C + Ca = Ca2C

C activated charcoal + Ca calcium ⟶ Ca2C

Balance the chemical equation algebraically: C + Ca ⟶ Ca2C Add stoichiometric coefficients, c_i, to the reactants and products: c_1 C + c_2 Ca ⟶ c_3 Ca2C Set the number of atoms in the reactants equal to the number of atoms in the products for C and Ca: C: | c_1 = c_3 Ca: | 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 2 c_3 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | C + 2 Ca ⟶ Ca2C

+ ⟶ Ca2C

activated charcoal + calcium ⟶ Ca2C

Construct the equilibrium constant, K, expression for: C + Ca ⟶ Ca2C 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 + 2 Ca ⟶ Ca2C 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 Ca | 2 | -2 Ca2C | 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) Ca | 2 | -2 | ([Ca])^(-2) Ca2C | 1 | 1 | [Ca2C] 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) ([Ca])^(-2) [Ca2C] = ([Ca2C])/([C] ([Ca])^2)

Construct the rate of reaction expression for: C + Ca ⟶ Ca2C 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 + 2 Ca ⟶ Ca2C 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 Ca | 2 | -2 Ca2C | 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) Ca | 2 | -2 | -1/2 (Δ[Ca])/(Δt) Ca2C | 1 | 1 | (Δ[Ca2C])/(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) = -1/2 (Δ[Ca])/(Δt) = (Δ[Ca2C])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| activated charcoal | calcium | Ca2C formula | C | Ca | Ca2C Hill formula | C | Ca | CCa2 name | activated charcoal | calcium | IUPAC name | carbon | calcium |

| activated charcoal | calcium | Ca2C molar mass | 12.011 g/mol | 40.078 g/mol | 92.167 g/mol phase | solid (at STP) | solid (at STP) | melting point | 3550 °C | 850 °C | boiling point | 4027 °C | 1484 °C | density | 2.26 g/cm^3 | 1.54 g/cm^3 | solubility in water | insoluble | decomposes |