As you know, the molecules and atoms that make up the objects around us have very small sizes. To carry out calculations during chemical reactions, as well as to analyze the behavior of a mixture of non-interacting components in liquids and gases, the concept of molar fractions is used. What it is, and how they can be used to obtain macroscopic physical quantities of a mixture, is considered in this article.
Avogadro number
At the beginning of the 20th century, while conducting experiments with gas mixtures, the French scientist Jean Perrin measured the number of H 2 molecules contained in 1 gram of this gas. This amount turned out to be a huge figure (6.022 * 10 23 ). Since it is extremely inconvenient to carry out calculations with such figures, Perrin proposed the name of this quantity - the Avogadro number. This name was chosen in honor of an Italian scientist of the beginning of the 19th century, Amedeo Avogadro, who, like Perrin, studied gas mixtures and was even able to formulate a law for them, which now bears his last name.
The Avogadro number is currently widely used in the study of various substances. It links macroscopic and microscopic characteristics.
Amount of substance and molar mass
In the 60s, the International Chamber of Weights and Measures introduced the seventh basic unit of measure into the system of physical units (SI). She became a mole. Moth shows the number of elements that make up the system in question. One mole is equal to the number of Avogadro.
By molar mass is meant the weight of one mole of a given substance. It is measured in grams per mole. The molar mass is an additive quantity, that is, to determine it for a particular chemical compound, it is necessary to add the mass masses of the chemical elements that make up this compound. For example, the molar mass of methane (CH 4 ) is equal to:
M CH4 = M C + 4M H = 12 + 4 * 1 = 16 g / mol.
That is, 1 mol of methane molecules will have a mass of 16 grams.
The concept of mole fraction
Pure substances are rare in nature. For example, various impurities (salts) are always dissolved in water; the air of our planet is a mixture of gases. In other words, any substance in a liquid and gaseous state is a mixture of various elements. The mole fraction is a value showing how much of a component in a mixture is in the molar equivalent. If the amount of substance of the whole mixture is denoted as n, and the amount of substance of component i is denoted as n i , then we can write the following equality:
x i = n i / n.
Here x i is the mole fraction of component i for a given mixture. As can be seen, this quantity is dimensionless. For all components of the mixture, the sum of their molar fractions by the formula is expressed as follows:
∑ i (x i ) = 1.
Obtaining this formula is not difficult. To do this, just substitute the previous expression for x i into it .
Atomic percent
When solving problems in chemistry, often the initial values are given in atomic percent. For example, in a mixture of oxygen and hydrogen, the latter is 60 atomic%. This means that out of 10 molecules of the mixture, 6 will correspond to hydrogen. Since the mole fraction is the ratio of the number of component atoms to their total number, atomic percentages are synonymous with the concept under consideration.
The conversion of shares to atomic percent is carried out by a simple increase of two orders of magnitude. For example, a 0.21 mole fraction of oxygen in air corresponds to 21 atomic%.
Perfect gas
The concept of molar fractions is often used in solving problems with gas mixtures. Most gases under normal conditions (temperature 300 K and pressure 1 atm.) Are ideal. This means that the atoms and molecules that make up the gas are at a great distance from each other and do not interact with each other.
For ideal gases, the following equation of state holds:
P * V = n * R * T.
Here P, V, and T are three macroscopic thermodynamic characteristics: pressure, volume, and temperature, respectively. The value of R = 8.314 J / (K * mol) is a constant for all gases, n is the number of particles in moles, that is, the amount of substance.
The equation of state shows how one of the three macroscopic characteristics of the gas (P, V or T) will change if we fix the second of them and change the third. For example, at a constant temperature, the pressure will be inversely proportional to the volume of the gas (Boyle-Mariotte law).
The most remarkable thing in the written down formula is that it does not take into account the chemical nature of the molecules and atoms of the gas, that is, it is valid both for pure gases and for their mixtures.
Dalton's law and partial pressure
How to calculate the molar fraction of gas in the mixture? To do this, it is enough to know the total number of particles and their number for the component under consideration. However, you can do otherwise.
The molar fraction of gas in the mixture can be found by knowing its partial pressure. The latter is understood to mean the pressure that this component of the gas mixture would create if it were possible to remove all other components. If we designate the partial pressure of the i-th component as P i , and the pressure of the whole mixture as P, then the molar fraction formula for this component will take the form:
x i = P i / P.
Since the sum of all x i is equal to one, we can write the following expression:
∑ i (P i / P) = 1; therefore, ∑ i (P i ) = P.
The last equality is called Dalton's law, which is so named in honor of John Dalton, a British scientist of the early 19th century.
Partial pressure law or Dalton's law is a direct consequence of the equation of state for ideal gases. If atoms or molecules in a gas begin to interact with each other (this occurs at high temperatures and high pressure), then Dalton’s law is unfair. In the latter case, to calculate the molar fractions of the components, it is necessary to use the formula through the amount of substance, and not through partial pressure.
Air like a gas mixture
Having considered the question of how to find the mole fraction of the component in the mixture, we will solve the following problem: we calculate the values of x i and P i for each component in the air.
If we consider dry air, then it consists of the following 4 gas components:
- nitrogen (78.09%);
- oxygen (20.95%);
- argon (0.93%);
- carbon dioxide (0.04%).
From this data, the mole fractions for each gas are very simple to calculate. To do this, it is enough to present percentages in relative terms, as was mentioned above in the article. Then we get:
x N2 = 0.7809;
x O2 = 0.2095;
x Ar = 0.0093;
x CO2 = 0.0004.
The partial pressure of these air components is calculated, given that the atmospheric pressure at sea level is 101 325 Pa or 1 atm. Then we get:
P N2 = x N2 * P = 0.7809 atm .;
P O2 = x O2 * P = 0.2095 atm .;
P Ar = x Ar * P = 0.0093 atm .;
P CO2 = x CO2 * P = 0.0004 atm.
These data mean that if you remove all oxygen and other gases from the atmosphere and leave only nitrogen, then the pressure will drop by 22%.
Knowing the partial pressure of oxygen plays a vital role for people who are submerged in water. So, if it is less than 0.16 atm., Then a person instantly loses consciousness. On the contrary, the partial oxygen pressure exceeds 1.6 atm. leads to poisoning with this gas, which is accompanied by convulsions. Thus, a safe partial pressure of oxygen for human life should be in the range 0.16 - 1.6 atm.