Input interpretation
Cu copper + Zn(NO3)2 ⟶ Zn zinc + Cu(NO_3)_2 copper(II) nitrate
Balanced equation
Balance the chemical equation algebraically: Cu + Zn(NO3)2 ⟶ Zn + Cu(NO_3)_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Cu + c_2 Zn(NO3)2 ⟶ c_3 Zn + c_4 Cu(NO_3)_2 Set the number of atoms in the reactants equal to the number of atoms in the products for Cu, Zn, N and O: Cu: | c_1 = c_4 Zn: | c_2 = c_3 N: | 2 c_2 = 2 c_4 O: | 6 c_2 = 6 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: | | Cu + Zn(NO3)2 ⟶ Zn + Cu(NO_3)_2
Structures
+ Zn(NO3)2 ⟶ +
Names
copper + Zn(NO3)2 ⟶ zinc + copper(II) nitrate
Equilibrium constant
![Construct the equilibrium constant, K, expression for: Cu + Zn(NO3)2 ⟶ Zn + Cu(NO_3)_2 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: Cu + Zn(NO3)2 ⟶ Zn + Cu(NO_3)_2 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 | 1 | -1 Zn(NO3)2 | 1 | -1 Zn | 1 | 1 Cu(NO_3)_2 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Cu | 1 | -1 | ([Cu])^(-1) Zn(NO3)2 | 1 | -1 | ([Zn(NO3)2])^(-1) Zn | 1 | 1 | [Zn] Cu(NO_3)_2 | 1 | 1 | [Cu(NO3)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 = ([Cu])^(-1) ([Zn(NO3)2])^(-1) [Zn] [Cu(NO3)2] = ([Zn] [Cu(NO3)2])/([Cu] [Zn(NO3)2])](../image_source/d8bc0b494044731326b871133536cc0e.png)
Construct the equilibrium constant, K, expression for: Cu + Zn(NO3)2 ⟶ Zn + Cu(NO_3)_2 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: Cu + Zn(NO3)2 ⟶ Zn + Cu(NO_3)_2 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 | 1 | -1 Zn(NO3)2 | 1 | -1 Zn | 1 | 1 Cu(NO_3)_2 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Cu | 1 | -1 | ([Cu])^(-1) Zn(NO3)2 | 1 | -1 | ([Zn(NO3)2])^(-1) Zn | 1 | 1 | [Zn] Cu(NO_3)_2 | 1 | 1 | [Cu(NO3)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 = ([Cu])^(-1) ([Zn(NO3)2])^(-1) [Zn] [Cu(NO3)2] = ([Zn] [Cu(NO3)2])/([Cu] [Zn(NO3)2])
Rate of reaction
![Construct the rate of reaction expression for: Cu + Zn(NO3)2 ⟶ Zn + Cu(NO_3)_2 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: Cu + Zn(NO3)2 ⟶ Zn + Cu(NO_3)_2 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 | 1 | -1 Zn(NO3)2 | 1 | -1 Zn | 1 | 1 Cu(NO_3)_2 | 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 | 1 | -1 | -(Δ[Cu])/(Δt) Zn(NO3)2 | 1 | -1 | -(Δ[Zn(NO3)2])/(Δt) Zn | 1 | 1 | (Δ[Zn])/(Δt) Cu(NO_3)_2 | 1 | 1 | (Δ[Cu(NO3)2])/(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[Cu])/(Δt) = -(Δ[Zn(NO3)2])/(Δt) = (Δ[Zn])/(Δt) = (Δ[Cu(NO3)2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)](../image_source/aac546412dc23242c72d058ac6e57163.png)
Construct the rate of reaction expression for: Cu + Zn(NO3)2 ⟶ Zn + Cu(NO_3)_2 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: Cu + Zn(NO3)2 ⟶ Zn + Cu(NO_3)_2 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 | 1 | -1 Zn(NO3)2 | 1 | -1 Zn | 1 | 1 Cu(NO_3)_2 | 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 | 1 | -1 | -(Δ[Cu])/(Δt) Zn(NO3)2 | 1 | -1 | -(Δ[Zn(NO3)2])/(Δt) Zn | 1 | 1 | (Δ[Zn])/(Δt) Cu(NO_3)_2 | 1 | 1 | (Δ[Cu(NO3)2])/(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[Cu])/(Δt) = -(Δ[Zn(NO3)2])/(Δt) = (Δ[Zn])/(Δt) = (Δ[Cu(NO3)2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Chemical names and formulas
| copper | Zn(NO3)2 | zinc | copper(II) nitrate formula | Cu | Zn(NO3)2 | Zn | Cu(NO_3)_2 Hill formula | Cu | N2O6Zn | Zn | CuN_2O_6 name | copper | | zinc | copper(II) nitrate