N2H4 + AgOH = H2O + N2 + Ag

NH_2NH_2 diazane + AgOH ⟶ H_2O water + N_2 nitrogen + Ag silver

Balance the chemical equation algebraically: NH_2NH_2 + AgOH ⟶ H_2O + N_2 + Ag Add stoichiometric coefficients, c_i, to the reactants and products: c_1 NH_2NH_2 + c_2 AgOH ⟶ c_3 H_2O + c_4 N_2 + c_5 Ag Set the number of atoms in the reactants equal to the number of atoms in the products for H, N, Ag and O: H: | 4 c_1 + c_2 = 2 c_3 N: | 2 c_1 = 2 c_4 Ag: | c_2 = c_5 O: | 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 4 c_3 = 4 c_4 = 1 c_5 = 4 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | NH_2NH_2 + 4 AgOH ⟶ 4 H_2O + N_2 + 4 Ag

+ AgOH ⟶ + +

diazane + AgOH ⟶ water + nitrogen + silver

Construct the equilibrium constant, K, expression for: NH_2NH_2 + AgOH ⟶ H_2O + N_2 + Ag 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: NH_2NH_2 + 4 AgOH ⟶ 4 H_2O + N_2 + 4 Ag 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_2NH_2 | 1 | -1 AgOH | 4 | -4 H_2O | 4 | 4 N_2 | 1 | 1 Ag | 4 | 4 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression NH_2NH_2 | 1 | -1 | ([NH2NH2])^(-1) AgOH | 4 | -4 | ([AgOH])^(-4) H_2O | 4 | 4 | ([H2O])^4 N_2 | 1 | 1 | [N2] Ag | 4 | 4 | ([Ag])^4 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 = ([NH2NH2])^(-1) ([AgOH])^(-4) ([H2O])^4 [N2] ([Ag])^4 = (([H2O])^4 [N2] ([Ag])^4)/([NH2NH2] ([AgOH])^4)

Construct the rate of reaction expression for: NH_2NH_2 + AgOH ⟶ H_2O + N_2 + Ag 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: NH_2NH_2 + 4 AgOH ⟶ 4 H_2O + N_2 + 4 Ag 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_2NH_2 | 1 | -1 AgOH | 4 | -4 H_2O | 4 | 4 N_2 | 1 | 1 Ag | 4 | 4 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_2NH_2 | 1 | -1 | -(Δ[NH2NH2])/(Δt) AgOH | 4 | -4 | -1/4 (Δ[AgOH])/(Δt) H_2O | 4 | 4 | 1/4 (Δ[H2O])/(Δt) N_2 | 1 | 1 | (Δ[N2])/(Δt) Ag | 4 | 4 | 1/4 (Δ[Ag])/(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 = -(Δ[NH2NH2])/(Δt) = -1/4 (Δ[AgOH])/(Δt) = 1/4 (Δ[H2O])/(Δt) = (Δ[N2])/(Δt) = 1/4 (Δ[Ag])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| diazane | AgOH | water | nitrogen | silver formula | NH_2NH_2 | AgOH | H_2O | N_2 | Ag Hill formula | H_4N_2 | HAgO | H_2O | N_2 | Ag name | diazane | | water | nitrogen | silver IUPAC name | hydrazine | | water | molecular nitrogen | silver

| diazane | AgOH | water | nitrogen | silver molar mass | 32.046 g/mol | 124.875 g/mol | 18.015 g/mol | 28.014 g/mol | 107.8682 g/mol phase | liquid (at STP) | | liquid (at STP) | gas (at STP) | solid (at STP) melting point | 1 °C | | 0 °C | -210 °C | 960 °C boiling point | 113.5 °C | | 99.9839 °C | -195.79 °C | 2212 °C density | 1.011 g/cm^3 | | 1 g/cm^3 | 0.001251 g/cm^3 (at 0 °C) | 10.49 g/cm^3 solubility in water | miscible | | | insoluble | insoluble surface tension | 0.0667 N/m | | 0.0728 N/m | 0.0066 N/m | dynamic viscosity | 8.76×10^-4 Pa s (at 25 °C) | | 8.9×10^-4 Pa s (at 25 °C) | 1.78×10^-5 Pa s (at 25 °C) | odor | | | odorless | odorless |