Cr + Be(NO3)2 = Be + Cr(NO3)

Cr chromium + Be(NO_3)_2 beryllium nitrate ⟶ Be beryllium + CrN_3O_9 chromium nitrate

Balance the chemical equation algebraically: Cr + Be(NO_3)_2 ⟶ Be + CrN_3O_9 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Cr + c_2 Be(NO_3)_2 ⟶ c_3 Be + c_4 CrN_3O_9 Set the number of atoms in the reactants equal to the number of atoms in the products for Cr, Be, N and O: Cr: | c_1 = c_4 Be: | c_2 = c_3 N: | 2 c_2 = 3 c_4 O: | 6 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 = 3/2 c_3 = 3/2 c_4 = 1 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 2 c_2 = 3 c_3 = 3 c_4 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 Cr + 3 Be(NO_3)_2 ⟶ 3 Be + 2 CrN_3O_9

+ ⟶ +

chromium + beryllium nitrate ⟶ beryllium + chromium nitrate

Construct the equilibrium constant, K, expression for: Cr + Be(NO_3)_2 ⟶ Be + 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: 2 Cr + 3 Be(NO_3)_2 ⟶ 3 Be + 2 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 | 2 | -2 Be(NO_3)_2 | 3 | -3 Be | 3 | 3 CrN_3O_9 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Cr | 2 | -2 | ([Cr])^(-2) Be(NO_3)_2 | 3 | -3 | ([Be(NO3)2])^(-3) Be | 3 | 3 | ([Be])^3 CrN_3O_9 | 2 | 2 | ([CrN3O9])^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 = ([Cr])^(-2) ([Be(NO3)2])^(-3) ([Be])^3 ([CrN3O9])^2 = (([Be])^3 ([CrN3O9])^2)/(([Cr])^2 ([Be(NO3)2])^3)

Construct the rate of reaction expression for: Cr + Be(NO_3)_2 ⟶ Be + 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: 2 Cr + 3 Be(NO_3)_2 ⟶ 3 Be + 2 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 | 2 | -2 Be(NO_3)_2 | 3 | -3 Be | 3 | 3 CrN_3O_9 | 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 Cr | 2 | -2 | -1/2 (Δ[Cr])/(Δt) Be(NO_3)_2 | 3 | -3 | -1/3 (Δ[Be(NO3)2])/(Δt) Be | 3 | 3 | 1/3 (Δ[Be])/(Δt) CrN_3O_9 | 2 | 2 | 1/2 (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 = -1/2 (Δ[Cr])/(Δt) = -1/3 (Δ[Be(NO3)2])/(Δt) = 1/3 (Δ[Be])/(Δt) = 1/2 (Δ[CrN3O9])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| chromium | beryllium nitrate | beryllium | chromium nitrate formula | Cr | Be(NO_3)_2 | Be | CrN_3O_9 Hill formula | Cr | BeN_2O_6 | Be | CrN_3O_9 name | chromium | beryllium nitrate | beryllium | chromium nitrate IUPAC name | chromium | beryllium dinitrate | beryllium | chromium(+3) cation trinitrate

| chromium | beryllium nitrate | beryllium | chromium nitrate molar mass | 51.9961 g/mol | 133.02 g/mol | 9.0121831 g/mol | 238.01 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | solid (at STP) melting point | 1857 °C | 1287.2 °C | 1278 °C | 66 °C boiling point | 2672 °C | | 2970 °C | density | 7.14 g/cm^3 | 1.2 g/cm^3 | 1.85 g/cm^3 | 1.8 g/cm^3 solubility in water | insoluble | very soluble | insoluble | soluble odor | odorless | | |