MgO + N2O5 = Mg(NO3)2

MgO magnesium oxide + N_2O_5 dinitrogen pentoxide ⟶ Mg(NO_3)_2 magnesium nitrate

Balance the chemical equation algebraically: MgO + N_2O_5 ⟶ Mg(NO_3)_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 MgO + c_2 N_2O_5 ⟶ c_3 Mg(NO_3)_2 Set the number of atoms in the reactants equal to the number of atoms in the products for Mg, O and N: Mg: | c_1 = c_3 O: | c_1 + 5 c_2 = 6 c_3 N: | 2 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 = 1 c_3 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | MgO + N_2O_5 ⟶ Mg(NO_3)_2

+ ⟶

magnesium oxide + dinitrogen pentoxide ⟶ magnesium nitrate

| magnesium oxide | dinitrogen pentoxide | magnesium nitrate molecular enthalpy | -601.6 kJ/mol | -43.1 kJ/mol | -790.7 kJ/mol total enthalpy | -601.6 kJ/mol | -43.1 kJ/mol | -790.7 kJ/mol | H_initial = -644.7 kJ/mol | | H_final = -790.7 kJ/mol ΔH_rxn^0 | -790.7 kJ/mol - -644.7 kJ/mol = -146 kJ/mol (exothermic) | |

| magnesium oxide | dinitrogen pentoxide | magnesium nitrate molecular free energy | -569.3 kJ/mol | 113.9 kJ/mol | -589.4 kJ/mol total free energy | -569.3 kJ/mol | 113.9 kJ/mol | -589.4 kJ/mol | G_initial = -455.4 kJ/mol | | G_final = -589.4 kJ/mol ΔG_rxn^0 | -589.4 kJ/mol - -455.4 kJ/mol = -134 kJ/mol (exergonic) | |

Construct the equilibrium constant, K, expression for: MgO + N_2O_5 ⟶ 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: MgO + N_2O_5 ⟶ 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 MgO | 1 | -1 N_2O_5 | 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 MgO | 1 | -1 | ([MgO])^(-1) N_2O_5 | 1 | -1 | ([N2O5])^(-1) 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 = ([MgO])^(-1) ([N2O5])^(-1) [Mg(NO3)2] = ([Mg(NO3)2])/([MgO] [N2O5])

Construct the rate of reaction expression for: MgO + N_2O_5 ⟶ 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: MgO + N_2O_5 ⟶ 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 MgO | 1 | -1 N_2O_5 | 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 MgO | 1 | -1 | -(Δ[MgO])/(Δt) N_2O_5 | 1 | -1 | -(Δ[N2O5])/(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[MgO])/(Δt) = -(Δ[N2O5])/(Δt) = (Δ[Mg(NO3)2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| magnesium oxide | dinitrogen pentoxide | magnesium nitrate formula | MgO | N_2O_5 | Mg(NO_3)_2 Hill formula | MgO | N_2O_5 | MgN_2O_6 name | magnesium oxide | dinitrogen pentoxide | magnesium nitrate IUPAC name | oxomagnesium | nitro nitrate | magnesium dinitrate

| magnesium oxide | dinitrogen pentoxide | magnesium nitrate molar mass | 40.304 g/mol | 108.01 g/mol | 148.31 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) melting point | 2852 °C | 30 °C | 88.9 °C boiling point | 3600 °C | 47 °C | 330 °C density | 3.58 g/cm^3 | 2.05 g/cm^3 | 1.2051 g/cm^3 odor | odorless | |