C + CaO = O2 + CaC2

C activated charcoal + CaO lime ⟶ O_2 oxygen + CaC_2 calcium carbide

Balance the chemical equation algebraically: C + CaO ⟶ O_2 + CaC_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 C + c_2 CaO ⟶ c_3 O_2 + c_4 CaC_2 Set the number of atoms in the reactants equal to the number of atoms in the products for C, Ca and O: C: | c_1 = 2 c_4 Ca: | c_2 = c_4 O: | 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 = 4 c_2 = 2 c_3 = 1 c_4 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 C + 2 CaO ⟶ O_2 + 2 CaC_2

+ ⟶ +

activated charcoal + lime ⟶ oxygen + calcium carbide

Construct the equilibrium constant, K, expression for: C + CaO ⟶ O_2 + CaC_2 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: 4 C + 2 CaO ⟶ O_2 + 2 CaC_2 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 | 4 | -4 CaO | 2 | -2 O_2 | 1 | 1 CaC_2 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression C | 4 | -4 | ([C])^(-4) CaO | 2 | -2 | ([CaO])^(-2) O_2 | 1 | 1 | [O2] CaC_2 | 2 | 2 | ([CaC2])^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 = ([C])^(-4) ([CaO])^(-2) [O2] ([CaC2])^2 = ([O2] ([CaC2])^2)/(([C])^4 ([CaO])^2)

Construct the rate of reaction expression for: C + CaO ⟶ O_2 + CaC_2 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: 4 C + 2 CaO ⟶ O_2 + 2 CaC_2 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 | 4 | -4 CaO | 2 | -2 O_2 | 1 | 1 CaC_2 | 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 C | 4 | -4 | -1/4 (Δ[C])/(Δt) CaO | 2 | -2 | -1/2 (Δ[CaO])/(Δt) O_2 | 1 | 1 | (Δ[O2])/(Δt) CaC_2 | 2 | 2 | 1/2 (Δ[CaC2])/(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 = -1/4 (Δ[C])/(Δt) = -1/2 (Δ[CaO])/(Δt) = (Δ[O2])/(Δt) = 1/2 (Δ[CaC2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| activated charcoal | lime | oxygen | calcium carbide formula | C | CaO | O_2 | CaC_2 Hill formula | C | CaO | O_2 | C_2Ca name | activated charcoal | lime | oxygen | calcium carbide IUPAC name | carbon | | molecular oxygen | calcium acetylide

| activated charcoal | lime | oxygen | calcium carbide molar mass | 12.011 g/mol | 56.077 g/mol | 31.998 g/mol | 64.1 g/mol phase | solid (at STP) | solid (at STP) | gas (at STP) | solid (at STP) melting point | 3550 °C | 2580 °C | -218 °C | 2300 °C boiling point | 4027 °C | 2850 °C | -183 °C | density | 2.26 g/cm^3 | 3.3 g/cm^3 | 0.001429 g/cm^3 (at 0 °C) | 2.22 g/cm^3 solubility in water | insoluble | reacts | | decomposes surface tension | | | 0.01347 N/m | dynamic viscosity | | | 2.055×10^-5 Pa s (at 25 °C) | odor | | | odorless |