Input interpretation
Na_2CrO_4 sodium chromate + BaCl_2 barium chloride ⟶ NaCl sodium chloride + BaCrO_4 barium chromate
Balanced equation
Balance the chemical equation algebraically: Na_2CrO_4 + BaCl_2 ⟶ NaCl + BaCrO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Na_2CrO_4 + c_2 BaCl_2 ⟶ c_3 NaCl + c_4 BaCrO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for Cr, Na, O, Ba and Cl: Cr: | c_1 = c_4 Na: | 2 c_1 = c_3 O: | 4 c_1 = 4 c_4 Ba: | c_2 = c_4 Cl: | 2 c_2 = 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 = 2 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | Na_2CrO_4 + BaCl_2 ⟶ 2 NaCl + BaCrO_4
Structures
+ ⟶ +
Names
sodium chromate + barium chloride ⟶ sodium chloride + barium chromate
Equilibrium constant
Construct the equilibrium constant, K, expression for: Na_2CrO_4 + BaCl_2 ⟶ NaCl + BaCrO_4 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: Na_2CrO_4 + BaCl_2 ⟶ 2 NaCl + BaCrO_4 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 Na_2CrO_4 | 1 | -1 BaCl_2 | 1 | -1 NaCl | 2 | 2 BaCrO_4 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Na_2CrO_4 | 1 | -1 | ([Na2CrO4])^(-1) BaCl_2 | 1 | -1 | ([BaCl2])^(-1) NaCl | 2 | 2 | ([NaCl])^2 BaCrO_4 | 1 | 1 | [BaCrO4] 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 = ([Na2CrO4])^(-1) ([BaCl2])^(-1) ([NaCl])^2 [BaCrO4] = (([NaCl])^2 [BaCrO4])/([Na2CrO4] [BaCl2])
Rate of reaction
Construct the rate of reaction expression for: Na_2CrO_4 + BaCl_2 ⟶ NaCl + BaCrO_4 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: Na_2CrO_4 + BaCl_2 ⟶ 2 NaCl + BaCrO_4 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 Na_2CrO_4 | 1 | -1 BaCl_2 | 1 | -1 NaCl | 2 | 2 BaCrO_4 | 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 Na_2CrO_4 | 1 | -1 | -(Δ[Na2CrO4])/(Δt) BaCl_2 | 1 | -1 | -(Δ[BaCl2])/(Δt) NaCl | 2 | 2 | 1/2 (Δ[NaCl])/(Δt) BaCrO_4 | 1 | 1 | (Δ[BaCrO4])/(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[Na2CrO4])/(Δt) = -(Δ[BaCl2])/(Δt) = 1/2 (Δ[NaCl])/(Δt) = (Δ[BaCrO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Chemical names and formulas
| sodium chromate | barium chloride | sodium chloride | barium chromate formula | Na_2CrO_4 | BaCl_2 | NaCl | BaCrO_4 Hill formula | CrNa_2O_4 | BaCl_2 | ClNa | BaCrO_4 name | sodium chromate | barium chloride | sodium chloride | barium chromate IUPAC name | disodium dioxido(dioxo)chromium | barium(+2) cation dichloride | sodium chloride | barium(+2) cation; dioxido-dioxochromium
Substance properties
| sodium chromate | barium chloride | sodium chloride | barium chromate molar mass | 161.97 g/mol | 208.2 g/mol | 58.44 g/mol | 253.32 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | solid (at STP) melting point | 780 °C | 963 °C | 801 °C | 210 °C boiling point | | | 1413 °C | density | 2.698 g/cm^3 | 3.856 g/cm^3 | 2.16 g/cm^3 | 4.5 g/cm^3 solubility in water | | | soluble | odor | | odorless | odorless |
Units