HBr + AgOH = H2O + AgBr

HBr hydrogen bromide + AgOH ⟶ H_2O water + AgBr silver bromide

Balance the chemical equation algebraically: HBr + AgOH ⟶ H_2O + AgBr Add stoichiometric coefficients, c_i, to the reactants and products: c_1 HBr + c_2 AgOH ⟶ c_3 H_2O + c_4 AgBr Set the number of atoms in the reactants equal to the number of atoms in the products for Br, H, Ag and O: Br: | c_1 = c_4 H: | c_1 + c_2 = 2 c_3 Ag: | c_2 = c_4 O: | 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 = 1 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | HBr + AgOH ⟶ H_2O + AgBr

+ AgOH ⟶ +

hydrogen bromide + AgOH ⟶ water + silver bromide

Construct the equilibrium constant, K, expression for: HBr + AgOH ⟶ H_2O + AgBr 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: HBr + AgOH ⟶ H_2O + AgBr 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 HBr | 1 | -1 AgOH | 1 | -1 H_2O | 1 | 1 AgBr | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression HBr | 1 | -1 | ([HBr])^(-1) AgOH | 1 | -1 | ([AgOH])^(-1) H_2O | 1 | 1 | [H2O] AgBr | 1 | 1 | [AgBr] 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 = ([HBr])^(-1) ([AgOH])^(-1) [H2O] [AgBr] = ([H2O] [AgBr])/([HBr] [AgOH])

Construct the rate of reaction expression for: HBr + AgOH ⟶ H_2O + AgBr 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: HBr + AgOH ⟶ H_2O + AgBr 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 HBr | 1 | -1 AgOH | 1 | -1 H_2O | 1 | 1 AgBr | 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 HBr | 1 | -1 | -(Δ[HBr])/(Δt) AgOH | 1 | -1 | -(Δ[AgOH])/(Δt) H_2O | 1 | 1 | (Δ[H2O])/(Δt) AgBr | 1 | 1 | (Δ[AgBr])/(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[HBr])/(Δt) = -(Δ[AgOH])/(Δt) = (Δ[H2O])/(Δt) = (Δ[AgBr])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| hydrogen bromide | AgOH | water | silver bromide formula | HBr | AgOH | H_2O | AgBr Hill formula | BrH | HAgO | H_2O | AgBr name | hydrogen bromide | | water | silver bromide IUPAC name | hydrogen bromide | | water | bromosilver

| hydrogen bromide | AgOH | water | silver bromide molar mass | 80.912 g/mol | 124.875 g/mol | 18.015 g/mol | 187.77 g/mol phase | gas (at STP) | | liquid (at STP) | solid (at STP) melting point | -86.8 °C | | 0 °C | 432 °C boiling point | -66.38 °C | | 99.9839 °C | 1300 °C density | 0.003307 g/cm^3 (at 25 °C) | | 1 g/cm^3 | 6.473 g/cm^3 solubility in water | miscible | | | insoluble surface tension | 0.0271 N/m | | 0.0728 N/m | dynamic viscosity | 8.4×10^-4 Pa s (at -75 °C) | | 8.9×10^-4 Pa s (at 25 °C) | odor | | | odorless |