H2O + Be2C = CH4 + Be(OH)2

H_2O water + Be2C ⟶ CH_4 methane + Be(OH)_2 beryllium hydroxide

Balance the chemical equation algebraically: H_2O + Be2C ⟶ CH_4 + Be(OH)_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 Be2C ⟶ c_3 CH_4 + c_4 Be(OH)_2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, Be and C: H: | 2 c_1 = 4 c_3 + 2 c_4 O: | c_1 = 2 c_4 Be: | 2 c_2 = c_4 C: | 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 = 4 c_2 = 1 c_3 = 1 c_4 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 H_2O + Be2C ⟶ CH_4 + 2 Be(OH)_2

+ Be2C ⟶ +

water + Be2C ⟶ methane + beryllium hydroxide

Construct the equilibrium constant, K, expression for: H_2O + Be2C ⟶ CH_4 + Be(OH)_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: 4 H_2O + Be2C ⟶ CH_4 + 2 Be(OH)_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 | 4 | -4 Be2C | 1 | -1 CH_4 | 1 | 1 Be(OH)_2 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 4 | -4 | ([H2O])^(-4) Be2C | 1 | -1 | ([Be2C])^(-1) CH_4 | 1 | 1 | [CH4] Be(OH)_2 | 2 | 2 | ([Be(OH)2])^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 = ([H2O])^(-4) ([Be2C])^(-1) [CH4] ([Be(OH)2])^2 = ([CH4] ([Be(OH)2])^2)/(([H2O])^4 [Be2C])

Construct the rate of reaction expression for: H_2O + Be2C ⟶ CH_4 + Be(OH)_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: 4 H_2O + Be2C ⟶ CH_4 + 2 Be(OH)_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 | 4 | -4 Be2C | 1 | -1 CH_4 | 1 | 1 Be(OH)_2 | 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 H_2O | 4 | -4 | -1/4 (Δ[H2O])/(Δt) Be2C | 1 | -1 | -(Δ[Be2C])/(Δt) CH_4 | 1 | 1 | (Δ[CH4])/(Δt) Be(OH)_2 | 2 | 2 | 1/2 (Δ[Be(OH)2])/(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 = -1/4 (Δ[H2O])/(Δt) = -(Δ[Be2C])/(Δt) = (Δ[CH4])/(Δt) = 1/2 (Δ[Be(OH)2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | Be2C | methane | beryllium hydroxide formula | H_2O | Be2C | CH_4 | Be(OH)_2 Hill formula | H_2O | CBe2 | CH_4 | BeH_2O_2 name | water | | methane | beryllium hydroxide IUPAC name | water | | methane | beryllium(+2) cation dihydroxide

| water | Be2C | methane | beryllium hydroxide molar mass | 18.015 g/mol | 30.035 g/mol | 16.04 g/mol | 43.026 g/mol phase | liquid (at STP) | | gas (at STP) | melting point | 0 °C | | -182.47 °C | boiling point | 99.9839 °C | | -161.48 °C | density | 1 g/cm^3 | | 6.67151×10^-4 g/cm^3 (at 20 °C) | 1.92 g/cm^3 solubility in water | | | soluble | surface tension | 0.0728 N/m | | 0.0137 N/m | dynamic viscosity | 8.9×10^-4 Pa s (at 25 °C) | | 1.114×10^-5 Pa s (at 25 °C) | odor | odorless | | odorless |