Cu + Zn = Cu2Zn

Cu copper + Zn zinc ⟶ Cu2Zn

Balance the chemical equation algebraically: Cu + Zn ⟶ Cu2Zn Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Cu + c_2 Zn ⟶ c_3 Cu2Zn Set the number of atoms in the reactants equal to the number of atoms in the products for Cu and Zn: Cu: | c_1 = 2 c_3 Zn: | 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 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 Cu + Zn ⟶ Cu2Zn

+ ⟶ Cu2Zn

copper + zinc ⟶ Cu2Zn

Construct the equilibrium constant, K, expression for: Cu + Zn ⟶ Cu2Zn 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 Cu + Zn ⟶ Cu2Zn 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 Cu | 2 | -2 Zn | 1 | -1 Cu2Zn | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Cu | 2 | -2 | ([Cu])^(-2) Zn | 1 | -1 | ([Zn])^(-1) Cu2Zn | 1 | 1 | [Cu2Zn] 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 = ([Cu])^(-2) ([Zn])^(-1) [Cu2Zn] = ([Cu2Zn])/(([Cu])^2 [Zn])

Construct the rate of reaction expression for: Cu + Zn ⟶ Cu2Zn 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 Cu + Zn ⟶ Cu2Zn 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 Cu | 2 | -2 Zn | 1 | -1 Cu2Zn | 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 Cu | 2 | -2 | -1/2 (Δ[Cu])/(Δt) Zn | 1 | -1 | -(Δ[Zn])/(Δt) Cu2Zn | 1 | 1 | (Δ[Cu2Zn])/(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[Cu])/(Δt) = -(Δ[Zn])/(Δt) = (Δ[Cu2Zn])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| copper | zinc | Cu2Zn formula | Cu | Zn | Cu2Zn name | copper | zinc |

| copper | zinc | Cu2Zn molar mass | 63.546 g/mol | 65.38 g/mol | 192.5 g/mol phase | solid (at STP) | solid (at STP) | melting point | 1083 °C | 420 °C | boiling point | 2567 °C | 907 °C | density | 8.96 g/cm^3 | 7.14 g/cm^3 | solubility in water | insoluble | insoluble | odor | odorless | odorless |