Na + Y2 = NaY

Na sodium + Y2 ⟶ NaY

Balance the chemical equation algebraically: Na + Y2 ⟶ NaY Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Na + c_2 Y2 ⟶ c_3 NaY Set the number of atoms in the reactants equal to the number of atoms in the products for Na and Y: Na: | c_1 = c_3 Y: | 2 c_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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 1 c_3 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 Na + Y2 ⟶ 2 NaY

+ Y2 ⟶ NaY

sodium + Y2 ⟶ NaY

Construct the equilibrium constant, K, expression for: Na + Y2 ⟶ NaY 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 Na + Y2 ⟶ 2 NaY 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 Na | 2 | -2 Y2 | 1 | -1 NaY | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Na | 2 | -2 | ([Na])^(-2) Y2 | 1 | -1 | ([Y2])^(-1) NaY | 2 | 2 | ([NaY])^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 = ([Na])^(-2) ([Y2])^(-1) ([NaY])^2 = ([NaY])^2/(([Na])^2 [Y2])

Construct the rate of reaction expression for: Na + Y2 ⟶ NaY 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 Na + Y2 ⟶ 2 NaY 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 Na | 2 | -2 Y2 | 1 | -1 NaY | 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 Na | 2 | -2 | -1/2 (Δ[Na])/(Δt) Y2 | 1 | -1 | -(Δ[Y2])/(Δt) NaY | 2 | 2 | 1/2 (Δ[NaY])/(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[Na])/(Δt) = -(Δ[Y2])/(Δt) = 1/2 (Δ[NaY])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sodium | Y2 | NaY formula | Na | Y2 | NaY name | sodium | |

| sodium | Y2 | NaY molar mass | 22.98976928 g/mol | 177.8117 g/mol | 111.8956 g/mol phase | solid (at STP) | | melting point | 97.8 °C | | boiling point | 883 °C | | density | 0.968 g/cm^3 | | solubility in water | decomposes | | dynamic viscosity | 1.413×10^-5 Pa s (at 527 °C) | |