Al + NiO = Al2O3 + Ni

Al aluminum + NiO nickel monoxide ⟶ Al_2O_3 aluminum oxide + Ni nickel

Balance the chemical equation algebraically: Al + NiO ⟶ Al_2O_3 + Ni Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Al + c_2 NiO ⟶ c_3 Al_2O_3 + c_4 Ni Set the number of atoms in the reactants equal to the number of atoms in the products for Al, Ni and O: Al: | c_1 = 2 c_3 Ni: | c_2 = c_4 O: | c_2 = 3 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 = 2 c_2 = 3 c_3 = 1 c_4 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 Al + 3 NiO ⟶ Al_2O_3 + 3 Ni

+ ⟶ +

aluminum + nickel monoxide ⟶ aluminum oxide + nickel

| aluminum | nickel monoxide | aluminum oxide | nickel molecular enthalpy | 0 kJ/mol | -241 kJ/mol | -1676 kJ/mol | 0 kJ/mol total enthalpy | 0 kJ/mol | -723 kJ/mol | -1676 kJ/mol | 0 kJ/mol | H_initial = -723 kJ/mol | | H_final = -1676 kJ/mol | ΔH_rxn^0 | -1676 kJ/mol - -723 kJ/mol = -953 kJ/mol (exothermic) | | |

| aluminum | nickel monoxide | aluminum oxide | nickel molecular entropy | 28.3 J/(mol K) | 30 J/(mol K) | 51 J/(mol K) | 30 J/(mol K) total entropy | 56.6 J/(mol K) | 90 J/(mol K) | 51 J/(mol K) | 90 J/(mol K) | S_initial = 146.6 J/(mol K) | | S_final = 141 J/(mol K) | ΔS_rxn^0 | 141 J/(mol K) - 146.6 J/(mol K) = -5.6 J/(mol K) (exoentropic) | | |

Construct the equilibrium constant, K, expression for: Al + NiO ⟶ Al_2O_3 + Ni 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: 2 Al + 3 NiO ⟶ Al_2O_3 + 3 Ni 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 Al | 2 | -2 NiO | 3 | -3 Al_2O_3 | 1 | 1 Ni | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Al | 2 | -2 | ([Al])^(-2) NiO | 3 | -3 | ([NiO])^(-3) Al_2O_3 | 1 | 1 | [Al2O3] Ni | 3 | 3 | ([Ni])^3 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 = ([Al])^(-2) ([NiO])^(-3) [Al2O3] ([Ni])^3 = ([Al2O3] ([Ni])^3)/(([Al])^2 ([NiO])^3)

Construct the rate of reaction expression for: Al + NiO ⟶ Al_2O_3 + Ni 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: 2 Al + 3 NiO ⟶ Al_2O_3 + 3 Ni 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 Al | 2 | -2 NiO | 3 | -3 Al_2O_3 | 1 | 1 Ni | 3 | 3 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 Al | 2 | -2 | -1/2 (Δ[Al])/(Δt) NiO | 3 | -3 | -1/3 (Δ[NiO])/(Δt) Al_2O_3 | 1 | 1 | (Δ[Al2O3])/(Δt) Ni | 3 | 3 | 1/3 (Δ[Ni])/(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 = -1/2 (Δ[Al])/(Δt) = -1/3 (Δ[NiO])/(Δt) = (Δ[Al2O3])/(Δt) = 1/3 (Δ[Ni])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| aluminum | nickel monoxide | aluminum oxide | nickel formula | Al | NiO | Al_2O_3 | Ni name | aluminum | nickel monoxide | aluminum oxide | nickel IUPAC name | aluminum | oxonickel | dialuminum;oxygen(2-) | nickel

| aluminum | nickel monoxide | aluminum oxide | nickel molar mass | 26.9815385 g/mol | 74.692 g/mol | 101.96 g/mol | 58.6934 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | solid (at STP) melting point | 660.4 °C | 1955 °C | 2040 °C | 1453 °C boiling point | 2460 °C | | | 2732 °C density | 2.7 g/cm^3 | 6.67 g/cm^3 | | 8.908 g/cm^3 solubility in water | insoluble | insoluble | | insoluble surface tension | 0.817 N/m | | | dynamic viscosity | 1.5×10^-4 Pa s (at 760 °C) | | | odor | odorless | | odorless | odorless