Input interpretation
NH_3 ammonia + NH4S2O8 ⟶ N_2 nitrogen + (NH_4)_2SO_4 ammonium sulfate
Balanced equation
Balance the chemical equation algebraically: NH_3 + NH4S2O8 ⟶ N_2 + (NH_4)_2SO_4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 NH_3 + c_2 NH4S2O8 ⟶ c_3 N_2 + c_4 (NH_4)_2SO_4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, N, S and O: H: | 3 c_1 + 4 c_2 = 8 c_4 N: | c_1 + c_2 = 2 c_3 + 2 c_4 S: | 2 c_2 = c_4 O: | 8 c_2 = 4 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_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 8 c_2 = 2 c_3 = 1 c_4 = 4 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 8 NH_3 + 2 NH4S2O8 ⟶ N_2 + 4 (NH_4)_2SO_4
Structures
+ NH4S2O8 ⟶ +
Names
ammonia + NH4S2O8 ⟶ nitrogen + ammonium sulfate
Equilibrium constant
Construct the equilibrium constant, K, expression for: NH_3 + NH4S2O8 ⟶ N_2 + (NH_4)_2SO_4 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: 8 NH_3 + 2 NH4S2O8 ⟶ N_2 + 4 (NH_4)_2SO_4 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 | 8 | -8 NH4S2O8 | 2 | -2 N_2 | 1 | 1 (NH_4)_2SO_4 | 4 | 4 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression NH_3 | 8 | -8 | ([NH3])^(-8) NH4S2O8 | 2 | -2 | ([NH4S2O8])^(-2) N_2 | 1 | 1 | [N2] (NH_4)_2SO_4 | 4 | 4 | ([(NH4)2SO4])^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 = ([NH3])^(-8) ([NH4S2O8])^(-2) [N2] ([(NH4)2SO4])^4 = ([N2] ([(NH4)2SO4])^4)/(([NH3])^8 ([NH4S2O8])^2)
Rate of reaction
Construct the rate of reaction expression for: NH_3 + NH4S2O8 ⟶ N_2 + (NH_4)_2SO_4 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: 8 NH_3 + 2 NH4S2O8 ⟶ N_2 + 4 (NH_4)_2SO_4 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 | 8 | -8 NH4S2O8 | 2 | -2 N_2 | 1 | 1 (NH_4)_2SO_4 | 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_3 | 8 | -8 | -1/8 (Δ[NH3])/(Δt) NH4S2O8 | 2 | -2 | -1/2 (Δ[NH4S2O8])/(Δt) N_2 | 1 | 1 | (Δ[N2])/(Δt) (NH_4)_2SO_4 | 4 | 4 | 1/4 (Δ[(NH4)2SO4])/(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 = -1/8 (Δ[NH3])/(Δt) = -1/2 (Δ[NH4S2O8])/(Δt) = (Δ[N2])/(Δt) = 1/4 (Δ[(NH4)2SO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)
Chemical names and formulas
| ammonia | NH4S2O8 | nitrogen | ammonium sulfate formula | NH_3 | NH4S2O8 | N_2 | (NH_4)_2SO_4 Hill formula | H_3N | H4NO8S2 | N_2 | H_8N_2O_4S name | ammonia | | nitrogen | ammonium sulfate IUPAC name | ammonia | | molecular nitrogen |
Substance properties
| ammonia | NH4S2O8 | nitrogen | ammonium sulfate molar mass | 17.031 g/mol | 210.2 g/mol | 28.014 g/mol | 132.1 g/mol phase | gas (at STP) | | gas (at STP) | solid (at STP) melting point | -77.73 °C | | -210 °C | 280 °C boiling point | -33.33 °C | | -195.79 °C | density | 6.96×10^-4 g/cm^3 (at 25 °C) | | 0.001251 g/cm^3 (at 0 °C) | 1.77 g/cm^3 solubility in water | | | insoluble | surface tension | 0.0234 N/m | | 0.0066 N/m | dynamic viscosity | 1.009×10^-5 Pa s (at 25 °C) | | 1.78×10^-5 Pa s (at 25 °C) | odor | | | odorless | odorless
Units