Input interpretation
![Cu copper + Ag(NO3)2 ⟶ Cu(NO_3)_2 copper(II) nitrate + Ag silver](../image_source/e02db60bdee4297b9b31298a54f89f70.png)
Cu copper + Ag(NO3)2 ⟶ Cu(NO_3)_2 copper(II) nitrate + Ag silver
Balanced equation
![Balance the chemical equation algebraically: Cu + Ag(NO3)2 ⟶ Cu(NO_3)_2 + Ag Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Cu + c_2 Ag(NO3)2 ⟶ c_3 Cu(NO_3)_2 + c_4 Ag Set the number of atoms in the reactants equal to the number of atoms in the products for Cu, Ag, N and O: Cu: | c_1 = c_3 Ag: | c_2 = c_4 N: | 2 c_2 = 2 c_3 O: | 6 c_2 = 6 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 = 1 c_3 = 1 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | Cu + Ag(NO3)2 ⟶ Cu(NO_3)_2 + Ag](../image_source/c060edb842b5d3ce0add7c33b9d46ede.png)
Balance the chemical equation algebraically: Cu + Ag(NO3)2 ⟶ Cu(NO_3)_2 + Ag Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Cu + c_2 Ag(NO3)2 ⟶ c_3 Cu(NO_3)_2 + c_4 Ag Set the number of atoms in the reactants equal to the number of atoms in the products for Cu, Ag, N and O: Cu: | c_1 = c_3 Ag: | c_2 = c_4 N: | 2 c_2 = 2 c_3 O: | 6 c_2 = 6 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 = 1 c_3 = 1 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | Cu + Ag(NO3)2 ⟶ Cu(NO_3)_2 + Ag
Structures
![+ Ag(NO3)2 ⟶ +](../image_source/6903692ff519061ebc3fecee8c496596.png)
+ Ag(NO3)2 ⟶ +
Names
![copper + Ag(NO3)2 ⟶ copper(II) nitrate + silver](../image_source/da8521433e3c697a99dcc8a97a268743.png)
copper + Ag(NO3)2 ⟶ copper(II) nitrate + silver
Equilibrium constant
![Construct the equilibrium constant, K, expression for: Cu + Ag(NO3)2 ⟶ Cu(NO_3)_2 + Ag 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 + Ag(NO3)2 ⟶ Cu(NO_3)_2 + Ag 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 Ag(NO3)2 | 1 | -1 Cu(NO_3)_2 | 1 | 1 Ag | 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) Ag(NO3)2 | 1 | -1 | ([Ag(NO3)2])^(-1) Cu(NO_3)_2 | 1 | 1 | [Cu(NO3)2] Ag | 1 | 1 | [Ag] 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) ([Ag(NO3)2])^(-1) [Cu(NO3)2] [Ag] = ([Cu(NO3)2] [Ag])/([Cu] [Ag(NO3)2])](../image_source/f3f256c2fd75565d02aa0862b3053576.png)
Construct the equilibrium constant, K, expression for: Cu + Ag(NO3)2 ⟶ Cu(NO_3)_2 + Ag 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 + Ag(NO3)2 ⟶ Cu(NO_3)_2 + Ag 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 Ag(NO3)2 | 1 | -1 Cu(NO_3)_2 | 1 | 1 Ag | 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) Ag(NO3)2 | 1 | -1 | ([Ag(NO3)2])^(-1) Cu(NO_3)_2 | 1 | 1 | [Cu(NO3)2] Ag | 1 | 1 | [Ag] 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) ([Ag(NO3)2])^(-1) [Cu(NO3)2] [Ag] = ([Cu(NO3)2] [Ag])/([Cu] [Ag(NO3)2])
Rate of reaction
![Construct the rate of reaction expression for: Cu + Ag(NO3)2 ⟶ Cu(NO_3)_2 + Ag 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 + Ag(NO3)2 ⟶ Cu(NO_3)_2 + Ag 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 Ag(NO3)2 | 1 | -1 Cu(NO_3)_2 | 1 | 1 Ag | 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) Ag(NO3)2 | 1 | -1 | -(Δ[Ag(NO3)2])/(Δt) Cu(NO_3)_2 | 1 | 1 | (Δ[Cu(NO3)2])/(Δt) Ag | 1 | 1 | (Δ[Ag])/(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[Ag(NO3)2])/(Δt) = (Δ[Cu(NO3)2])/(Δt) = (Δ[Ag])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)](../image_source/f934de81b33ee8358f91ea6fd00ec49d.png)
Construct the rate of reaction expression for: Cu + Ag(NO3)2 ⟶ Cu(NO_3)_2 + Ag 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 + Ag(NO3)2 ⟶ Cu(NO_3)_2 + Ag 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 Ag(NO3)2 | 1 | -1 Cu(NO_3)_2 | 1 | 1 Ag | 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) Ag(NO3)2 | 1 | -1 | -(Δ[Ag(NO3)2])/(Δt) Cu(NO_3)_2 | 1 | 1 | (Δ[Cu(NO3)2])/(Δt) Ag | 1 | 1 | (Δ[Ag])/(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[Ag(NO3)2])/(Δt) = (Δ[Cu(NO3)2])/(Δt) = (Δ[Ag])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Chemical names and formulas
![| copper | Ag(NO3)2 | copper(II) nitrate | silver formula | Cu | Ag(NO3)2 | Cu(NO_3)_2 | Ag Hill formula | Cu | AgN2O6 | CuN_2O_6 | Ag name | copper | | copper(II) nitrate | silver](../image_source/929ba786c518a9c20aacb6cef098620a.png)
| copper | Ag(NO3)2 | copper(II) nitrate | silver formula | Cu | Ag(NO3)2 | Cu(NO_3)_2 | Ag Hill formula | Cu | AgN2O6 | CuN_2O_6 | Ag name | copper | | copper(II) nitrate | silver
Substance properties
![| copper | Ag(NO3)2 | copper(II) nitrate | silver molar mass | 63.546 g/mol | 231.88 g/mol | 187.55 g/mol | 107.8682 g/mol phase | solid (at STP) | | | solid (at STP) melting point | 1083 °C | | | 960 °C boiling point | 2567 °C | | | 2212 °C density | 8.96 g/cm^3 | | | 10.49 g/cm^3 solubility in water | insoluble | | | insoluble odor | odorless | | |](../image_source/00a0d0379581c5da5a28d56af0a3df01.png)
| copper | Ag(NO3)2 | copper(II) nitrate | silver molar mass | 63.546 g/mol | 231.88 g/mol | 187.55 g/mol | 107.8682 g/mol phase | solid (at STP) | | | solid (at STP) melting point | 1083 °C | | | 960 °C boiling point | 2567 °C | | | 2212 °C density | 8.96 g/cm^3 | | | 10.49 g/cm^3 solubility in water | insoluble | | | insoluble odor | odorless | | |
Units