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.

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