Question

The phosphorus pentoxide used to produce phosphoric acid for cola soft drinks is prepared by burning phosphorus in oxygen.

P₄ + 5O₂ ⟶ P₄O₁₀

Calculate the percent yield if 9.4 g of P4 reacts with 24.5 g of O2 to yield 4.9 g of P₄O₁₀ from the reaction.

Answer 1

First calculate molar masses of reactants and products and their no. of moles.

Molar Mass of P₄ = ( 4 x 30.97 ) = 123.88 g / mol

Molar mass of O ₂ = ( 2 x 16.00 ) = 32.00 g / mol

Molar mass of P₄O₁₀ = ( 4 x 30.97 ) + ( 10 x 16.00 ) = 283.88 g / mol

We know that, No. of moles = Mass / Molar Mass

No. of moles of P₄ = 9.4 g / 123.88 g / mol = 0.0759 mol

No. of moles of O ₂ = 24.5 g / 32.00 g / mol = 0.766 mol

No. of moles of P₄O₁₀ = 4.9 g / 283.88 g / mol = 0.0173 mol

Consider a balanced chemical reaction, P₄ + 5 O ₂ P₄O₁₀

From reaction, stoichiometric ratio of reactants is P₄ : O ₂ = 1: 5

Provided molar ratio of reactants is P₄ : O ₂ = 0.0759 : 0.766 = 1: 10.0

Comparing this mole ratio with theoretical mole ratio of reactants it is clear that P₄ is limiting reactant. Hence, yield of product will depend on amount of P₄.

Calculation of theoretical yield

From reaction , we can write

1 mole P₄ 1 mole P₄O₁₀

123.88 g P₄ 283.88 g P₄O₁₀

9.4 g P₄ 283.88 x 9.4 / 123.88 g P₄O₁₀

21.54 g P₄O₁₀

Theoretical yield of product = 21.54 g

Practical yield of product = 4.9 g

% yield of product = [(Practical yield / Theoretical yield) x 100 ]

=( 4.9 g / 21.54 g) x 100

= 22.75 %

ANSWER : % yield of P₄O₁₀ = 22.75 %