C + Na = Na2C2

C activated charcoal + Na sodium ⟶ Na2C2

Balance the chemical equation algebraically: C + Na ⟶ Na2C2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 C + c_2 Na ⟶ c_3 Na2C2 Set the number of atoms in the reactants equal to the number of atoms in the products for C and Na: C: | c_1 = 2 c_3 Na: | c_2 = 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 2 c_3 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 C + 2 Na ⟶ Na2C2

+ ⟶ Na2C2

activated charcoal + sodium ⟶ Na2C2

Construct the equilibrium constant, K, expression for: C + Na ⟶ Na2C2 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 C + 2 Na ⟶ Na2C2 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 C | 2 | -2 Na | 2 | -2 Na2C2 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression C | 2 | -2 | ([C])^(-2) Na | 2 | -2 | ([Na])^(-2) Na2C2 | 1 | 1 | [Na2C2] 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 = ([C])^(-2) ([Na])^(-2) [Na2C2] = ([Na2C2])/(([C])^2 ([Na])^2)

Construct the rate of reaction expression for: C + Na ⟶ Na2C2 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 C + 2 Na ⟶ Na2C2 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 C | 2 | -2 Na | 2 | -2 Na2C2 | 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 C | 2 | -2 | -1/2 (Δ[C])/(Δt) Na | 2 | -2 | -1/2 (Δ[Na])/(Δt) Na2C2 | 1 | 1 | (Δ[Na2C2])/(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[C])/(Δt) = -1/2 (Δ[Na])/(Δt) = (Δ[Na2C2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| activated charcoal | sodium | Na2C2 formula | C | Na | Na2C2 Hill formula | C | Na | C2Na2 name | activated charcoal | sodium | IUPAC name | carbon | sodium |

| activated charcoal | sodium | Na2C2 molar mass | 12.011 g/mol | 22.98976928 g/mol | 70.002 g/mol phase | solid (at STP) | solid (at STP) | melting point | 3550 °C | 97.8 °C | boiling point | 4027 °C | 883 °C | density | 2.26 g/cm^3 | 0.968 g/cm^3 | solubility in water | insoluble | decomposes | dynamic viscosity | | 1.413×10^-5 Pa s (at 527 °C) |