How To Find Mole Fraction Of A Gas

Learning Objective

Calculate the mole fraction and mole per centum for a given concentration of mixture

Key Points

Mole fraction describes the number of molecules (or moles) of one component divided by total the number of molecules (or moles) in the mixture.
Mole fraction is useful when two reactive components are mixed together, every bit the ratio of the two components is known if the mole fraction of each is known.
Multiplying mole fraction past 100 gives mole percent, which describes the same thing as mole fraction, just in a different form. Mole fractions tin be generated from various concentrations including molality, molarity and mass percent compositions.

Terms

mole fractionThe ratio of the number of moles of 1 component in a mixture to the full number of moles.
moleThe SI base unit for the amount of a substance; the amount of substance that contains equally many simple entities as there are atoms in 0.012 kg of carbon-12.

Mole Fraction

In chemistry, the mole fraction, x_i , is defined as the amount of moles of a constituent, n_i , divided past the total amount of moles of all constituents in a mixture, due north_tot :

[latex]x_{i}=\frac{n_{i}}{n_{tot}}[/latex]

Mole fractions are dimensionless, and the sum of all mole fractions in a given mixture is always equal to one.

Properties of the Mole Fraction

The mole fraction is used very oftentimes in the construction of stage diagrams. It has a number of advantages:

Information technology is non temperature dependent, as opposed to molar concentration, and does not crave noesis of the densities of the stage(s) involved.
A mixture of known mole fractions can be prepared by weighing the appropriate masses of the constituents.
The measure is symmetric; in the mole fractions x=0.1 and 10=0.9, the roles of 'solvent' and 'solute' are reversible.
In a mixture of ideal gases, the mole fraction tin be expressed as the ratio of partial pressure to total force per unit area of the mixture.

**Mole fraction in a sodium chloride solution**Mole fraction increases proportionally to mass fraction in a solution of sodium chloride.

Mole Percent

Multiplying the mole fraction by 100 gives the mole per centum, likewise referred as amount/amount percent (abbreviated as north/n%). For general chemistry, all the mole percents of a mixture add together up to 100 mole percent. We can easily catechumen mole pct dorsum to mole fraction by dividing past 100. Then, a mole fraction of 0.sixty is equal to a mole per centum of sixty.0%.

Calculations with Mole fraction and Mole Percent

Mole Fraction in Mixtures

A mixture of gases was formed by combining six.3 moles of O₂ and v.6 moles of N₂. What is the mole fraction of nitrogen in the mixture?

First, we must find the total number of moles with northward_total= n_N2 + northward_O2.

[latex]n_{total}=6.iii\ moles+5.6 \ moles = eleven.9\ moles[/latex].

Side by side we must divide the moles of N₂ by the total number of moles:

[latex]x (\text{mole fraction}) = (\frac {\text{ moles } N_2}{\text{ moles } N_2 + \text{ moles } O_2})= (\frac {5.6 \text { moles}}{11.ix \text{ moles}})= 0.47[/latex]

The mole fraction of nitrogen in the mixture is 0.47.

Mole Fraction in Solutions

Mole fraction tin also exist applied in the case of solutions. For example, 0.100 moles of NaCl are dissolved in 100.0 mL of water. What is the mole fraction of NaCl?

We are given the number of moles of NaCl, but the volume of h2o. Start, we convert this volume to a mass by using the density of h2o (1.00 g/mL), and then we convert this mass to moles of water:

[latex]100\ mL\ H_2O \times (\frac {1.0g}{1mL})= 100.0\ g\ H_2O \times (\frac {1 \text{ moles}}{xviii.0 g}) = 5.55 \text{ moles } H_2O[/latex]

With this data we tin can find the total number of moles present: 5.55 + 0.100 = 5.65 moles. If we divide the moles of NaCl by the total number of moles, we find the mole fraction of this component:

[latex]x = (\frac {0.100 \text moles}{5.65 \text moles}) = 0.0176[/latex]

We discover that the mole fraction of NaCl is 0.0176.

Mole Fraction with Multi-Component Mixtures

Mole fractions tin too exist institute for mixtures that are formed from multiple components. These are treated no differently than before; again, the total mole fraction of the mixture must be equal to i.

For case, a solution is formed by mixing 10.0 g of pentane (C₅H₁₂), x.0 g of hexane (C₆H₁₄) and 10.0 g of benzene (C₆H_{half dozen}). What is the mole fraction of hexane in this mixture?

We must start discover the number of moles nowadays in 10.0 g of each component, given their chemical formulas and molecular weights. The number of moles for each is found by dividing its mass past its corresponding molecular weight. Nosotros detect that there are 0.138 moles of pentane, 0.116 moles of hexane, and 0.128 moles of benzene.

We tin can find the total number of moles by taking the sum of all the moles: 0.138+0.116+0.128 = 0.382 total moles. If we split moles of hexane by the full moles, we calculate the mole fraction:

[latex]ten = (\frac {0.116 \text{ moles}}{0.382 \text{ moles}}) = 0.303[/latex]

The mole fraction for hexane is 0.303.

Mole Fraction from Molality

Mole fraction can also be calculated from molality. If we have a 1.62 thou solution of table sugar (C₆H₁₂O₆) in water, what is the mole fraction of the table sugar?

Since nosotros are given molality, nosotros can convert it to the equivalent mole fraction, which is already a mass ratio; remember that molality = moles solute/kg solvent. Given the definition of molality, we know that we accept a solution with 1.62 moles of sugar and i.00 kg (1000 g) of h2o. Since we know the number of moles of carbohydrate, we need to notice the moles of water using its molecular weight:

[latex]1000\ g\ H_2O \times (\frac {1\ mole}{18.0\ one thousand}) = 55.5 \text{ moles }H_2O[/latex]

The total number of moles is the sum of the moles of h2o and sugar, or 57.ane moles full of solution. Nosotros can now find the mole fraction of the saccharide:

[latex]x = (\frac {1.62 \text{ moles sugar}}{57.i \text{ moles solution}})= 0.0284 [/latex]

With the mole fraction of 0.0284, we see that nosotros have a ii.84% solution of saccharide in water.

Mole Fraction from Mass Percent

The mole fraction can also be calculated from a mass percent. What is the mole fraction of cinnamic acid that has a mole percent of 50.00% urea in cinnamic acid? The molecular weight of urea is threescore.16 g/mol and the molecular weight of cinnamic acid is 148.16 yard/mol.

Kickoff, we assume a total mass of 100.0 k, although any mass could exist assumed. This means that we take 50.0 g of urea and 50.0 g of cinnamic acid. Nosotros can then calculate the moles present by dividing each by its molecular weight. We accept 0.833 moles urea and 0.388 moles cinnamic acid, so we have i.22 moles full.

To find the mole fraction, we divide the moles of cinnamic acid past total number of moles:

[latex]x = (\frac {.388 \text{ moles cinnamic acid}}{1.22 \text{ moles solution}})= 0.318[/latex]

The mole fraction for cinnamic acid is 0.318.