K + MgBr2 = Mg + KBr

K potassium + MgBr_2 magnesium bromide ⟶ Mg magnesium + KBr potassium bromide

Balance the chemical equation algebraically: K + MgBr_2 ⟶ Mg + KBr Add stoichiometric coefficients, c_i, to the reactants and products: c_1 K + c_2 MgBr_2 ⟶ c_3 Mg + c_4 KBr Set the number of atoms in the reactants equal to the number of atoms in the products for K, Br and Mg: K: | c_1 = c_4 Br: | 2 c_2 = c_4 Mg: | 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 1 c_3 = 1 c_4 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 K + MgBr_2 ⟶ Mg + 2 KBr

+ ⟶ +

potassium + magnesium bromide ⟶ magnesium + potassium bromide

Construct the equilibrium constant, K, expression for: K + MgBr_2 ⟶ Mg + KBr 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 K + MgBr_2 ⟶ Mg + 2 KBr 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 K | 2 | -2 MgBr_2 | 1 | -1 Mg | 1 | 1 KBr | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression K | 2 | -2 | ([K])^(-2) MgBr_2 | 1 | -1 | ([MgBr2])^(-1) Mg | 1 | 1 | [Mg] KBr | 2 | 2 | ([KBr])^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 = ([K])^(-2) ([MgBr2])^(-1) [Mg] ([KBr])^2 = ([Mg] ([KBr])^2)/(([K])^2 [MgBr2])

Construct the rate of reaction expression for: K + MgBr_2 ⟶ Mg + KBr 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 K + MgBr_2 ⟶ Mg + 2 KBr 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 K | 2 | -2 MgBr_2 | 1 | -1 Mg | 1 | 1 KBr | 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 K | 2 | -2 | -1/2 (Δ[K])/(Δt) MgBr_2 | 1 | -1 | -(Δ[MgBr2])/(Δt) Mg | 1 | 1 | (Δ[Mg])/(Δt) KBr | 2 | 2 | 1/2 (Δ[KBr])/(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[K])/(Δt) = -(Δ[MgBr2])/(Δt) = (Δ[Mg])/(Δt) = 1/2 (Δ[KBr])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| potassium | magnesium bromide | magnesium | potassium bromide formula | K | MgBr_2 | Mg | KBr Hill formula | K | Br_2Mg | Mg | BrK name | potassium | magnesium bromide | magnesium | potassium bromide IUPAC name | potassium | magnesium dibromide | magnesium | potassium bromide

| potassium | magnesium bromide | magnesium | potassium bromide molar mass | 39.0983 g/mol | 184.11 g/mol | 24.305 g/mol | 119 g/mol phase | solid (at STP) | solid (at STP) | solid (at STP) | solid (at STP) melting point | 64 °C | 711 °C | 648 °C | 734 °C boiling point | 760 °C | | 1090 °C | 1435 °C density | 0.86 g/cm^3 | 3.72 g/cm^3 | 1.738 g/cm^3 | 2.75 g/cm^3 solubility in water | reacts | soluble | reacts | soluble