A metal, M, of atomic mass 96 amu reacts with fluorine to...

A metal, $M,$ of atomic mass 96 amu reacts with fluorine to form a salt that can be represented as $M F_{x}$ . In order to determine $x$ and therefore the formula of the salt, a boiling point elevation experiment is performed. A 9.18 -g sample of the salt is dissolved in 100.0 g of water, and the boiling point of the solution is found to be 374.38 $\mathrm{K}$ . Find the formula of the salt. (Assume complete dissociation of the salt in solution.)

Key Concepts

Empirical Formula Determination

Empirical formula determination involves using experimental data and stoichiometric relationships to deduce the simplest whole-number ratio of elements in a compound. In this context, the formula of the salt can be deduced by combining the data from the boiling point elevation experiment with the known atomic mass of the metal and the behavior of the salt in solution.

van’t Hoff Factor

The van’t Hoff factor represents the number of particles that a solute yields when it dissolves. For ionic compounds that dissociate completely, the actual number of particles in solution will be greater than one. This factor is crucial for relating the observed boiling point elevation to the degree of dissociation and, subsequently, to the stoichiometry of the salt.

Boiling Point Elevation

Boiling point elevation refers to the phenomenon in which the boiling point of a solvent is raised when a non-volatile solute is dissolved in it. This elevation is directly proportional to the molal concentration of the solute particles and the boiling point elevation constant of the solvent, enabling the determination of the number of particles present in solution.

Colligative Properties

Colligative properties are characteristics of solutions that depend on the number of solute particles present rather than their identity. Boiling point elevation, a key colligative property, increases with the concentration of dissolved particles and is used to infer properties such as the degree of dissociation in ionic compounds.

Molality

Molality is a concentration unit defined as the number of moles of solute per kilogram of solvent. It is used in colligative property calculations because it is independent of temperature, making it ideal for experiments such as boiling point elevation where temperature changes occur.

Transcript

00:01 All right, the problem 130 is to find the formula of the salt.

00:06 So first we know the boiling point of water is equal to 100 celsius degree.

00:15 And the boiling point of the solution, it's 374 .38 kelvin.

00:27 So if we want to convert this into celsius degree minus 273 .15.

00:34 So we get this equal to 101 .23 celsius degree.

00:41 So now we can calculate delta tb is the elevation and boiling point equal to 101 .23 minus 100.

00:54 That's equal to 1 .23 celsius degree.

00:58 And delta tb is also equal to kb times m or kb is the elevation boiling point constant of water.

01:13 So that's delta tb equal to 1 .23, and kb for water is 0 .512 celsius degree per molar, times m is the molality.

01:28 So m is equal to 1 .23 celsius degree divided by 0 .512 celsius per molar, we will get 2 .4 molar.

01:47 So 2 .4 molar is the molality of the solution.

02:03 All right.

02:04 Next step.

02:06 The mass of the sample.

02:08 So we assume the sample mfx.

02:12 So the mass of the sample, we know that's equal to 9 .18 grams.

02:23 And the mass of the solvent is equal to 100 grams.

02:31 The molar mass of the metal m is equal to 96 grams per mole.

02:48 So now we can use the formula of molality equal to number of moles of mfx divided by the mass of water...

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