Input interpretation
H_2O water + NaBr sodium bromide + CaOCl2 ⟶ NaOH sodium hydroxide + Br_2 bromine + CaCl_2 calcium chloride
Balanced equation
Balance the chemical equation algebraically: H_2O + NaBr + CaOCl2 ⟶ NaOH + Br_2 + CaCl_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 NaBr + c_3 CaOCl2 ⟶ c_4 NaOH + c_5 Br_2 + c_6 CaCl_2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, Br, Na, Ca and Cl: H: | 2 c_1 = c_4 O: | c_1 + c_3 = c_4 Br: | c_2 = 2 c_5 Na: | c_2 = c_4 Ca: | c_3 = c_6 Cl: | 2 c_3 = 2 c_6 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 = 2 c_3 = 1 c_4 = 2 c_5 = 1 c_6 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | H_2O + 2 NaBr + CaOCl2 ⟶ 2 NaOH + Br_2 + CaCl_2
Structures
+ + CaOCl2 ⟶ + +
Names
water + sodium bromide + CaOCl2 ⟶ sodium hydroxide + bromine + calcium chloride
Equilibrium constant
![Construct the equilibrium constant, K, expression for: H_2O + NaBr + CaOCl2 ⟶ NaOH + Br_2 + CaCl_2 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: H_2O + 2 NaBr + CaOCl2 ⟶ 2 NaOH + Br_2 + CaCl_2 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 H_2O | 1 | -1 NaBr | 2 | -2 CaOCl2 | 1 | -1 NaOH | 2 | 2 Br_2 | 1 | 1 CaCl_2 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 1 | -1 | ([H2O])^(-1) NaBr | 2 | -2 | ([NaBr])^(-2) CaOCl2 | 1 | -1 | ([CaOCl2])^(-1) NaOH | 2 | 2 | ([NaOH])^2 Br_2 | 1 | 1 | [Br2] CaCl_2 | 1 | 1 | [CaCl2] 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 = ([H2O])^(-1) ([NaBr])^(-2) ([CaOCl2])^(-1) ([NaOH])^2 [Br2] [CaCl2] = (([NaOH])^2 [Br2] [CaCl2])/([H2O] ([NaBr])^2 [CaOCl2])](../image_source/828f23c346aca52bf808bc4c8787b95f.png)
Construct the equilibrium constant, K, expression for: H_2O + NaBr + CaOCl2 ⟶ NaOH + Br_2 + CaCl_2 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: H_2O + 2 NaBr + CaOCl2 ⟶ 2 NaOH + Br_2 + CaCl_2 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 H_2O | 1 | -1 NaBr | 2 | -2 CaOCl2 | 1 | -1 NaOH | 2 | 2 Br_2 | 1 | 1 CaCl_2 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 1 | -1 | ([H2O])^(-1) NaBr | 2 | -2 | ([NaBr])^(-2) CaOCl2 | 1 | -1 | ([CaOCl2])^(-1) NaOH | 2 | 2 | ([NaOH])^2 Br_2 | 1 | 1 | [Br2] CaCl_2 | 1 | 1 | [CaCl2] 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 = ([H2O])^(-1) ([NaBr])^(-2) ([CaOCl2])^(-1) ([NaOH])^2 [Br2] [CaCl2] = (([NaOH])^2 [Br2] [CaCl2])/([H2O] ([NaBr])^2 [CaOCl2])
Rate of reaction
![Construct the rate of reaction expression for: H_2O + NaBr + CaOCl2 ⟶ NaOH + Br_2 + CaCl_2 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: H_2O + 2 NaBr + CaOCl2 ⟶ 2 NaOH + Br_2 + CaCl_2 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 H_2O | 1 | -1 NaBr | 2 | -2 CaOCl2 | 1 | -1 NaOH | 2 | 2 Br_2 | 1 | 1 CaCl_2 | 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 H_2O | 1 | -1 | -(Δ[H2O])/(Δt) NaBr | 2 | -2 | -1/2 (Δ[NaBr])/(Δt) CaOCl2 | 1 | -1 | -(Δ[CaOCl2])/(Δt) NaOH | 2 | 2 | 1/2 (Δ[NaOH])/(Δt) Br_2 | 1 | 1 | (Δ[Br2])/(Δt) CaCl_2 | 1 | 1 | (Δ[CaCl2])/(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[H2O])/(Δt) = -1/2 (Δ[NaBr])/(Δt) = -(Δ[CaOCl2])/(Δt) = 1/2 (Δ[NaOH])/(Δt) = (Δ[Br2])/(Δt) = (Δ[CaCl2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)](../image_source/c8d863c900719b2e2baea8709e40e186.png)
Construct the rate of reaction expression for: H_2O + NaBr + CaOCl2 ⟶ NaOH + Br_2 + CaCl_2 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: H_2O + 2 NaBr + CaOCl2 ⟶ 2 NaOH + Br_2 + CaCl_2 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 H_2O | 1 | -1 NaBr | 2 | -2 CaOCl2 | 1 | -1 NaOH | 2 | 2 Br_2 | 1 | 1 CaCl_2 | 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 H_2O | 1 | -1 | -(Δ[H2O])/(Δt) NaBr | 2 | -2 | -1/2 (Δ[NaBr])/(Δt) CaOCl2 | 1 | -1 | -(Δ[CaOCl2])/(Δt) NaOH | 2 | 2 | 1/2 (Δ[NaOH])/(Δt) Br_2 | 1 | 1 | (Δ[Br2])/(Δt) CaCl_2 | 1 | 1 | (Δ[CaCl2])/(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[H2O])/(Δt) = -1/2 (Δ[NaBr])/(Δt) = -(Δ[CaOCl2])/(Δt) = 1/2 (Δ[NaOH])/(Δt) = (Δ[Br2])/(Δt) = (Δ[CaCl2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Chemical names and formulas
| water | sodium bromide | CaOCl2 | sodium hydroxide | bromine | calcium chloride formula | H_2O | NaBr | CaOCl2 | NaOH | Br_2 | CaCl_2 Hill formula | H_2O | BrNa | CaCl2O | HNaO | Br_2 | CaCl_2 name | water | sodium bromide | | sodium hydroxide | bromine | calcium chloride IUPAC name | water | sodium bromide | | sodium hydroxide | molecular bromine | calcium dichloride