H2SO4 + K = H2O + K2SO4 + SO2

H_2SO_4 sulfuric acid + K potassium ⟶ H_2O water + K_2SO_4 potassium sulfate + SO_2 sulfur dioxide

Balance the chemical equation algebraically: H_2SO_4 + K ⟶ H_2O + K_2SO_4 + SO_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2SO_4 + c_2 K ⟶ c_3 H_2O + c_4 K_2SO_4 + c_5 SO_2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, S and K: H: | 2 c_1 = 2 c_3 O: | 4 c_1 = c_3 + 4 c_4 + 2 c_5 S: | c_1 = c_4 + c_5 K: | c_2 = 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_4 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 2 c_3 = 2 c_4 = 1 c_5 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 H_2SO_4 + 2 K ⟶ 2 H_2O + K_2SO_4 + SO_2

+ ⟶ + +

sulfuric acid + potassium ⟶ water + potassium sulfate + sulfur dioxide

Construct the equilibrium constant, K, expression for: H_2SO_4 + K ⟶ H_2O + K_2SO_4 + SO_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: 2 H_2SO_4 + 2 K ⟶ 2 H_2O + K_2SO_4 + SO_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_2SO_4 | 2 | -2 K | 2 | -2 H_2O | 2 | 2 K_2SO_4 | 1 | 1 SO_2 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2SO_4 | 2 | -2 | ([H2SO4])^(-2) K | 2 | -2 | ([K])^(-2) H_2O | 2 | 2 | ([H2O])^2 K_2SO_4 | 1 | 1 | [K2SO4] SO_2 | 1 | 1 | [SO2] 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 = ([H2SO4])^(-2) ([K])^(-2) ([H2O])^2 [K2SO4] [SO2] = (([H2O])^2 [K2SO4] [SO2])/(([H2SO4])^2 ([K])^2)

Construct the rate of reaction expression for: H_2SO_4 + K ⟶ H_2O + K_2SO_4 + SO_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: 2 H_2SO_4 + 2 K ⟶ 2 H_2O + K_2SO_4 + SO_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_2SO_4 | 2 | -2 K | 2 | -2 H_2O | 2 | 2 K_2SO_4 | 1 | 1 SO_2 | 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_2SO_4 | 2 | -2 | -1/2 (Δ[H2SO4])/(Δt) K | 2 | -2 | -1/2 (Δ[K])/(Δt) H_2O | 2 | 2 | 1/2 (Δ[H2O])/(Δt) K_2SO_4 | 1 | 1 | (Δ[K2SO4])/(Δt) SO_2 | 1 | 1 | (Δ[SO2])/(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[H2SO4])/(Δt) = -1/2 (Δ[K])/(Δt) = 1/2 (Δ[H2O])/(Δt) = (Δ[K2SO4])/(Δt) = (Δ[SO2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| sulfuric acid | potassium | water | potassium sulfate | sulfur dioxide formula | H_2SO_4 | K | H_2O | K_2SO_4 | SO_2 Hill formula | H_2O_4S | K | H_2O | K_2O_4S | O_2S name | sulfuric acid | potassium | water | potassium sulfate | sulfur dioxide IUPAC name | sulfuric acid | potassium | water | dipotassium sulfate | sulfur dioxide