The sugar fructose contains 40.0 % C, 6.7 % H, and 53% O by mass. A solution of 11.7 g of fructo

The sugar fructose contains 40.0 % C, 6.7 % H, and 53% O by...

The sugar fructose contains $40.0 \% \mathrm{C}, 6.7 \% \mathrm{H},$ and 53$\% \mathrm{O}$ by mass. A solution of 11.7 $\mathrm{g}$ of fructose in 325 $\mathrm{g}$ of ethanol has a boiling point of $78.59^{\circ} \mathrm{C}$ . The boiling point of ethanol is $78.35^{\circ} \mathrm{C},$ and $K_{\mathrm{b}}$ for ethanol is $1.20^{\circ} \mathrm{C} / \mathrm{m} .$ What is the molecular formula of fructose?

Key Concepts

Molar Mass Determination via Freezing/Boiling Point Elevation

This concept involves using the observed change in boiling point (or freezing point) to calculate the molality of the solution. From the molality and the known mass of the solute, the molar mass can be determined, which in turn helps in deducing the molecular formula from the empirical formula.

Ebullioscopic Constant (Kb)

The ebullioscopic constant is a property of a given solvent that quantifies the boiling point elevation per molal concentration of a solute. It is an essential parameter in calculations that relate the observed boiling point elevation to the molality of the solute.

Molality

Molality is a concentration unit defined as moles of solute per kilogram of solvent. It is used in calculations involving colligative properties because it remains temperature independent, providing an accurate measure for properties like boiling point elevation.

Empirical Formula Determination

Empirical formula determination is the process of finding the simplest whole-number ratio of atoms in a compound using the mass percentages of its constituent elements. This is often the first step in characterizing the molecular composition of a substance.

Colligative Properties

Colligative properties are physical properties of solutions that depend on the concentration of solute particles rather than their identity. Boiling point elevation is one of these properties and serves as a tool to determine molar masses of solutes in a solution.

Percentage Composition

This concept involves expressing the mass of each element in a compound as a percentage of the total mass. It is fundamental in determining the empirical formula of a compound by converting mass percentages to moles of each element.

Boiling Point Elevation

Boiling point elevation refers to the increase in the boiling point of a solvent when a non-volatile solute is dissolved in it. The magnitude of this elevation is directly proportional to the molal concentration of the solute particles and is quantified by the ebullioscopic constant.

Transcript

00:01 Hello, everyone.

00:02 This is ricky, and today we're working on problem 64, and we will be solving for the molecular formula of fructose.

00:09 All right, so what do we know? well, we know the boiling point of ethanol.

00:16 We know the kb for ethanol, and we know the boiling point, the elevated boiling point point when we add 11 .7 grams of fructose to the ethanol.

00:27 So that means we can rearrange our boiling point equation to solve for malality, to get the moles of, at the malality of fructose.

00:38 So malality is equal to delta k, sorry, delta t b over kb.

00:58 And then so to get our delta tb, we use the original blowing point of ethanol and subtract.

01:11 And so we use the, we have the elevated blowing point of ethanol, 78 .5.

01:16 9 degrees celsius, subtract that from the original boiling point of the solution to get delta tb, all over kb for ethanol, which is 1 .2o.

01:35 And we get that our molality is equal to 0 .2o.

01:41 Now we're going to be calculating the moles of fructose.

01:48 And so moles solute is equal to molality times mass solvent.

02:03 And that's just the rearranged malality equation.

02:06 So we have 0 .2 .0 .m.

02:09 Molal times 0 .325 kilograms of ethanol, which is the solvent is equal to 0 .065 moles of ethanol.

02:25 Of fructose.

02:34 And now we will be calculating the molecular mass of fructose...

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