sodium sulfate | sodium permanganate IUPAC name | molecular oxygen | manganese(+2) cation sulfate | disodium carbonate | carbon dioxide | disodium sulfate | sodium permanganate

| oxygen | manganese(II) sulfate | soda ash | carbon dioxide | sodium sulfate | sodium permanganate molar mass | 31.998 g/mol | 150.99 g/mol | 105.99 g/mol | 44.009 g/mol | 142.04 g/mol | 141.92 g/mol phase | gas (at STP) | solid (at STP) | solid (at STP) | gas (at STP) | solid (at STP) | liquid (at STP) melting point | -218 °C | 710 °C | 851 °C | -56.56 °C (at triple point) | 884 °C | boiling point | -183 °C | | 1600 °C | -78.5 °C (at sublimation point) | 1429 °C | 100 °C density | 0.001429 g/cm^3 (at 0 °C) | 3.25 g/cm^3 | | 0.00184212 g/cm^3 (at 20 °C) | 2.68 g/cm^3 | 1.391 g/cm^3 solubility in water | | soluble | soluble | | soluble | surface tension | 0.01347 N/m | | | | | dynamic viscosity | 2.055×10^-5 Pa s (at 25 °C) | | 0.00355 Pa s (at 900 °C) | 1.491×10^-5 Pa s (at 25 °C) | | odor | odorless | | | odorless | |