CO + MgO = CO2 + Mg

CO carbon monoxide + MgO magnesium oxide ⟶ CO_2 carbon dioxide + Mg magnesium

Balance the chemical equation algebraically: CO + MgO ⟶ CO_2 + Mg Add stoichiometric coefficients, c_i, to the reactants and products: c_1 CO + c_2 MgO ⟶ c_3 CO_2 + c_4 Mg Set the number of atoms in the reactants equal to the number of atoms in the products for C, O and Mg: C: | c_1 = c_3 O: | c_1 + c_2 = 2 c_3 Mg: | c_2 = 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: | | CO + MgO ⟶ CO_2 + Mg

+ ⟶ +

carbon monoxide + magnesium oxide ⟶ carbon dioxide + magnesium

| carbon monoxide | magnesium oxide | carbon dioxide | magnesium molecular enthalpy | -110.5 kJ/mol | -601.6 kJ/mol | -393.5 kJ/mol | 0 kJ/mol total enthalpy | -110.5 kJ/mol | -601.6 kJ/mol | -393.5 kJ/mol | 0 kJ/mol | H_initial = -712.1 kJ/mol | | H_final = -393.5 kJ/mol | ΔH_rxn^0 | -393.5 kJ/mol - -712.1 kJ/mol = 318.6 kJ/mol (endothermic) | | |

| carbon monoxide | magnesium oxide | carbon dioxide | magnesium molecular entropy | 198 J/(mol K) | 27 J/(mol K) | 214 J/(mol K) | 33 J/(mol K) total entropy | 198 J/(mol K) | 27 J/(mol K) | 214 J/(mol K) | 33 J/(mol K) | S_initial = 225 J/(mol K) | | S_final = 247 J/(mol K) | ΔS_rxn^0 | 247 J/(mol K) - 225 J/(mol K) = 22 J/(mol K) (endoentropic) | | |

Construct the equilibrium constant, K, expression for: CO + MgO ⟶ CO_2 + Mg 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: CO + MgO ⟶ CO_2 + Mg 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 CO | 1 | -1 MgO | 1 | -1 CO_2 | 1 | 1 Mg | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression CO | 1 | -1 | ([CO])^(-1) MgO | 1 | -1 | ([MgO])^(-1) CO_2 | 1 | 1 | [CO2] Mg | 1 | 1 | [Mg] 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 = ([CO])^(-1) ([MgO])^(-1) [CO2] [Mg] = ([CO2] [Mg])/([CO] [MgO])

Construct the rate of reaction expression for: CO + MgO ⟶ CO_2 + Mg 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: CO + MgO ⟶ CO_2 + Mg 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 CO | 1 | -1 MgO | 1 | -1 CO_2 | 1 | 1 Mg | 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 CO | 1 | -1 | -(Δ[CO])/(Δt) MgO | 1 | -1 | -(Δ[MgO])/(Δt) CO_2 | 1 | 1 | (Δ[CO2])/(Δt) Mg | 1 | 1 | (Δ[Mg])/(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[CO])/(Δt) = -(Δ[MgO])/(Δt) = (Δ[CO2])/(Δt) = (Δ[Mg])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| carbon monoxide | magnesium oxide | carbon dioxide | magnesium formula | CO | MgO | CO_2 | Mg name | carbon monoxide | magnesium oxide | carbon dioxide | magnesium IUPAC name | carbon monoxide | oxomagnesium | carbon dioxide | magnesium

| carbon monoxide | magnesium oxide | carbon dioxide | magnesium molar mass | 28.01 g/mol | 40.304 g/mol | 44.009 g/mol | 24.305 g/mol phase | gas (at STP) | solid (at STP) | gas (at STP) | solid (at STP) melting point | -205 °C | 2852 °C | -56.56 °C (at triple point) | 648 °C boiling point | -191.5 °C | 3600 °C | -78.5 °C (at sublimation point) | 1090 °C density | 0.001145 g/cm^3 (at 25 °C) | 3.58 g/cm^3 | 0.00184212 g/cm^3 (at 20 °C) | 1.738 g/cm^3 solubility in water | | | | reacts dynamic viscosity | 1.772×10^-5 Pa s (at 25 °C) | | 1.491×10^-5 Pa s (at 25 °C) | odor | odorless | odorless | odorless |