K + Si = K4Si

K potassium + Si silicon ⟶ K4Si

Balance the chemical equation algebraically: K + Si ⟶ K4Si Add stoichiometric coefficients, c_i, to the reactants and products: c_1 K + c_2 Si ⟶ c_3 K4Si Set the number of atoms in the reactants equal to the number of atoms in the products for K and Si: K: | c_1 = 4 c_3 Si: | 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 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 K + Si ⟶ K4Si

+ ⟶ K4Si

potassium + silicon ⟶ K4Si

Construct the equilibrium constant, K, expression for: K + Si ⟶ K4Si 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 K + Si ⟶ K4Si 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 | 4 | -4 Si | 1 | -1 K4Si | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression K | 4 | -4 | ([K])^(-4) Si | 1 | -1 | ([Si])^(-1) K4Si | 1 | 1 | [K4Si] 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])^(-4) ([Si])^(-1) [K4Si] = ([K4Si])/(([K])^4 [Si])

Construct the rate of reaction expression for: K + Si ⟶ K4Si 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 K + Si ⟶ K4Si 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 | 4 | -4 Si | 1 | -1 K4Si | 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 K | 4 | -4 | -1/4 (Δ[K])/(Δt) Si | 1 | -1 | -(Δ[Si])/(Δt) K4Si | 1 | 1 | (Δ[K4Si])/(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[K])/(Δt) = -(Δ[Si])/(Δt) = (Δ[K4Si])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| potassium | silicon | K4Si formula | K | Si | K4Si name | potassium | silicon |

| potassium | silicon | K4Si molar mass | 39.0983 g/mol | 28.085 g/mol | 184.478 g/mol phase | solid (at STP) | solid (at STP) | melting point | 64 °C | 1410 °C | boiling point | 760 °C | 2355 °C | density | 0.86 g/cm^3 | 2.33 g/cm^3 | solubility in water | reacts | insoluble |