NaOH + NaNO2 + Be = H2O + NH3 + Na2BeO2

Input interpretation

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NaOH sodium hydroxide + NaNO_2 sodium nitrite + Be beryllium ⟶ H_2O water + NH_3 ammonia + Na2BeO2

Balanced equation

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Balance the chemical equation algebraically: NaOH + NaNO_2 + Be ⟶ H_2O + NH_3 + Na2BeO2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 NaOH + c_2 NaNO_2 + c_3 Be ⟶ c_4 H_2O + c_5 NH_3 + c_6 Na2BeO2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, Na, O, N and Be: H: | c_1 = 2 c_4 + 3 c_5 Na: | c_1 + c_2 = 2 c_6 O: | c_1 + 2 c_2 = c_4 + 2 c_6 N: | c_2 = c_5 Be: | c_3 = c_6 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 = 5 c_2 = 1 c_3 = 3 c_4 = 1 c_5 = 1 c_6 = 3 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 5 NaOH + NaNO_2 + 3 Be ⟶ H_2O + NH_3 + 3 Na2BeO2

+ + ⟶ + + Na2BeO2

Names

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sodium hydroxide + sodium nitrite + beryllium ⟶ water + ammonia + Na2BeO2

Equilibrium constant

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Construct the equilibrium constant, K, expression for: NaOH + NaNO_2 + Be ⟶ H_2O + NH_3 + Na2BeO2 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: 5 NaOH + NaNO_2 + 3 Be ⟶ H_2O + NH_3 + 3 Na2BeO2 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 NaOH | 5 | -5 NaNO_2 | 1 | -1 Be | 3 | -3 H_2O | 1 | 1 NH_3 | 1 | 1 Na2BeO2 | 3 | 3 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression NaOH | 5 | -5 | ([NaOH])^(-5) NaNO_2 | 1 | -1 | ([NaNO2])^(-1) Be | 3 | -3 | ([Be])^(-3) H_2O | 1 | 1 | [H2O] NH_3 | 1 | 1 | [NH3] Na2BeO2 | 3 | 3 | ([Na2BeO2])^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 = ([NaOH])^(-5) ([NaNO2])^(-1) ([Be])^(-3) [H2O] [NH3] ([Na2BeO2])^3 = ([H2O] [NH3] ([Na2BeO2])^3)/(([NaOH])^5 [NaNO2] ([Be])^3)

Rate of reaction

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Construct the rate of reaction expression for: NaOH + NaNO_2 + Be ⟶ H_2O + NH_3 + Na2BeO2 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: 5 NaOH + NaNO_2 + 3 Be ⟶ H_2O + NH_3 + 3 Na2BeO2 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 NaOH | 5 | -5 NaNO_2 | 1 | -1 Be | 3 | -3 H_2O | 1 | 1 NH_3 | 1 | 1 Na2BeO2 | 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 NaOH | 5 | -5 | -1/5 (Δ[NaOH])/(Δt) NaNO_2 | 1 | -1 | -(Δ[NaNO2])/(Δt) Be | 3 | -3 | -1/3 (Δ[Be])/(Δt) H_2O | 1 | 1 | (Δ[H2O])/(Δt) NH_3 | 1 | 1 | (Δ[NH3])/(Δt) Na2BeO2 | 3 | 3 | 1/3 (Δ[Na2BeO2])/(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 = -1/5 (Δ[NaOH])/(Δt) = -(Δ[NaNO2])/(Δt) = -1/3 (Δ[Be])/(Δt) = (Δ[H2O])/(Δt) = (Δ[NH3])/(Δt) = 1/3 (Δ[Na2BeO2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)