H2 + K2SO4 = H2O + K2S

H_2 hydrogen + K_2SO_4 potassium sulfate ⟶ H_2O water + K2S

Balance the chemical equation algebraically: H_2 + K_2SO_4 ⟶ H_2O + K2S Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2 + c_2 K_2SO_4 ⟶ c_3 H_2O + c_4 K2S Set the number of atoms in the reactants equal to the number of atoms in the products for H, K, O and S: H: | 2 c_1 = 2 c_3 K: | 2 c_2 = 2 c_4 O: | 4 c_2 = c_3 S: | 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_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 4 c_2 = 1 c_3 = 4 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 4 H_2 + K_2SO_4 ⟶ 4 H_2O + K2S

+ ⟶ + K2S

hydrogen + potassium sulfate ⟶ water + K2S

Construct the equilibrium constant, K, expression for: H_2 + K_2SO_4 ⟶ H_2O + K2S 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_2 + K_2SO_4 ⟶ 4 H_2O + K2S 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_2 | 4 | -4 K_2SO_4 | 1 | -1 H_2O | 4 | 4 K2S | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2 | 4 | -4 | ([H2])^(-4) K_2SO_4 | 1 | -1 | ([K2SO4])^(-1) H_2O | 4 | 4 | ([H2O])^4 K2S | 1 | 1 | [K2S] 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 = ([H2])^(-4) ([K2SO4])^(-1) ([H2O])^4 [K2S] = (([H2O])^4 [K2S])/(([H2])^4 [K2SO4])

Construct the rate of reaction expression for: H_2 + K_2SO_4 ⟶ H_2O + K2S 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_2 + K_2SO_4 ⟶ 4 H_2O + K2S 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_2 | 4 | -4 K_2SO_4 | 1 | -1 H_2O | 4 | 4 K2S | 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_2 | 4 | -4 | -1/4 (Δ[H2])/(Δt) K_2SO_4 | 1 | -1 | -(Δ[K2SO4])/(Δt) H_2O | 4 | 4 | 1/4 (Δ[H2O])/(Δt) K2S | 1 | 1 | (Δ[K2S])/(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[H2])/(Δt) = -(Δ[K2SO4])/(Δt) = 1/4 (Δ[H2O])/(Δt) = (Δ[K2S])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| hydrogen | potassium sulfate | water | K2S formula | H_2 | K_2SO_4 | H_2O | K2S Hill formula | H_2 | K_2O_4S | H_2O | K2S name | hydrogen | potassium sulfate | water | IUPAC name | molecular hydrogen | dipotassium sulfate | water |

| hydrogen | potassium sulfate | water | K2S molar mass | 2.016 g/mol | 174.25 g/mol | 18.015 g/mol | 110.26 g/mol phase | gas (at STP) | | liquid (at STP) | melting point | -259.2 °C | | 0 °C | boiling point | -252.8 °C | | 99.9839 °C | density | 8.99×10^-5 g/cm^3 (at 0 °C) | | 1 g/cm^3 | solubility in water | | soluble | | surface tension | | | 0.0728 N/m | dynamic viscosity | 8.9×10^-6 Pa s (at 25 °C) | | 8.9×10^-4 Pa s (at 25 °C) | odor | odorless | | odorless |