Mg + C = MgC2

Mg magnesium + C activated charcoal ⟶ MgC2

Balance the chemical equation algebraically: Mg + C ⟶ MgC2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Mg + c_2 C ⟶ c_3 MgC2 Set the number of atoms in the reactants equal to the number of atoms in the products for Mg and C: Mg: | c_1 = c_3 C: | 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: | | Mg + 2 C ⟶ MgC2

+ ⟶ MgC2

magnesium + activated charcoal ⟶ MgC2

Construct the equilibrium constant, K, expression for: Mg + C ⟶ MgC2 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: Mg + 2 C ⟶ MgC2 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 Mg | 1 | -1 C | 2 | -2 MgC2 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Mg | 1 | -1 | ([Mg])^(-1) C | 2 | -2 | ([C])^(-2) MgC2 | 1 | 1 | [MgC2] 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 = ([Mg])^(-1) ([C])^(-2) [MgC2] = ([MgC2])/([Mg] ([C])^2)

Construct the rate of reaction expression for: Mg + C ⟶ MgC2 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: Mg + 2 C ⟶ MgC2 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 Mg | 1 | -1 C | 2 | -2 MgC2 | 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 Mg | 1 | -1 | -(Δ[Mg])/(Δt) C | 2 | -2 | -1/2 (Δ[C])/(Δt) MgC2 | 1 | 1 | (Δ[MgC2])/(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[Mg])/(Δt) = -1/2 (Δ[C])/(Δt) = (Δ[MgC2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| magnesium | activated charcoal | MgC2 formula | Mg | C | MgC2 Hill formula | Mg | C | C2Mg name | magnesium | activated charcoal | IUPAC name | magnesium | carbon |

| magnesium | activated charcoal | MgC2 molar mass | 24.305 g/mol | 12.011 g/mol | 48.327 g/mol phase | solid (at STP) | solid (at STP) | melting point | 648 °C | 3550 °C | boiling point | 1090 °C | 4027 °C | density | 1.738 g/cm^3 | 2.26 g/cm^3 | solubility in water | reacts | insoluble |