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

Understanding mole fraction is crucial in chemistry, particularly when dealing with solutions. The mole fraction, denoted by the capital letter X, is calculated by dividing the moles of a component (solute) by the total moles in the solution. This concept is vital for predicting the behavior of solutions, such as their boiling point elevation or freezing point depression. Remember that the mole fraction is dimensionless and provides a way to express the concentration of a component within a mixture without the need for units, allowing for easier comparison between different substances or mixtures.

Mole Fraction

Now the concept of the mole fraction which is represented by the variable X represents the mole component divided by your total moles. Now mole component itself represents the element or compound whose mole fraction you must determine.

Taking this information, we now have our mole fraction formula, a whole fraction again, which is X=mole componenttotal moles. So what they're asking to find the mole fraction of divided by your total moles.

Now that we know the formula for mole fraction, continue on to the next video and let's take a look at an example question.

Mole Fraction Example 1

In this example question, it says we have 25 grams of dichloromethane, which is CH₂Cl₂, and it's dissolved in 125 grams of water. They say here, what is the mole fraction of dichloromethane? So we're going to start out with step one, and in step one we have to convert all the masses given to us into moles. Now to avoid rounding errors, make sure you have at least 4 decimal places when you convert to moles.

We're going to take the 25 grams of dichloromethane and we're going to say it's composed of 1 carbon, two hydrogens and two chlorines. Looking up their atomic masses from the periodic table and adding them together, we get a combined mass of 84.926 grams of CH₂Cl₂ for every one mole. So here the grams cancel out and then I'll get 0.2944 moles of our dichloromethane. Now take the 125 grams of water. At this point we've seen water so many times, you know that the mass of two hydrogens and one oxygen is 18.016 grams for every one mole of water. So again, our grams cancel out and now we're going to have 6.9383 moles for water.

Step 2, we're now going to place the mole component as the numerator of the mole fraction formula. So remember, the mole fraction of the mole component is based on who we're asked to find the mole fraction of, and we're asked to find the mole fraction of dichloromethane. So we're going to say here mole fraction equals the moles of dichloromethane and then determine the total value of moles added together and place it as the denominator of the mole fraction formula. So here we're going to take the 0.2944 moles of dichloromethane plus the moles of the water, and that'll give you my total moles, which is 7.2327.

So those moles here go on the bottom. So again, this is our total moles from adding up the moles of dichloromethane and water together. Now this is important. Your final answer should have no units because mole fraction is a unitless expression. That makes sense because the moles here would cancel out. So when we do that, we'll get as our final answer, 0.04070 as our mole fraction. This has four sig figs, just like 0.2944 moles had four sig figs.

So this is all we need to do when it comes to the mole fraction formula. Just remember who your mole component is. It's based on who you need to determine the mole fraction for. If you know that that goes as your numerator and then just total moles on the bottom as your denominator and you'll get your mole fraction at the end.

A reaction vessel is composed of 20.3 g Cl₂, 4.27 g N₂ and 10.8 g Ne. Calculate the mole fraction of nitrogen.

• A. 0.157
• B. 0.261
• C. 0.482
• D. 0.721
• E. 0.874

Here’s what students ask on this topic:

How do you calculate mole fraction?

In covalent compounds, atoms share electrons to achieve stability. When naming these compounds, there are specific rules to follow:

1. The element with the lower group number in the periodic table (or the one that is furthest left if both are in the same group) is written first. If both elements are in the same group, the one with the higher period number is named first.
2. The second element is named by taking its root and adding the suffix '-ide.'
3. Prefixes are used to denote the number of atoms of each element in the compound (mono- for one, di- for two, tri- for three, tetra- for four, penta- for five, etc.). The prefix 'mono-' is often omitted for the first element.
4. If the prefix ends in a vowel and the element name starts with a vowel, the final vowel of the prefix is often dropped to make the name easier to pronounce.

For example, $\mathrm{CO}$ is carbon monoxide, not monocarbon monoxide, and ${\mathrm{CO}}_2$ is carbon dioxide.

How can I find mole fraction?

To find the mole fraction of a component in a mixture, you need to know the number of moles of all components present in the mixture. The mole fraction is calculated by dividing the number of moles of the component of interest by the total number of moles of all components in the mixture.

Here's the formula for mole fraction (X):

$X_i=\frac{n_i}{n}$

Where:

• Xi is the mole fraction of component i,
• ni is the number of moles of component i,
• n is the total number of moles of all components in the mixture.

For example, if you have a mixture of nitrogen and oxygen gases and you know there are 3 moles of nitrogen and 1 mole of oxygen, the mole fraction of nitrogen ($X_{N2}$) is:

$X_{N2}=\frac{n_{N2}}{n_{N2}+n_{O2}}=\frac{3}{3+1}=\frac{3}{4} or 0.75$

And the mole fraction of oxygen ($X_{O2}$) is:

$X_{O2}=\frac{n_{O2}}{n_{N2}+n_{O2}}=\frac{1}{3+1}=\frac{1}{4} or 0.25$

Remember, the sum of the mole fractions of all components in a mixture is always equal to 1.

What is mole fraction?

Mole fraction is a way of expressing the concentration of a component in a mixture. It is defined as the ratio of the number of moles of a particular substance to the total number of moles of all substances present in the mixture. The mole fraction is a dimensionless quantity, which means it has no units.

To calculate the mole fraction, you can use the formula:

Mole fraction ($X$) of a substance = $\frac{\text{Number of moles of the substance}}{\text{Total number of moles of all substances in the mixture}}$

For example, if you have a mixture of nitrogen and oxygen gases with 3 moles of nitrogen and 2 moles of oxygen, the mole fraction of nitrogen would be $\frac{3}{3+2}=\; 0.6$, and the mole fraction of oxygen would be $\frac{2}{3+2}=\; 0.4$.

The sum of the mole fractions of all components in a mixture always equals 1. Mole fraction is particularly useful in the study of gas mixtures and solutions, and it's important for calculations involving partial pressures, vapor pressures, and colligative properties.

How do you calculate the mole fraction of a gas?

To calculate the mole fraction of a gas in a mixture, you'll need to know the number of moles of each gas present in the mixture. The mole fraction is the ratio of the number of moles of the gas of interest to the total number of moles of all gases in the mixture.

Here's how you do it step by step:

1. Determine the number of moles of each gas in the mixture. This can often be done using the ideal gas law or by measuring the mass of each gas and dividing by its molar mass.
2. Add up the moles of all the gases to find the total number of moles in the mixture.
3. Calculate the mole fraction ($X$) of the gas of interest by dividing the number of moles of that specific gas ($n_{\mathrm{gas}}$) by the total number of moles in the mixture ($n_{\mathrm{total}}$):

$X_{\mathrm{gas}}=\frac{n_{\mathrm{gas}}}{n_{\mathrm{total}}}$

The result is a dimensionless number (since moles divided by moles cancel out), which represents the fraction of the gas in the mixture. If you want to express it as a percentage, simply multiply the mole fraction by 100.