NH3 + (N2H5)HSO4 = (NH4)2SO4 + N2H4

NH_3 ammonia + NH_2NH_2·H_2SO_4 hydrazine sulfate ⟶ (NH_4)_2SO_4 ammonium sulfate + NH_2NH_2 diazane

Balance the chemical equation algebraically: NH_3 + NH_2NH_2·H_2SO_4 ⟶ (NH_4)_2SO_4 + NH_2NH_2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 NH_3 + c_2 NH_2NH_2·H_2SO_4 ⟶ c_3 (NH_4)_2SO_4 + c_4 NH_2NH_2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, N, O and S: H: | 3 c_1 + 6 c_2 = 8 c_3 + 4 c_4 N: | c_1 + 2 c_2 = 2 c_3 + 2 c_4 O: | 4 c_2 = 4 c_3 S: | 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 = 2 c_2 = 1 c_3 = 1 c_4 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 NH_3 + NH_2NH_2·H_2SO_4 ⟶ (NH_4)_2SO_4 + NH_2NH_2

+ ⟶ +

ammonia + hydrazine sulfate ⟶ ammonium sulfate + diazane

Construct the equilibrium constant, K, expression for: NH_3 + NH_2NH_2·H_2SO_4 ⟶ (NH_4)_2SO_4 + NH_2NH_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 NH_3 + NH_2NH_2·H_2SO_4 ⟶ (NH_4)_2SO_4 + NH_2NH_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 NH_3 | 2 | -2 NH_2NH_2·H_2SO_4 | 1 | -1 (NH_4)_2SO_4 | 1 | 1 NH_2NH_2 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression NH_3 | 2 | -2 | ([NH3])^(-2) NH_2NH_2·H_2SO_4 | 1 | -1 | ([NH2NH2·H2SO4])^(-1) (NH_4)_2SO_4 | 1 | 1 | [(NH4)2SO4] NH_2NH_2 | 1 | 1 | [NH2NH2] 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 = ([NH3])^(-2) ([NH2NH2·H2SO4])^(-1) [(NH4)2SO4] [NH2NH2] = ([(NH4)2SO4] [NH2NH2])/(([NH3])^2 [NH2NH2·H2SO4])

Construct the rate of reaction expression for: NH_3 + NH_2NH_2·H_2SO_4 ⟶ (NH_4)_2SO_4 + NH_2NH_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 NH_3 + NH_2NH_2·H_2SO_4 ⟶ (NH_4)_2SO_4 + NH_2NH_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 NH_3 | 2 | -2 NH_2NH_2·H_2SO_4 | 1 | -1 (NH_4)_2SO_4 | 1 | 1 NH_2NH_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 NH_3 | 2 | -2 | -1/2 (Δ[NH3])/(Δt) NH_2NH_2·H_2SO_4 | 1 | -1 | -(Δ[NH2NH2·H2SO4])/(Δt) (NH_4)_2SO_4 | 1 | 1 | (Δ[(NH4)2SO4])/(Δt) NH_2NH_2 | 1 | 1 | (Δ[NH2NH2])/(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[NH3])/(Δt) = -(Δ[NH2NH2·H2SO4])/(Δt) = (Δ[(NH4)2SO4])/(Δt) = (Δ[NH2NH2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| ammonia | hydrazine sulfate | ammonium sulfate | diazane formula | NH_3 | NH_2NH_2·H_2SO_4 | (NH_4)_2SO_4 | NH_2NH_2 Hill formula | H_3N | H_6N_2O_4S | H_8N_2O_4S | H_4N_2 name | ammonia | hydrazine sulfate | ammonium sulfate | diazane IUPAC name | ammonia | hydrazine; sulfuric acid | | hydrazine

| ammonia | hydrazine sulfate | ammonium sulfate | diazane molar mass | 17.031 g/mol | 130.1 g/mol | 132.1 g/mol | 32.046 g/mol phase | gas (at STP) | solid (at STP) | solid (at STP) | liquid (at STP) melting point | -77.73 °C | 254 °C | 280 °C | 1 °C boiling point | -33.33 °C | | | 113.5 °C density | 6.96×10^-4 g/cm^3 (at 25 °C) | 1.37 g/cm^3 | 1.77 g/cm^3 | 1.011 g/cm^3 solubility in water | | soluble | | miscible surface tension | 0.0234 N/m | | | 0.0667 N/m dynamic viscosity | 1.009×10^-5 Pa s (at 25 °C) | | | 8.76×10^-4 Pa s (at 25 °C) odor | | | odorless |