C + Ba = BaC

C activated charcoal + Ba barium ⟶ BaC

Balance the chemical equation algebraically: C + Ba ⟶ BaC Add stoichiometric coefficients, c_i, to the reactants and products: c_1 C + c_2 Ba ⟶ c_3 BaC Set the number of atoms in the reactants equal to the number of atoms in the products for C and Ba: C: | c_1 = c_3 Ba: | 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 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | C + Ba ⟶ BaC

+ ⟶ BaC

activated charcoal + barium ⟶ BaC

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

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

| activated charcoal | barium | BaC formula | C | Ba | BaC Hill formula | C | Ba | CBa name | activated charcoal | barium | IUPAC name | carbon | barium |

| activated charcoal | barium | BaC molar mass | 12.011 g/mol | 137.327 g/mol | 149.338 g/mol phase | solid (at STP) | solid (at STP) | melting point | 3550 °C | 725 °C | boiling point | 4027 °C | 1640 °C | density | 2.26 g/cm^3 | 3.6 g/cm^3 | solubility in water | insoluble | insoluble | surface tension | | 0.224 N/m |