Mg + Ca(NO3)2 = Ca + Mg(NO3)2

Mg magnesium + Ca(NO_3)_2 calcium nitrate ⟶ Ca calcium + Mg(NO_3)_2 magnesium nitrate

Balance the chemical equation algebraically: Mg + Ca(NO_3)_2 ⟶ Ca + Mg(NO_3)_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Mg + c_2 Ca(NO_3)_2 ⟶ c_3 Ca + c_4 Mg(NO_3)_2 Set the number of atoms in the reactants equal to the number of atoms in the products for Mg, Ca, N and O: Mg: | c_1 = c_4 Ca: | c_2 = c_3 N: | 2 c_2 = 2 c_4 O: | 6 c_2 = 6 c_4 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 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | Mg + Ca(NO_3)_2 ⟶ Ca + Mg(NO_3)_2

+ ⟶ +

magnesium + calcium nitrate ⟶ calcium + magnesium nitrate

| magnesium | calcium nitrate | calcium | magnesium nitrate molecular enthalpy | 0 kJ/mol | -938.2 kJ/mol | 0 kJ/mol | -790.7 kJ/mol total enthalpy | 0 kJ/mol | -938.2 kJ/mol | 0 kJ/mol | -790.7 kJ/mol | H_initial = -938.2 kJ/mol | | H_final = -790.7 kJ/mol | ΔH_rxn^0 | -790.7 kJ/mol - -938.2 kJ/mol = 147.5 kJ/mol (endothermic) | | |

Construct the equilibrium constant, K, expression for: Mg + Ca(NO_3)_2 ⟶ Ca + Mg(NO_3)_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: Mg + Ca(NO_3)_2 ⟶ Ca + Mg(NO_3)_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 Mg | 1 | -1 Ca(NO_3)_2 | 1 | -1 Ca | 1 | 1 Mg(NO_3)_2 | 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) Ca(NO_3)_2 | 1 | -1 | ([Ca(NO3)2])^(-1) Ca | 1 | 1 | [Ca] Mg(NO_3)_2 | 1 | 1 | [Mg(NO3)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 = ([Mg])^(-1) ([Ca(NO3)2])^(-1) [Ca] [Mg(NO3)2] = ([Ca] [Mg(NO3)2])/([Mg] [Ca(NO3)2])

Construct the rate of reaction expression for: Mg + Ca(NO_3)_2 ⟶ Ca + Mg(NO_3)_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: Mg + Ca(NO_3)_2 ⟶ Ca + Mg(NO_3)_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 Mg | 1 | -1 Ca(NO_3)_2 | 1 | -1 Ca | 1 | 1 Mg(NO_3)_2 | 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) Ca(NO_3)_2 | 1 | -1 | -(Δ[Ca(NO3)2])/(Δt) Ca | 1 | 1 | (Δ[Ca])/(Δt) Mg(NO_3)_2 | 1 | 1 | (Δ[Mg(NO3)2])/(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) = -(Δ[Ca(NO3)2])/(Δt) = (Δ[Ca])/(Δt) = (Δ[Mg(NO3)2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| magnesium | calcium nitrate | calcium | magnesium nitrate formula | Mg | Ca(NO_3)_2 | Ca | Mg(NO_3)_2 Hill formula | Mg | CaN_2O_6 | Ca | MgN_2O_6 name | magnesium | calcium nitrate | calcium | magnesium nitrate IUPAC name | magnesium | calcium dinitrate | calcium | magnesium dinitrate