H3PO4 + Na = H2 + NaPO4

Input interpretation

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H_3PO_4 phosphoric acid + Na sodium ⟶ H_2 hydrogen + NaPO4

Balanced equation

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$Balance the chemical equation algebraically: H_3PO_4 + Na ⟶ H_2 + NaPO4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_3PO_4 + c_2 Na ⟶ c_3 H_2 + c_4 NaPO4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, P and Na: H: | 3 c_1 = 2 c_3 O: | 4 c_1 = 4 c_4 P: | c_1 = c_4 Na: | c_2 = c_4 Since the coefficients are relative quantities and underdetermined, choose a coefficient to set arbitrarily. To keep the coefficients small, the arbitrary value is ordinarily one. For instance, set c_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 1 c_3 = 3/2 c_4 = 1 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 2 c_2 = 2 c_3 = 3 c_4 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 H_3PO_4 + 2 Na ⟶ 3 H_2 + 2 NaPO4$

Balance the chemical equation algebraically: H_3PO_4 + Na ⟶ H_2 + NaPO4 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_3PO_4 + c_2 Na ⟶ c_3 H_2 + c_4 NaPO4 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, P and Na: H: | 3 c_1 = 2 c_3 O: | 4 c_1 = 4 c_4 P: | c_1 = c_4 Na: | c_2 = 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_1 = 1 and solve the system of equations for the remaining coefficients: c_1 = 1 c_2 = 1 c_3 = 3/2 c_4 = 1 Multiply by the least common denominator, 2, to eliminate fractional coefficients: c_1 = 2 c_2 = 2 c_3 = 3 c_4 = 2 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 H_3PO_4 + 2 Na ⟶ 3 H_2 + 2 NaPO4

+ ⟶ + NaPO4

Names

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phosphoric acid + sodium ⟶ hydrogen + NaPO4

Equilibrium constant

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Construct the equilibrium constant, K, expression for: H_3PO_4 + Na ⟶ H_2 + NaPO4 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: 2 H_3PO_4 + 2 Na ⟶ 3 H_2 + 2 NaPO4 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 H_3PO_4 | 2 | -2 Na | 2 | -2 H_2 | 3 | 3 NaPO4 | 2 | 2 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_3PO_4 | 2 | -2 | ([H3PO4])^(-2) Na | 2 | -2 | ([Na])^(-2) H_2 | 3 | 3 | ([H2])^3 NaPO4 | 2 | 2 | ([NaPO4])^2 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 = ([H3PO4])^(-2) ([Na])^(-2) ([H2])^3 ([NaPO4])^2 = (([H2])^3 ([NaPO4])^2)/(([H3PO4])^2 ([Na])^2)

Rate of reaction

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Construct the rate of reaction expression for: H_3PO_4 + Na ⟶ H_2 + NaPO4 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: 2 H_3PO_4 + 2 Na ⟶ 3 H_2 + 2 NaPO4 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 H_3PO_4 | 2 | -2 Na | 2 | -2 H_2 | 3 | 3 NaPO4 | 2 | 2 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 H_3PO_4 | 2 | -2 | -1/2 (Δ[H3PO4])/(Δt) Na | 2 | -2 | -1/2 (Δ[Na])/(Δt) H_2 | 3 | 3 | 1/3 (Δ[H2])/(Δt) NaPO4 | 2 | 2 | 1/2 (Δ[NaPO4])/(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 = -1/2 (Δ[H3PO4])/(Δt) = -1/2 (Δ[Na])/(Δt) = 1/3 (Δ[H2])/(Δt) = 1/2 (Δ[NaPO4])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)