H2O + C2H5MgI = C2H6 + Mg(OH)I

H_2O water + C2H5MgI ⟶ CH_3CH_3 ethane + MgOHI

Balance the chemical equation algebraically: H_2O + C2H5MgI ⟶ CH_3CH_3 + MgOHI Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 C2H5MgI ⟶ c_3 CH_3CH_3 + c_4 MgOHI Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, C, Mg and I: H: | 2 c_1 + 5 c_2 = 6 c_3 + c_4 O: | c_1 = c_4 C: | 2 c_2 = 2 c_3 Mg: | c_2 = c_4 I: | c_2 = 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 = 1 c_3 = 1 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | H_2O + C2H5MgI ⟶ CH_3CH_3 + MgOHI

+ C2H5MgI ⟶ + MgOHI

water + C2H5MgI ⟶ ethane + MgOHI

Construct the equilibrium constant, K, expression for: H_2O + C2H5MgI ⟶ CH_3CH_3 + MgOHI 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 + C2H5MgI ⟶ CH_3CH_3 + MgOHI 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 C2H5MgI | 1 | -1 CH_3CH_3 | 1 | 1 MgOHI | 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) C2H5MgI | 1 | -1 | ([C2H5MgI])^(-1) CH_3CH_3 | 1 | 1 | [CH3CH3] MgOHI | 1 | 1 | [MgOHI] 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) ([C2H5MgI])^(-1) [CH3CH3] [MgOHI] = ([CH3CH3] [MgOHI])/([H2O] [C2H5MgI])

Construct the rate of reaction expression for: H_2O + C2H5MgI ⟶ CH_3CH_3 + MgOHI 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 + C2H5MgI ⟶ CH_3CH_3 + MgOHI 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 C2H5MgI | 1 | -1 CH_3CH_3 | 1 | 1 MgOHI | 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) C2H5MgI | 1 | -1 | -(Δ[C2H5MgI])/(Δt) CH_3CH_3 | 1 | 1 | (Δ[CH3CH3])/(Δt) MgOHI | 1 | 1 | (Δ[MgOHI])/(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) = -(Δ[C2H5MgI])/(Δt) = (Δ[CH3CH3])/(Δt) = (Δ[MgOHI])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | C2H5MgI | ethane | MgOHI formula | H_2O | C2H5MgI | CH_3CH_3 | MgOHI Hill formula | H_2O | C2H5IMg | C_2H_6 | HIMgO name | water | | ethane |

| water | C2H5MgI | ethane | MgOHI molar mass | 18.015 g/mol | 180.27 g/mol | 30.07 g/mol | 168.216 g/mol phase | liquid (at STP) | | gas (at STP) | melting point | 0 °C | | -182.79 °C | boiling point | 99.9839 °C | | -88.6 °C | density | 1 g/cm^3 | | 0.00125324 g/cm^3 (at 20 °C) | solubility in water | | | soluble | surface tension | 0.0728 N/m | | | dynamic viscosity | 8.9×10^-4 Pa s (at 25 °C) | | 9.446×10^-6 Pa s (at 25 °C) | odor | odorless | | odorless |