Mole Fraction of Solutions - Online Tutor, Practice Problems & Exam Prep

Mole fraction, denoted as X, is a crucial concept in chemistry representing the ratio of moles of solute to moles of solution. The formula for mole fraction is expressed as X = \frac{n_{solute}}{n_{solution}}, where n_{solute} is the number of moles of solute and n_{solution} is the total number of moles in the solution. Understanding mole fraction is essential for calculations involving solutions, mixtures, and various chemical reactions.

Mole Fraction Concept 1

Mole fraction is represented by our variable capital X and it represents moles of solute per moles of solution. So if we were to take a look at the mole fraction formula, we're just going to say again, mole fraction which is represented by capital X equals moles of solute divided by moles of solution.

So keep this in mind anytime you're faced with any question dealing with the mole fraction of a compound, a substance, a mixture or solution.

X = moles of solute moles of solution

Mole Fraction Example 1

A solution contains eight 5.2 grams of ascorbic acid, which has a molecular formula of C₆H₈O₆. It's a water soluble vitamin and it's in 270 grams of water. Here we need to calculate the mole fraction of ascorbic acid in this solution. All right, so we're going to say here X of ascorbic acid, C₆H₈O₆, would equal the moles of ascorbic acid divided by the moles of solution.

Now remember a solution is composed of solute and solvent together. So really we could transform the bottom to say, moles of our solute plus moles of our solvent, which in this case is water. We have here 85.2g of ascorbic acid. We're going to sit here for every one mole of ascorbic acid. Oops. Which has six carbons, 8 hydrogens, and six oxygen. The combined mass is 176.124 grams, so here grams cancel out and I'll have the moles of ascorbic acid as 0.48375 moles.

So here we're going to plug in 0.48375 moles of ascorbic acid on the top and here on the bottom, plus we the moles of water. So here we have 270 grams of water which is H₂O. The mass of water from the two hydrogens and the one oxygen is 18.016g according to our periodic table. And that's for every one mole of water. Grams cancel out and I'll have the moles of water which come out to be 14.9867 moles.

So take those moles and plug them into our formula. Now what's going to happen is we're going to have moles on the top and on the bottom, and they're going to cancel one another out. So that means mole fraction is a unitless value. So here when we plug that into our calculator, we get back 0.0313 as my mole fraction. Here my answer has three sig figs because from our question 85.2 has three sig figs and 270.0 has four sig figs.

Calculate mole fraction of a 2.4 m aqueous solution of citric acid (C₆H₈O₇).

• A. 0.96
• B. 0.041
• C. 0.55
• D. 0.024

If mole fraction of urea is 4.55 x 10^-1, what is the mass of urea needed to dissolve in 38.0 g of water? The molar mass of urea is 60.062 g/mol.

• A. 26.7 g
• B. 106 g
• C. 39.6 g
• D. 8.19 g

Here’s what students ask on this topic:

What is the mole fraction formula and how is it used in chemistry?

The mole fraction formula is represented by the variable capital X and is given by the equation:

$X=\frac{\mathrm{moles} \mathrm{of} \mathrm{solute}}{\mathrm{moles} \mathrm{of} \mathrm{solution}}$

This formula is used to calculate the mole fraction of a compound, substance, mixture, or solution. The mole fraction is a dimensionless quantity that helps in understanding the concentration of a solution. It is used in chemical calculations to determine reactions and properties of a solution, such as colligative properties. The mole fraction is also useful in comparing the solubility of two substances and is an important concept in various fields of chemistry.

How do you calculate the mole fraction of a solute in a solution?

To calculate the mole fraction of a solute in a solution, you need to know the number of moles of the solute and the total number of moles in the solution. The mole fraction (X) is calculated using the formula:

$X=\frac{\mathrm{moles} \mathrm{of} \mathrm{solute}}{\mathrm{moles} \mathrm{of} \mathrm{solution}}$

First, determine the moles of the solute and the moles of the solvent. Then, add these values to get the total moles of the solution. Finally, divide the moles of the solute by the total moles of the solution to obtain the mole fraction. This value is dimensionless and provides insight into the concentration of the solute within the solution.

Why is the mole fraction considered a dimensionless quantity?

The mole fraction is considered a dimensionless quantity because it is a ratio of two quantities with the same unit (moles). When you divide the moles of solute by the total moles of the solution, the units cancel out, leaving a pure number without any units. This makes the mole fraction a dimensionless quantity. This property is useful in various chemical calculations, as it allows for easy comparison and manipulation of concentrations without worrying about unit conversions. The dimensionless nature of the mole fraction also simplifies the understanding of colligative properties and other solution behaviors.

How is the mole fraction used to determine colligative properties?

The mole fraction is used to determine colligative properties, which are properties that depend on the number of solute particles in a solution rather than their identity. Examples of colligative properties include boiling point elevation, freezing point depression, and osmotic pressure. By knowing the mole fraction of the solute, you can calculate these properties using specific formulas. For instance, the freezing point depression (ΔT_f) can be calculated using the formula:

$\mathrm{\Delta T\_f}=i \mathrm{K\_f} X$

where i is the van 't Hoff factor, K_f is the cryoscopic constant, and X is the mole fraction of the solute. By using the mole fraction, you can accurately determine how the presence of a solute affects the physical properties of a solution.

Can the mole fraction be greater than 1?

No, the mole fraction cannot be greater than 1. The mole fraction is defined as the ratio of the moles of a component to the total moles of all components in the solution. Since the total moles of the solution include the moles of the component itself, the mole fraction will always be a value between 0 and 1. A mole fraction of 1 would indicate that the solution is composed entirely of that component, while a mole fraction of 0 would indicate that the component is not present in the solution at all. This constraint ensures that the mole fraction remains a meaningful and useful measure of concentration.