NaOH + P2 = H2O + NaP + NaPO3

Input interpretation

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NaOH sodium hydroxide + P_2 diphosphorus ⟶ H_2O water + NaP + NaPO_3 calgon pT

Balanced equation

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Balance the chemical equation algebraically: NaOH + P_2 ⟶ H_2O + NaP + NaPO_3 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 NaOH + c_2 P_2 ⟶ c_3 H_2O + c_4 NaP + c_5 NaPO_3 Set the number of atoms in the reactants equal to the number of atoms in the products for H, Na, O and P: H: | c_1 = 2 c_3 Na: | c_1 = c_4 + c_5 O: | c_1 = c_3 + 3 c_5 P: | 2 c_2 = c_4 + c_5 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_5 = 1 and solve the system of equations for the remaining coefficients: c_1 = 6 c_2 = 3 c_3 = 3 c_4 = 5 c_5 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 6 NaOH + 3 P_2 ⟶ 3 H_2O + 5 NaP + NaPO_3

+ ⟶ + NaP + NaPO_3

Names

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sodium hydroxide + diphosphorus ⟶ water + NaP + calgon pT

Equilibrium constant

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Construct the equilibrium constant, K, expression for: NaOH + P_2 ⟶ H_2O + NaP + NaPO_3 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 NaOH + 3 P_2 ⟶ 3 H_2O + 5 NaP + NaPO_3 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 | 6 | -6 P_2 | 3 | -3 H_2O | 3 | 3 NaP | 5 | 5 NaPO_3 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression NaOH | 6 | -6 | ([NaOH])^(-6) P_2 | 3 | -3 | ([P2])^(-3) H_2O | 3 | 3 | ([H2O])^3 NaP | 5 | 5 | ([NaP])^5 NaPO_3 | 1 | 1 | [NaPO3] 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])^(-6) ([P2])^(-3) ([H2O])^3 ([NaP])^5 [NaPO3] = (([H2O])^3 ([NaP])^5 [NaPO3])/(([NaOH])^6 ([P2])^3)

Rate of reaction

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Construct the rate of reaction expression for: NaOH + P_2 ⟶ H_2O + NaP + NaPO_3 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 NaOH + 3 P_2 ⟶ 3 H_2O + 5 NaP + NaPO_3 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 | 6 | -6 P_2 | 3 | -3 H_2O | 3 | 3 NaP | 5 | 5 NaPO_3 | 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 NaOH | 6 | -6 | -1/6 (Δ[NaOH])/(Δt) P_2 | 3 | -3 | -1/3 (Δ[P2])/(Δt) H_2O | 3 | 3 | 1/3 (Δ[H2O])/(Δt) NaP | 5 | 5 | 1/5 (Δ[NaP])/(Δt) NaPO_3 | 1 | 1 | (Δ[NaPO3])/(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[NaOH])/(Δt) = -1/3 (Δ[P2])/(Δt) = 1/3 (Δ[H2O])/(Δt) = 1/5 (Δ[NaP])/(Δt) = (Δ[NaPO3])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)