H2O + NaBr + Ca(ClO)2 = NaOH + Br2 + CaCl2

Input interpretation

Image
Text

H_2O water + NaBr sodium bromide + Ca(ClO)2 ⟶ NaOH sodium hydroxide + Br_2 bromine + CaCl_2 calcium chloride

Balanced equation

Image
Text

Balance the chemical equation algebraically: H_2O + NaBr + Ca(ClO)2 ⟶ NaOH + Br_2 + CaCl_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 NaBr + c_3 Ca(ClO)2 ⟶ 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 + 2 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 4 c_3 = 1 c_4 = 4 c_5 = 2 c_6 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 H_2O + 4 NaBr + Ca(ClO)2 ⟶ 4 NaOH + 2 Br_2 + CaCl_2

+ + Ca(ClO)2 ⟶ + +

Names

Image
Text

water + sodium bromide + Ca(ClO)2 ⟶ sodium hydroxide + bromine + calcium chloride

Equilibrium constant

Image
Text

Construct the equilibrium constant, K, expression for: H_2O + NaBr + Ca(ClO)2 ⟶ 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: 2 H_2O + 4 NaBr + Ca(ClO)2 ⟶ 4 NaOH + 2 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 | 2 | -2 NaBr | 4 | -4 Ca(ClO)2 | 1 | -1 NaOH | 4 | 4 Br_2 | 2 | 2 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 | 2 | -2 | ([H2O])^(-2) NaBr | 4 | -4 | ([NaBr])^(-4) Ca(ClO)2 | 1 | -1 | ([Ca(ClO)2])^(-1) NaOH | 4 | 4 | ([NaOH])^4 Br_2 | 2 | 2 | ([Br2])^2 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])^(-2) ([NaBr])^(-4) ([Ca(ClO)2])^(-1) ([NaOH])^4 ([Br2])^2 [CaCl2] = (([NaOH])^4 ([Br2])^2 [CaCl2])/(([H2O])^2 ([NaBr])^4 [Ca(ClO)2])

Rate of reaction

Image
Text

Construct the rate of reaction expression for: H_2O + NaBr + Ca(ClO)2 ⟶ 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: 2 H_2O + 4 NaBr + Ca(ClO)2 ⟶ 4 NaOH + 2 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 | 2 | -2 NaBr | 4 | -4 Ca(ClO)2 | 1 | -1 NaOH | 4 | 4 Br_2 | 2 | 2 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 | 2 | -2 | -1/2 (Δ[H2O])/(Δt) NaBr | 4 | -4 | -1/4 (Δ[NaBr])/(Δt) Ca(ClO)2 | 1 | -1 | -(Δ[Ca(ClO)2])/(Δt) NaOH | 4 | 4 | 1/4 (Δ[NaOH])/(Δt) Br_2 | 2 | 2 | 1/2 (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 = -1/2 (Δ[H2O])/(Δt) = -1/4 (Δ[NaBr])/(Δt) = -(Δ[Ca(ClO)2])/(Δt) = 1/4 (Δ[NaOH])/(Δt) = 1/2 (Δ[Br2])/(Δt) = (Δ[CaCl2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)