The density of a certain gaseous fluoride of phosphorus is 3.93 g/L at STP. Calculate the molar

The density of a certain gaseous fluoride of phosphorus is...

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Key Concepts

Molecular Formula Determination

Determining the molecular formula involves using the calculated molar mass of the compound and the known atomic masses of the constituent elements. By comparing the molar mass obtained from experimental data with the sum of the atomic masses for different combinations of atoms, one can deduce the empirical and consequently the molecular formula of the substance.

Ideal Gas Law

The ideal gas law (PV = nRT) is a fundamental equation in physical chemistry that relates the pressure, volume, number of moles, and temperature of a gas. It allows one to determine any one of these variables if the others are known, and is particularly useful for calculations under standard conditions (STP) where the volume of one mole of an ideal gas is known.

Density and Molar Mass Relationship for Gases

A key concept in gas calculations is the relationship between a gas's density and its molar mass. Under STP, knowing the density (mass per unit volume) allows one to calculate the molar mass by using the fact that one mole of an ideal gas occupies a fixed volume (approximately 22.4 L), linking the measured density directly to the molar mass.

Transcript

00:01 All right, so let's try to find the formula and the molar mass of a substance that we know contains phosphorus and fluorine.

00:13 And what we do know is that the density of this substance is 3 .93 grams per liter at stp.

00:26 So stp is standard temperature and pressure, 0 degrees celsius 1 atmosphere.

00:32 Now, this is an important thing to know because there is a shortcut for us to be able to get to our molar mass.

00:42 Because at stp, one mole of any gas doesn't matter what it is.

00:53 Any gas has a volume of 22 .40.

01:04 Liters.

01:06 So how are we going to use that? well, we know what the definition is of molar mass.

01:16 It's grams per mole.

01:19 So let's use our density and the fact that 22 .4 liters is one mole at stp to convert to grams per mole.

01:32 So if we take our 3 .93 grams per liter, so that's per one liter and we multiply that by the fact that we know that there's 22 .4 liters in every one mole, then that means to our three significant figures that we have, because our one liter and our one molar infinite, that we have a molar mass of 88 .0 grams per mole.

02:16 All right, so we've got molar mass.

02:19 How are we going to use that to figure out the formula? well, what do we know about phosphorus and fluorine? well, the mass of phosphorus, if you look at your periodic table, is 30 .97 grams per mole...

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