Cr + NiSO4 = Ni + CrSO4

Cr chromium + NiSO_4 nickel(II) sulfate ⟶ Ni nickel + CrSO4

Balance the chemical equation algebraically: Cr + NiSO_4 ⟶ Ni + CrSO4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Cr + c_2 NiSO_4 ⟶ c_3 Ni + c_4 CrSO4 Set the number of atoms in the reactants equal to the number of atoms in the products for Cr, Ni, O and S: Cr: | c_1 = c_4 Ni: | c_2 = c_3 O: | 4 c_2 = 4 c_4 S: | c_2 = 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: | | Cr + NiSO_4 ⟶ Ni + CrSO4

+ ⟶ + CrSO4

chromium + nickel(II) sulfate ⟶ nickel + CrSO4

Construct the equilibrium constant, K, expression for: Cr + NiSO_4 ⟶ Ni + CrSO4 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 + NiSO_4 ⟶ Ni + CrSO4 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 NiSO_4 | 1 | -1 Ni | 1 | 1 CrSO4 | 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) NiSO_4 | 1 | -1 | ([NiSO4])^(-1) Ni | 1 | 1 | [Ni] CrSO4 | 1 | 1 | [CrSO4] 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) ([NiSO4])^(-1) [Ni] [CrSO4] = ([Ni] [CrSO4])/([Cr] [NiSO4])

Construct the rate of reaction expression for: Cr + NiSO_4 ⟶ Ni + CrSO4 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 + NiSO_4 ⟶ Ni + CrSO4 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 NiSO_4 | 1 | -1 Ni | 1 | 1 CrSO4 | 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) NiSO_4 | 1 | -1 | -(Δ[NiSO4])/(Δt) Ni | 1 | 1 | (Δ[Ni])/(Δt) CrSO4 | 1 | 1 | (Δ[CrSO4])/(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) = -(Δ[NiSO4])/(Δt) = (Δ[Ni])/(Δt) = (Δ[CrSO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| chromium | nickel(II) sulfate | nickel | CrSO4 formula | Cr | NiSO_4 | Ni | CrSO4 Hill formula | Cr | NiO_4S | Ni | CrO4S name | chromium | nickel(II) sulfate | nickel | IUPAC name | chromium | nickelous sulfate | nickel |

| chromium | nickel(II) sulfate | nickel | CrSO4 molar mass | 51.9961 g/mol | 154.75 g/mol | 58.6934 g/mol | 148.05 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | melting point | 1857 °C | | 1453 °C | boiling point | 2672 °C | | 2732 °C | density | 7.14 g/cm^3 | 4.01 g/cm^3 | 8.908 g/cm^3 | solubility in water | insoluble | | insoluble | odor | odorless | | odorless |