- Characteristics and symbol
- How it is calculated
- Examples
- Example 1
- Example 2
- Exercises
- Exercise 1
- Exercise 2
- Exercise 3
- References
The mole fraction is a way of expressing the concentration of the elements present in a compound, or the concentration of a compound in a mixture.
The mole fraction of the elements of a compound is defined as a quotient between the number of moles of each of the different elements present in the compound and the total number of moles of them.
Equation for the determination of the molar fraction. Source: Gabriel Bolívar.
For example: if a compound has an element A and an element B, the mole fraction of A is the number of moles of A divided by the number of moles of A plus the number of moles of B. Similarly, for the mole fraction of B The same operation is carried out but placing the moles of B.
This operation is represented in the image above. The sum of the mole fractions is equal to 1 (one). The mole fraction is a dimensionless (dimensionless) number. Many laws can be expressed in terms of them, such as Dalton's Law.
Characteristics and symbol
The value of the mole fraction is independent of temperature and in an ideal gas mixture it can be used to calculate the partial pressures of each of the gases present in the gas mixture; as stated in Dalton's law.
The mole fraction is usually represented or symbolized by a capital X (X) on the right side, as a subscript, the element symbol or the compound formula is placed if there is a mixture of compounds.
How it is calculated
If the number of moles is known for each of the elements that make up a given compound, adding the moles of the elements can give the total number of moles that exist in the compound.
Then, to obtain the mole fraction of each element, the number of its moles is divided by the number of total moles present in the compound. The sum of the values of the mole fraction of the different elements is equal to unity (1).
Examples
The following are examples of uses of the mole fraction.
Example 1
The molality of a solution, expressed as moles of solute per kilogram of water, can be transformed into the mole fraction of the solute. To do this, 1,000 g of water are converted into moles of water, simply dividing the mass of water of 1,000 g by the molecular weight of water (18 g / mol).
Then, dividing the number of moles of the solute by the number of moles of water plus those of the solute, the mole fraction of the solute will be obtained.
For example, substance A has a molality of 0.03 m. This means that you have 0.3 moles of A dissolved in one kilogram of water. One kilogram of water corresponds to 55.55 moles of water (1,000 g ÷ 18g / mol). Thus, the mole fraction of A becomes:
X (A) or X A = 0.03 ÷ (55.55 + 0.03)
= 0.0005398 or 5.398 10 -4
Example 2
Calculation of the partial pressures of gases as a function of their molar fractions. The Law of Partial Pressures was enunciated by Dalton and indicates that in a mixture of gases each gas exerts its pressure as if it occupied the entire volume of the mixture of gases.
The total pressure of the gas mixture is the sum of the pressures exerted, separately, by each of the gases that are part of the gas mixture.
The atmosphere is mainly made up of a mixture of four gases: nitrogen, oxygen, carbon dioxide and water vapor, each exerting the following partial pressures separately:
Nitrogen: 596 mmHg
Oxygen: 158 mmHg
Carbon dioxide: 0.3 mmHg
Water vapor: 5.7 mmHg.
Which produces an atmospheric pressure value of 760 mmHg. By using these gas pressures, the following values of their mole fractions can be calculated:
Nitrogen
X N2 = 596 mmHg / 760 mmHg
= 0.7842
Oxygen
X O2 = 158 mmHg / 760 mmHg
= 0.2079
Carbon dioxide
X CO2 = 0.3 mmHg / 760 mmHg
= 0.00039
Water steam
X H2O = 5.7 mmHg / 760 mmHg
= 0.075
Reciprocally, the partial pressure of each of the gases present in a mixture can be calculated by multiplying the value of its mole fraction by the total pressure exerted by the gaseous mixture.
Exercises
Exercise 1
What is the mole fraction of a solution of methanol (CH 3 OH) and water (H 2 O) containing 145 g of CH 3 OH and 120 g of H 2 O? Molecular weights: CH 3 OH = 32 g / mol and water = 18 g / mol.
We first calculate the moles of methanol and water:
Moles of CH 3 OH = 145 g · 1 mol CH 3 OH ÷ 32 g of CH 3 OH
= 4.53 mol CH 3 OH
Moles of H 2 O = 120 g · 1 mol of H 2 O ÷ 18 g of H 2 O
= 6.67 mol H 2 O
Then we calculate the total moles:
Total moles of CH 3 OH and H 2 O = 4.53 + 6.67
= 11.2 moles
And so we determine the mole fractions of methanol and water:
X (CH 3 OH) = 4.53 moles / 11.2 moles
= 0.404
X (H 2 O) = 6.67 moles / 11.2 moles
= 0.596
Exercise 2
A mixture of 1.56 moles of nitrogen (N 2) and 1.2 moles of oxygen (O 2) exerts a pressure of 0.8 atmospheres (atm). Calculate the partial pressure exerted by each of the gases.
The first step in solving the problem is the calculation of the mole fractions of the gases. In a second stage, the partial pressures exerted by the gases are obtained, multiplying their mole fraction by the total pressure exerted by the gas mixture.
Molar fraction of nitrogen:
X N2 = 1.56 moles / (1.56 moles + 1.2 moles)
= 0.565
Molar fraction of oxygen:
X O2 = 1.2 moles / (1.56 moles + 1.2 moles)
= 0.435
And finally we calculate the partial pressures of each gas:
P N2 = X N2 P T
= 0.565 · 0.8 atm
= 0.452 atm
P O2 = X O2 P t
= 0.435 · 0.8 atm
= 0.348 atm
Exercise 3
What is the mole fraction of formaldehyde (CH 2 O) if 23 g of the compound are dissolved in 4 moles of carbon tetrachloride (CCl 4)? CH 2 O molecular weight = 30.03 g / mol.
We first calculate the moles of formaldehyde:
Moles CH 2 O = 23 g CH 2 O · 1 mol CH 2 O ÷ 30.03 g CH 2 O
= 0.766 moles
And for the second we calculate the mole fraction:
X CH2OH = 0.766 moles CH 2 OH / (0.766 moles CH 2 OH + 4 moles CCl 4)
= 0.161
References
- Whitten, Davis, Peck & Stanley. (2008). Chemistry (8th ed.). CENGAGE Learning.
- Helmenstine, Anne Marie, Ph.D. (February 11, 2020). What Is a Mole Fraction? Recovered from: thoughtco.com
- Wikipedia. (2020). Mole fraction. Recovered from: en.wikipedia.org
- CK-12 Foundation. (October 16, 2019). Mole Fraction. Chemistry LibreTexts. Recovered from: chem.libretexts.org
- Chris Deziel. (November 12, 2018). How to Calculate a Mole Fraction. Recovered from: sciencing.com