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A compound of P and F was analyzed as follows:

Heating 0.2324 g of the compound in a 378 cm³ container turned all of it to gas, which had a pressure of 97.3 mmHg at 77°C. Then the gas was mixed with calcium chloride solution, which turned all of the F to 0.2631 g of CaF₂.

Determine the molecular formula of the compound.

Answer :

The molecular formula of the compound is determined as P₂F₄.

What is meant by molecular formula?

Molecular formula tells us which atoms and how many of each type of atom are present in the molecule.

Molar mass of CaF₂ is 78.07 g/mol(0.2631 g CaF₂) × (1 mol CaF₂ / 78.07 g CaF₂) = 0.00337 mol CaF₂

2F- + Ca₂+ → CaF₂

(0.00337 mol CaF₂) × (2 mol F / 1 mol CaF₂) = 0.00674 mol F

As, Molar mass of F is 18.9984 g/mol

So, (0.00674 mol F) × (18.9984 g F / 1 mol F) = 0.12805 g F

1 mmHg = 0.00131578947 atm

(97.3 mmHg) × (0.00131578947 atm / 1 atm) = 0.128 atm

(378 cm³) × (1L / 1000 cm³) = 0.378 L

Now, T = 77 + 273 = 350 K

As, PV = nRT

n(PxFy) = PV / RT

n(PxFy) = (0.128 atm × 0.378 L) / (0.0821 L atm mol-1 K-1 × 350 K) = 0.001684 mol

n(PxFy) = 0.001684 mol

n(PxFy) = m(PxFy) / M(PxFy)

M(PxFy) = m(PxFy) / n(PxFy) = (0.2324 g) / (0.001684 mol) = 138 g/mol

m(PxFy) = m(P) + m(F)

0.2324 g = m(P) + 0.12805 g

m(P) = 0.2324 - 0.12805 = 0.10435

m(P) = 0.10435 g

Molar mass of P is 30.9737 g/mol

so, (0.10435 g P) × (1 mol P / 30.9737 g P) = 0.003369 mol P

Now, n(P) : n(F) = 0.003369 mol : 0.00674 mol = 1 : 2

Therefore, empirical formula of PxFy is PF₂

Molar mass of PF₂ 68.9705 g/mol

Molecular formula of PxFy is ( PF₂)n

n = M(PxFy) / M( PF₂) = (138) / (68.9705) = 2

Therefore, the molecular formula of PxFy is P₂F₄.

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