Mole Fraction of Gases: Videos & Practice Problems

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 Formula

The mole fraction, denoted by the variable x, is a crucial concept in chemistry that quantifies the proportion of a specific component in a mixture. It is calculated by dividing the number of moles of the component of interest by the total number of moles in the mixture. This relationship can be expressed with the formula:

x = \frac{n_{component}}{n_{total}}

In this formula, n_component represents the number of moles of the element or compound for which the mole fraction is being determined, while n_total signifies the total number of moles present in the mixture. Understanding how to calculate mole fraction is essential for various applications in chemistry, including determining concentrations and understanding the behavior of gases and solutions.

Mole Fraction Example

To calculate the mole fraction of dichloromethane (CH₂Cl₂) dissolved in water, we begin by converting the given masses into moles. For dichloromethane, we have 25 grams. The molar mass is calculated by summing the atomic masses of its components: 1 carbon (C) at approximately 12.011 g/mol, 2 hydrogens (H) at about 1.008 g/mol each, and 2 chlorines (Cl) at around 35.453 g/mol each. This gives us:

$$\text{Molar mass of CH}_2\text{Cl}_2 = 12.011 + (2 \times 1.008) + (2 \times 35.453) = 84.926 \text{ g/mol}$$

Next, we convert the mass of dichloromethane to moles:

$$\text{Moles of CH}_2\text{Cl}_2 = \frac{25 \text{ g}}{84.926 \text{ g/mol}} \approx 0.2944 \text{ moles}$$

For water, we have 125 grams. The molar mass of water (H₂O) is calculated as follows: 2 hydrogens (1.008 g/mol each) and 1 oxygen (O) at approximately 15.999 g/mol:

$$\text{Molar mass of H}_2\text{O} = (2 \times 1.008) + 15.999 = 18.016 \text{ g/mol}$$

Now, we convert the mass of water to moles:

$$\text{Moles of H}_2\text{O} = \frac{125 \text{ g}}{18.016 \text{ g/mol}} \approx 6.9383 \text{ moles}$$

With both components converted to moles, we can now calculate the mole fraction of dichloromethane. The mole fraction (X) is defined as the ratio of the moles of the component of interest to the total moles of all components:

$$X_{\text{CH}_2\text{Cl}_2} = \frac{\text{Moles of CH}_2\text{Cl}_2}{\text{Total moles}}$$

Calculating the total moles:

$$\text{Total moles} = 0.2944 + 6.9383 = 7.2327$$

Now, substituting the values into the mole fraction formula:

$$X_{\text{CH}_2\text{Cl}_2} = \frac{0.2944}{7.2327} \approx 0.04070$$

This result is unitless, as mole fraction is a ratio of moles, and thus cancels out the units. The final answer, with four significant figures, is 0.04070. Remember, the mole fraction is determined by identifying the component of interest and dividing its moles by the total moles of all components involved.

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

Answer: (A)

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.