Input interpretation
Al aluminum + Y2 ⟶ AlY3
Balanced equation
Balance the chemical equation algebraically: Al + Y2 ⟶ AlY3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Al + c_2 Y2 ⟶ c_3 AlY3 Set the number of atoms in the reactants equal to the number of atoms in the products for Al and Y: Al: | c_1 = c_3 Y: | 2 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 3/2 c_3 = 1 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 2 c_2 = 3 c_3 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 Al + 3 Y2 ⟶ 2 AlY3
Structures
+ Y2 ⟶ AlY3
Names
aluminum + Y2 ⟶ AlY3
Equilibrium constant
![Construct the equilibrium constant, K, expression for: Al + Y2 ⟶ AlY3 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 Y2 ⟶ 2 AlY3 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 Y2 | 3 | -3 AlY3 | 2 | 2 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) Y2 | 3 | -3 | ([Y2])^(-3) AlY3 | 2 | 2 | ([AlY3])^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 = ([Al])^(-2) ([Y2])^(-3) ([AlY3])^2 = ([AlY3])^2/(([Al])^2 ([Y2])^3)](../image_source/d761a78ab21a2d334c1151b3ed80f4c4.png)
Construct the equilibrium constant, K, expression for: Al + Y2 ⟶ AlY3 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 Y2 ⟶ 2 AlY3 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 Y2 | 3 | -3 AlY3 | 2 | 2 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) Y2 | 3 | -3 | ([Y2])^(-3) AlY3 | 2 | 2 | ([AlY3])^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 = ([Al])^(-2) ([Y2])^(-3) ([AlY3])^2 = ([AlY3])^2/(([Al])^2 ([Y2])^3)
Rate of reaction
![Construct the rate of reaction expression for: Al + Y2 ⟶ AlY3 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 Y2 ⟶ 2 AlY3 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 Y2 | 3 | -3 AlY3 | 2 | 2 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) Y2 | 3 | -3 | -1/3 (Δ[Y2])/(Δt) AlY3 | 2 | 2 | 1/2 (Δ[AlY3])/(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[Y2])/(Δt) = 1/2 (Δ[AlY3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)](../image_source/017caf18f664a0e75110a64cc49921d5.png)
Construct the rate of reaction expression for: Al + Y2 ⟶ AlY3 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 Y2 ⟶ 2 AlY3 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 Y2 | 3 | -3 AlY3 | 2 | 2 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) Y2 | 3 | -3 | -1/3 (Δ[Y2])/(Δt) AlY3 | 2 | 2 | 1/2 (Δ[AlY3])/(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[Y2])/(Δt) = 1/2 (Δ[AlY3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Chemical names and formulas
| aluminum | Y2 | AlY3 formula | Al | Y2 | AlY3 name | aluminum | |
Substance properties
| aluminum | Y2 | AlY3 molar mass | 26.9815385 g/mol | 177.8117 g/mol | 293.6991 g/mol phase | solid (at STP) | | melting point | 660.4 °C | | boiling point | 2460 °C | | density | 2.7 g/cm^3 | | solubility in water | insoluble | | surface tension | 0.817 N/m | | dynamic viscosity | 1.5×10^-4 Pa s (at 760 °C) | | odor | odorless | |
Units
