NH4NO3 + Li3N = LiNO3 + (NH4)3N

Input interpretation

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NH_4NO_3 ammonium nitrate + Li_3N lithium nitride ⟶ LiNO_3 lithium nitrate + (NH4)3N

Balanced equation

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$Balance the chemical equation algebraically: NH_4NO_3 + Li_3N ⟶ LiNO_3 + (NH4)3N Add stoichiometric coefficients, c_i, to the reactants and products: c_1 NH_4NO_3 + c_2 Li_3N ⟶ c_3 LiNO_3 + c_4 (NH4)3N Set the number of atoms in the reactants equal to the number of atoms in the products for H, N, O and Li: H: | 4 c_1 + 6 c_2 = 12 c_4 N: | 2 c_1 + 3 c_2 = c_3 + 4 c_4 O: | 3 c_1 = 3 c_3 Li: | 3 c_2 = c_3 Since the coefficients are relative quantities and underdetermined, choose a coefficient to set arbitrarily. To keep the coefficients small, the arbitrary value is ordinarily one. For instance, set c_2 = 1 and solve the system of equations for the remaining coefficients: c_1 = 3 c_2 = 1 c_3 = 3 c_4 = 3/2 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 6 c_2 = 2 c_3 = 6 c_4 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 6 NH_4NO_3 + 2 Li_3N ⟶ 6 LiNO_3 + 3 (NH4)3N$

Balance the chemical equation algebraically: NH_4NO_3 + Li_3N ⟶ LiNO_3 + (NH4)3N Add stoichiometric coefficients, c_i, to the reactants and products: c_1 NH_4NO_3 + c_2 Li_3N ⟶ c_3 LiNO_3 + c_4 (NH4)3N Set the number of atoms in the reactants equal to the number of atoms in the products for H, N, O and Li: H: | 4 c_1 + 6 c_2 = 12 c_4 N: | 2 c_1 + 3 c_2 = c_3 + 4 c_4 O: | 3 c_1 = 3 c_3 Li: | 3 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 = 3 c_2 = 1 c_3 = 3 c_4 = 3/2 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 6 c_2 = 2 c_3 = 6 c_4 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 6 NH_4NO_3 + 2 Li_3N ⟶ 6 LiNO_3 + 3 (NH4)3N

+ ⟶ + (NH4)3N

Names

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ammonium nitrate + lithium nitride ⟶ lithium nitrate + (NH4)3N

Equilibrium constant

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Construct the equilibrium constant, K, expression for: NH_4NO_3 + Li_3N ⟶ LiNO_3 + (NH4)3N 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: 6 NH_4NO_3 + 2 Li_3N ⟶ 6 LiNO_3 + 3 (NH4)3N 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_4NO_3 | 6 | -6 Li_3N | 2 | -2 LiNO_3 | 6 | 6 (NH4)3N | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression NH_4NO_3 | 6 | -6 | ([NH4NO3])^(-6) Li_3N | 2 | -2 | ([Li3N])^(-2) LiNO_3 | 6 | 6 | ([LiNO3])^6 (NH4)3N | 3 | 3 | ([(NH4)3N])^3 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 = ([NH4NO3])^(-6) ([Li3N])^(-2) ([LiNO3])^6 ([(NH4)3N])^3 = (([LiNO3])^6 ([(NH4)3N])^3)/(([NH4NO3])^6 ([Li3N])^2)

Rate of reaction

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Construct the rate of reaction expression for: NH_4NO_3 + Li_3N ⟶ LiNO_3 + (NH4)3N 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: 6 NH_4NO_3 + 2 Li_3N ⟶ 6 LiNO_3 + 3 (NH4)3N 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_4NO_3 | 6 | -6 Li_3N | 2 | -2 LiNO_3 | 6 | 6 (NH4)3N | 3 | 3 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_4NO_3 | 6 | -6 | -1/6 (Δ[NH4NO3])/(Δt) Li_3N | 2 | -2 | -1/2 (Δ[Li3N])/(Δt) LiNO_3 | 6 | 6 | 1/6 (Δ[LiNO3])/(Δt) (NH4)3N | 3 | 3 | 1/3 (Δ[(NH4)3N])/(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 = -1/6 (Δ[NH4NO3])/(Δt) = -1/2 (Δ[Li3N])/(Δt) = 1/6 (Δ[LiNO3])/(Δt) = 1/3 (Δ[(NH4)3N])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)