An unidentified compound contains only phosphorous and fluorine, meaning we could write its formula as PxFy. Heating 0.2324 g of the compound in a 378-mL container converted all of it to gas with a pressure of 97.3 torr at 77°C. The gaseous PxFy was then reacted with an aqueous solution of calcium chloride, and all of the fluorine was converted to 0.2631 g of CaF2. Find the molecular formula of the compound.

Question

Chemistry

Sadie Rocha

6 October, 15:48

An unidentified compound contains only phosphorous and fluorine, meaning we could write its formula as PxFy. Heating 0.2324 g of the compound in a 378-mL container converted all of it to gas with a pressure of 97.3 torr at 77°C. The gaseous PxFy was then reacted with an aqueous solution of calcium chloride, and all of the fluorine was converted to 0.2631 g of CaF2. Find the molecular formula of the compound.

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Lorenzo · Answer 1

The molecular formula of the compound is P2F4

Explanation:

Step 1: Data given

Mass of the compound = 0.2324 grams

Volume of container = 378 mL

Pressure at 77 °C = 97.3 torr

The gaseous PxFy was then reacted with an aqueous solution of calcium chloride, and all of the fluorine was converted to 0.2631 g of CaF2.

Molar mass CaF2 = 78.07 g/mol

Step 2: Calculate moles CaF2

Moles CaF2 = 0.2631 g / 78.07 g/mol=0.003370

Step 3: Calculate moles F

For every 1 mol CaF2 we have 1 mol Ca2 + and 2 moles F-

moles F - = 2 * 0.003370=0.006740

Step 4: Calculate mass of F

mass F = 0.006740 mol * 19.00 g/mol=0.1281 g

Step 5: Calculate mass of P

mass P = mass of compound - mass of F = 0.2324 - 0.1281 = 0.1043 g

Step 6: Calculate moles P

moles P = 0.1043 g / 30.97 g/mol=0.003368 moles

Step 7: Calculate mol ratio

We divide by the smallest amount of moles

P: 0.003368/0.003368 = 1

F: 0.006740 / 0.003368 = 2

The empirical formula is PF2

The empirical formula has a molar mass of 68.97 g/mol

Step 8: Calculate moles of compound

p*V = n*R*T

n = (p*V) / (R*T)

⇒ with p = the pressure of the gas = 97.3 torr = 97.3/760 = 0.128 atm

⇒ with V = the volume of the gas = 0.378 L

⇒ with R = the gas constant = 0.08206 L*atm/K*mol

⇒ with T = the temperature = 77.0 °C = 350 Kelvin

Number of moles = (0.128 * 0.378) / (0.08206*350)

Number of moles =

moles gas = pV/RT = 0.128 atm x 0.378 dm^3 / 0.08206x350 K=0.00168

Step 9: Calculate molar mass

Molar mass = mass / moles

Molar mass = 0.2324 grams / 0.00168 moles

Molar mass = 138 g/mol

Step 10: Calculate the molecular formula

138.0 / 68.97 = 2

2 * (PF2) = P2F4

The molecular formula of the compound is P2F4