Cl2 + KBrO3 = Br2 + KClO3

Cl_2 chlorine + KBrO_3 potassium bromate ⟶ Br_2 bromine + KClO_3 potassium chlorate

Balance the chemical equation algebraically: Cl_2 + KBrO_3 ⟶ Br_2 + KClO_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 Cl_2 + c_2 KBrO_3 ⟶ c_3 Br_2 + c_4 KClO_3 Set the number of atoms in the reactants equal to the number of atoms in the products for Cl, Br, K and O: Cl: | 2 c_1 = c_4 Br: | c_2 = 2 c_3 K: | c_2 = c_4 O: | 3 c_2 = 3 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 = 2 c_3 = 1 c_4 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | Cl_2 + 2 KBrO_3 ⟶ Br_2 + 2 KClO_3

+ ⟶ +

chlorine + potassium bromate ⟶ bromine + potassium chlorate

| chlorine | potassium bromate | bromine | potassium chlorate molecular enthalpy | 0 kJ/mol | -360.2 kJ/mol | 0 kJ/mol | -397.7 kJ/mol total enthalpy | 0 kJ/mol | -720.4 kJ/mol | 0 kJ/mol | -795.4 kJ/mol | H_initial = -720.4 kJ/mol | | H_final = -795.4 kJ/mol | ΔH_rxn^0 | -795.4 kJ/mol - -720.4 kJ/mol = -75 kJ/mol (exothermic) | | |

| chlorine | potassium bromate | bromine | potassium chlorate molecular free energy | 0 kJ/mol | -2712 kJ/mol | 0 kJ/mol | -296.3 kJ/mol total free energy | 0 kJ/mol | -5424 kJ/mol | 0 kJ/mol | -592.6 kJ/mol | G_initial = -5424 kJ/mol | | G_final = -592.6 kJ/mol | ΔG_rxn^0 | -592.6 kJ/mol - -5424 kJ/mol = 4831 kJ/mol (endergonic) | | |

Construct the equilibrium constant, K, expression for: Cl_2 + KBrO_3 ⟶ Br_2 + KClO_3 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: Cl_2 + 2 KBrO_3 ⟶ Br_2 + 2 KClO_3 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 Cl_2 | 1 | -1 KBrO_3 | 2 | -2 Br_2 | 1 | 1 KClO_3 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression Cl_2 | 1 | -1 | ([Cl2])^(-1) KBrO_3 | 2 | -2 | ([KBrO3])^(-2) Br_2 | 1 | 1 | [Br2] KClO_3 | 2 | 2 | ([KClO3])^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 = ([Cl2])^(-1) ([KBrO3])^(-2) [Br2] ([KClO3])^2 = ([Br2] ([KClO3])^2)/([Cl2] ([KBrO3])^2)

Construct the rate of reaction expression for: Cl_2 + KBrO_3 ⟶ Br_2 + KClO_3 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: Cl_2 + 2 KBrO_3 ⟶ Br_2 + 2 KClO_3 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 Cl_2 | 1 | -1 KBrO_3 | 2 | -2 Br_2 | 1 | 1 KClO_3 | 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 Cl_2 | 1 | -1 | -(Δ[Cl2])/(Δt) KBrO_3 | 2 | -2 | -1/2 (Δ[KBrO3])/(Δt) Br_2 | 1 | 1 | (Δ[Br2])/(Δt) KClO_3 | 2 | 2 | 1/2 (Δ[KClO3])/(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[Cl2])/(Δt) = -1/2 (Δ[KBrO3])/(Δt) = (Δ[Br2])/(Δt) = 1/2 (Δ[KClO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| chlorine | potassium bromate | bromine | potassium chlorate formula | Cl_2 | KBrO_3 | Br_2 | KClO_3 Hill formula | Cl_2 | BrKO_3 | Br_2 | ClKO_3 name | chlorine | potassium bromate | bromine | potassium chlorate IUPAC name | molecular chlorine | potassium bromate | molecular bromine | potassium chlorate

| chlorine | potassium bromate | bromine | potassium chlorate molar mass | 70.9 g/mol | 167 g/mol | 159.81 g/mol | 122.5 g/mol phase | gas (at STP) | solid (at STP) | liquid (at STP) | solid (at STP) melting point | -101 °C | 350 °C | -7.2 °C | 356 °C boiling point | -34 °C | | 58.8 °C | density | 0.003214 g/cm^3 (at 0 °C) | 3.218 g/cm^3 | 3.119 g/cm^3 | 2.34 g/cm^3 solubility in water | | | insoluble | soluble surface tension | | | 0.0409 N/m | dynamic viscosity | | | 9.44×10^-4 Pa s (at 25 °C) |