Cr + Ag(NO3) = Ag + Cr(NO3)

Cr chromium + AgNO_3 silver nitrate ⟶ Ag silver + CrN_3O_9 chromium nitrate

Balance the chemical equation algebraically: Cr + AgNO_3 ⟶ Ag + CrN_3O_9 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Cr + c_2 AgNO_3 ⟶ c_3 Ag + c_4 CrN_3O_9 Set the number of atoms in the reactants equal to the number of atoms in the products for Cr, Ag, N and O: Cr: | c_1 = c_4 Ag: | c_2 = c_3 N: | c_2 = 3 c_4 O: | 3 c_2 = 9 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 = 3 c_3 = 3 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | Cr + 3 AgNO_3 ⟶ 3 Ag + CrN_3O_9

+ ⟶ +

chromium + silver nitrate ⟶ silver + chromium nitrate

Construct the equilibrium constant, K, expression for: Cr + AgNO_3 ⟶ Ag + CrN_3O_9 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: Cr + 3 AgNO_3 ⟶ 3 Ag + CrN_3O_9 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 Cr | 1 | -1 AgNO_3 | 3 | -3 Ag | 3 | 3 CrN_3O_9 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Cr | 1 | -1 | ([Cr])^(-1) AgNO_3 | 3 | -3 | ([AgNO3])^(-3) Ag | 3 | 3 | ([Ag])^3 CrN_3O_9 | 1 | 1 | [CrN3O9] 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 = ([Cr])^(-1) ([AgNO3])^(-3) ([Ag])^3 [CrN3O9] = (([Ag])^3 [CrN3O9])/([Cr] ([AgNO3])^3)

Construct the rate of reaction expression for: Cr + AgNO_3 ⟶ Ag + CrN_3O_9 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: Cr + 3 AgNO_3 ⟶ 3 Ag + CrN_3O_9 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 Cr | 1 | -1 AgNO_3 | 3 | -3 Ag | 3 | 3 CrN_3O_9 | 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 Cr | 1 | -1 | -(Δ[Cr])/(Δt) AgNO_3 | 3 | -3 | -1/3 (Δ[AgNO3])/(Δt) Ag | 3 | 3 | 1/3 (Δ[Ag])/(Δt) CrN_3O_9 | 1 | 1 | (Δ[CrN3O9])/(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[Cr])/(Δt) = -1/3 (Δ[AgNO3])/(Δt) = 1/3 (Δ[Ag])/(Δt) = (Δ[CrN3O9])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| chromium | silver nitrate | silver | chromium nitrate formula | Cr | AgNO_3 | Ag | CrN_3O_9 name | chromium | silver nitrate | silver | chromium nitrate IUPAC name | chromium | silver nitrate | silver | chromium(+3) cation trinitrate

| chromium | silver nitrate | silver | chromium nitrate molar mass | 51.9961 g/mol | 169.87 g/mol | 107.8682 g/mol | 238.01 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | solid (at STP) melting point | 1857 °C | 212 °C | 960 °C | 66 °C boiling point | 2672 °C | | 2212 °C | density | 7.14 g/cm^3 | | 10.49 g/cm^3 | 1.8 g/cm^3 solubility in water | insoluble | soluble | insoluble | soluble odor | odorless | odorless | |