Numerology 

Mass fraction in the compound formula. Calculation of the mass fraction of chemical elements according to the formula of the substance

Even one gram of a substance can contain up to a thousand different compounds. Each compound is responsible for a specific property of a substance, and it happens that it is not a specific substance, but a mixture. In any case, recycling situations often arise in production. chemical waste and the challenge of using recycled materials. It is the chemical reactions that make it possible to find and isolate a certain substance that are dominant. But to do this, you must first know how to find mass fraction.

The concept of mass fraction of a substance reflects its content and concentration in a complex chemical structure, be it a mixture or an alloy. Knowing the total mass of an alloy or mixture, you can find the masses of their constituent substances, provided that their mass fractions are known. How to find the mass fraction, the formula is usually expressed as a fraction: mass fraction of a substance mass of a substance / mass of the entire mixture.

Let's do a little experiment! To do this, we will need a periodic table of chemical elements. Mendeleev, scales and calculator.

How to find the mass fraction of a substance

It is necessary to determine the mass fraction of the substance; the substance is in the form of a mixture. First, we put the substance itself on the scale. We obtained a mass of substance. Knowing a certain mass of a substance in a mixture, we can easily obtain its mass fraction. For example, there is 170g. water. They contain 30 grams of cherry juice. Total weight=170+30=230 grams. Let's divide the mass of cherry juice to the total mass of the mixture: 30/200=0.15 or 15%.

How to find the mass fraction of a solution

A solution to this problem may be needed when determining the concentration of food solutions (vinegar) or medicines. The mass of a KOH solution, also known as potassium hydroxide, weighing 400 grams is given. KOH (mass of the substance itself) is 80 grams. It is necessary to find the mass fraction of bile in the resulting solution. Formula for finding the solution: KOH (mass of potassium hydroxide solution) 300 g, mass of dissolved substance (KOH) 40 g. Find KOH (mass fraction of alkali) in the resulting solution, t-mass fraction. m- mass, t (substance) = 100%* m (substance) / m (solution (substance). Thus KOH (mass fraction of potassium hydroxide solution): t (KOH) = 80 g / 400 g x 100% = 20 %.

How to find the mass fraction of carbon in a hydrocarbon

To do this, we use the periodic table. We look for substances in the table. The table shows the atomic mass of the elements. 6 carbons with atomic mass 12 and 12 hydrogens with atomic mass equal to 1. m (C6H12) = 6 x 12 + 12 x 1 = 84 g/mol, ω (C) = 6 m1(C) / m (C6H12) = 6 x 12 / 84 = 85%

Determination of the mass fraction in production is carried out in special chemical laboratories. To begin with, a small sample is taken and various chemical reactions are tested. Or they introduce litmus tests that can show the presence of one or another component. After determining the initial structure of the substance, the isolation of components can begin. This is achieved through simple chemical reactions, when one substance comes into contact with another and a new one is formed, a precipitate is possible. There are also more advanced methods, such as electrolysis, heating, cooling, evaporation. Such reactions require large industrial equipment. Production, of course, can hardly be called environmentally friendly, nevertheless modern technologies waste treatment allows minimizing the burden on nature.

Since the 17th century chemistry has ceased to be a descriptive science. Chemical scientists began to widely use methods for measuring various parameters of a substance. The design of scales was increasingly improved, making it possible to determine the mass of samples for gaseous substances; in addition to mass, volume and pressure were also measured. Application quantitative measurements made it possible to understand the essence of chemical transformations and determine the composition of complex substances.

As you already know, a complex substance contains two or more chemical elements. It is obvious that the mass of all matter is made up of the masses of its constituent elements. This means that each element accounts for a certain portion of the mass of the substance.

The mass fraction of an element in a substance is denoted by the Latin small letter w (double-ve) and shows the share (part of the mass) of a given element in the total mass of the substance. This value can be expressed in fractions of a unit or as a percentage (Fig. 69). Of course, the mass fraction of an element in a complex substance is always less than unity (or less than 100%). After all, a part of the whole is always smaller than the whole, just as a slice of an orange is smaller than the whole orange.

Rice. 69.
Elemental composition diagram of mercury oxide

For example, the composition of mercury oxide HgO includes two elements - mercury and oxygen. When heating 50 g of this substance, 46.3 g of mercury and 3.7 g of oxygen are obtained. Let's calculate the mass fraction of mercury in a complex substance:

The mass fraction of oxygen in this substance can be calculated in two ways. By definition, the mass fraction of oxygen in mercury oxide is equal to the ratio of the mass of oxygen to the mass of mercury oxide:

Knowing that the sum of the mass fractions of elements in a substance is equal to one (100%), the mass fraction of oxygen can be calculated from the difference:

In order to find the mass fractions of elements using the proposed method, it is necessary to conduct a complex and labor-intensive chemical experiment to determine the mass of each element. If the formula of a complex substance is known, the same problem can be solved much easier.

To calculate the mass fraction of an element, you need to multiply its relative atomic mass by the number of atoms of this element in the formula and divide by the relative molecular mass of the substance.

For example, for water (Fig. 70):

Let's practice solving problems on calculating the mass fractions of elements in complex substances.

Task 1. Calculate the mass fractions of elements in ammonia, the formula of which is NH 3.

Task 2. Calculate the mass fractions of elements in sulfuric acid having the formula H 2 SO 4.

More often, chemists have to solve the inverse problem: using the mass fractions of elements to determine the formula of a complex substance.

Let us illustrate how such problems are solved with one historical example.

Problem 3. Two compounds of copper with oxygen (oxides) were isolated from natural minerals - tenorite and cuprite (Fig. 71). They differed from each other in color and mass fractions of elements. In the black oxide (Fig. 72), isolated from tenorite, the mass fraction of copper was 80%, and the mass fraction of oxygen was 20%. In red copper oxide isolated from cuprite, the mass fractions of elements were 88.9% and 11.1%, respectively. What are the formulas of these complex substances? Let's solve these two simple problems.

Rice. 71. Mineral cuprite
Rice. 72. Black copper oxide isolated from the mineral tenorite

3. The resulting relationship must be reduced to the values ​​of integers: after all, the indices in the formula showing the number of atoms cannot be fractional. To do this, the resulting numbers must be divided by the smaller of them (in our case they are equal).

Now let's complicate the task a little.

Problem 4. According to elemental analysis, calcined bitter salt has the following composition: mass fraction of magnesium 20.0%, mass fraction of sulfur - 26.7%, mass fraction of oxygen - 53.3%.



Questions and tasks

  1. What is the mass fraction of an element in a complex substance? How is this value calculated?
  2. Calculate the mass fractions of elements in the substances: a) carbon dioxide CO 2; b) calcium sulfide CaS; c) sodium nitrate NaNO 3; d) aluminum oxide A1 2 O 3.
  3. Which of the nitrogen fertilizers contains the largest mass fraction of the nutrient element nitrogen: a) ammonium chloride NH 4 C1; b) ammonium sulfate (NH 4) 2 SO 4; c) urea (NH 2) 2 CO?
  4. In the mineral pyrite, there are 8 g of sulfur per 7 g of iron. Calculate the mass fractions of each element in this substance and determine its formula.
  5. The mass fraction of nitrogen in one of its oxides is 30.43%, and the mass fraction of oxygen is 69.57%. Determine the formula of the oxide.
  6. In the Middle Ages, a substance called potash was isolated from the ashes of fires and was used to make soap. The mass fractions of elements in this substance are: potassium - 56.6%, carbon - 8.7%, oxygen - 34.7%. Determine the formula of potash.

Instructions

The mass fraction of a substance is found by the formula: w = m(in)/m(cm), where w is the mass fraction of the substance, m(in) is the mass of the substance, m(cm) is the mass of the mixture. If dissolved, then it looks like this: w = m(in)/m(solution), where m(solution) is the mass of the solution. If necessary, the mass of the solution can also be found: m(solution) = m(in) + m(solution), where m(solution) is the mass of the solvent. If desired, the mass fraction can be multiplied by 100%.

If the problem statement does not give a mass value, then it can be calculated using several formulas; the values ​​given in the statement will help you choose the right one. The first formula for: m = V*p, where m is mass, V is volume, p is density. The following formula looks like this: m = n*M, where m is mass, n is the amount of substance, M is molar mass. The molar mass, in turn, consists of the atomic masses of the elements that make up the substance.

To better understand this material, let’s solve the problem. A mixture of copper and magnesium filings weighing 1.5 g was treated with excess . As a result of the reaction, hydrogen volume is 0.56 l (). Calculate the mass fraction of copper in the mixture.
In this problem, we write down its equation. Of the two substances with excess hydrochloric acid, only magnesium: Mg + 2HCl = MgCl2 + H2. To find the mass fraction of copper in the mixture, you need to substitute the values ​​into the following formula: w(Cu) = m(Cu)/m(cm). The mass of the mixture is given, let’s find the mass of copper: m(Cu) = m(cm) – m(Mg). We are looking for mass: m(Mg) = n(Mg)*M(Mg). The reaction equation will help you find the amount of magnesium. We find the amount of hydrogen substance: n = V/Vm = 0.56/22.4 = 0.025 mol. The equation shows that n(H2) = n(Mg) = 0.025 mol. We calculate the mass of magnesium, knowing that the molar is 24 g/mol: m(Mg) = 0.025*24 = 0.6 g. Find the mass of copper: m(Cu) = 1.5 – 0.6 = 0.9 g. Remaining calculate the mass fraction: w(Cu) = 0.9/1.5 = 0.6 or 60%.

Video on the topic

Please note

The mass fraction cannot be greater than one or, if expressed as a percentage, greater than 100%.

Sources:

  • "Chemistry Manual", G.P. Khomchenko, 2005.
  • Calculation of the share of sales by region

The mass fraction shows, as a percentage or in fractions, the content of a substance in a solution or an element in the composition of a substance. The ability to calculate mass fraction is useful not only in chemistry lessons, but also when you want to prepare a solution or mixture, for example, for culinary purposes. Or change the percentage in your existing composition.

Instructions

For example, you need at least 15 cubic meters for the winter. meters of birch firewood.
Look for the density of birch firewood in the reference book. This is: 650 kg/m3.
Calculate the mass by substituting the values ​​into the same specific gravity formula.

m = 650*15 = 9750 (kg)

Now, based on the load capacity and capacity of the body, you can decide on the type vehicle and the number of trips.

Video on the topic

Please note

Older people are more familiar with the concept of specific gravity. The specific density of a substance is the same as specific gravity.

The mass fraction of a substance shows its content in more complex structure, for example, in an alloy or mixture. If known total mass mixture or alloy, then knowing the mass fractions of the constituent substances, you can find their masses. You can find the mass fraction of a substance by knowing its mass and the mass of the entire mixture. This value can be expressed in fractions or percentages.

You will need

  • scales;
  • periodic table of chemical elements;
  • calculator.

Instructions

Determine the mass fraction of the substance that is in the mixture through the masses of the mixture and the substance itself. To do this, use a scale to determine the masses that make up the mixture or. Then fold them. Take the resulting mass as 100%. To find the mass fraction of a substance in a mixture, divide its mass m by the mass of the mixture M, and multiply the result by 100% (ω%=(m/M)∙100%). For example, 20 g of table salt is dissolved in 140 g of water. To find the mass fraction of salt, add the masses of these two substances M = 140 + 20 = 160 g. Then find the mass fraction of the substance ω% = (20/160)∙100% = 12.5%.

If you need to find or the mass fraction of an element in a substance with well-known formula, use periodic table elements. Using it, find the atomic masses of the elements that are in the substance. If one is in the formula several times, multiply its atomic mass by that number and add the results. This will be the molecular weight of the substance. To find the mass fraction of any element in such a substance, divide its mass number in a given chemical formula M0 by the molecular weight of a given substance M. Multiply the result by 100% (ω%=(M0/M)∙100%).

For example, determine the mass fraction of chemical elements in copper sulfate. Copper (copper II sulfate), has the chemical formula CuSO4. Atomic masses elements included in its composition are equal to Ar(Cu)=64, Ar(S)=32, Ar(O)=16, the mass numbers of these elements will be equal to M0(Cu)=64, M0(S)=32, M0( O)=16∙4=64, taking into account that the molecule contains 4 atoms. Calculate the molecular mass of the substance, it is equal to the sum of the mass numbers of the substances that make up the molecule 64+32+64=160. Determine the mass fraction of copper (Cu) in the composition copper sulfate(ω%=(64/160)∙100%)=40%. Using the same principle, one can determine the mass fractions of all elements in this substance. Mass fraction of sulfur (S) ω%=(32/160)∙100%=20%, oxygen (O) ω%=(64/160)∙100%=40%. Please note that the sum of all mass fractions of the substance must be 100%.

The mass fraction of an element ω(E)% is the ratio of the mass of a given element m (E) in a given molecule of a substance to the molecular mass of this substance Mr (in-va).


The mass fraction of an element is expressed in fractions of a unit or as a percentage:


ω(E) = m (E) / Mr(in-va) (1)


ω% (E) = m(E) 100%/Mr(in-va)


The sum of the mass fractions of all elements of a substance is equal to 1 or 100%.


As a rule, to calculate the mass fraction of an element, they take a portion of a substance equal to the molar mass of the substance, then the mass of a given element in this portion is equal to its molar mass multiplied by the number of atoms of a given element in the molecule.


So, for a substance A x B y in fractions of unity:


ω(A) = Ar(E) X / Мr(in-va) (2)


From proportion (2) we derive a calculation formula for determining the indices (x, y) in the chemical formula of a substance, if the mass fractions of both elements and the molar mass of the substance are known:


X = ω%(A) Mr(in-va) / Ar(E) 100% (3)


Dividing ω% (A) by ω% (B), i.e. transforming formula (2), we obtain:


ω(A) / ω(B) = X Ar(A) / Y Ar(B) (4)


Calculation formula (4) can be transformed as follows:


X: Y = ω%(A) / Ar(A) : ω%(B) / Ar(B) = X(A) : Y(B) (5)


Calculation formulas (3) and (5) are used to determine the formula of a substance.


If the number of atoms in a molecule of a substance for one of the elements and its mass fraction are known, we can determine molar mass substances:


Mr(v-va) = Ar(E) X / W(A)

Examples of solving problems on calculating the mass fractions of chemical elements in a complex substance

Calculation of mass fractions of chemical elements in a complex substance

Example 1. Determine the mass fractions of chemical elements in sulfuric acid H 2 SO 4 and express them as percentages.

Solution

1. Calculate the relative molecular weight of sulfuric acid:


Mr (H 2 SO 4) = 1 2 + 32 + 16 4 = 98


2. Calculate the mass fractions of elements.


To do this, the numerical value of the mass of the element (taking into account the index) is divided by the molar mass of the substance:


Taking this into account and denoting the mass fraction of an element with the letter ω, calculations of mass fractions are carried out as follows:


ω(H) = 2: 98 = 0.0204, or 2.04%;


ω(S) = 32: 98 = 0.3265, or 32.65%;


ω(O) = 64: 98 =0.6531, or 65.31%


Example 2. Determine the mass fractions of chemical elements in aluminum oxide Al 2 O 3 and express them as percentages.

Solution

1. Calculate the relative molecular weight of aluminum oxide:


Mr(Al 2 O 3) = 27 2 + 16 3 = 102


2. Calculate the mass fractions of elements:


ω(Al) = 54: 102 = 0.53 = 53%


ω(O) = 48: 102 = 0.47 = 47%

How to calculate the mass fraction of a substance in a crystalline hydrate

Mass fraction of a substance is the ratio of the mass of a given substance in a system to the mass of the entire system, i.e. ω(X) = m(X) / m,


where ω(X) is the mass fraction of substance X,


m(X) - mass of substance X,


m - mass of the entire system


Mass fraction is a dimensionless quantity. It is expressed as a fraction of a unit or as a percentage.


Example 1. Determine the mass fraction of water of crystallization in barium chloride dihydrate BaCl 2 2H 2 O.

Solution

The molar mass of BaCl 2 2H 2 O is:


M(BaCl 2 2H 2 O) = 137+ 2 35.5 + 2 18 = 244 g/mol


From the formula BaCl 2 2H 2 O it follows that 1 mol of barium chloride dihydrate contains 2 mol H 2 O. From here we can determine the mass of water contained in BaCl 2 2H 2 O:


m(H2O) = 2 18 = 36 g.


We find the mass fraction of water of crystallization in barium chloride dihydrate BaCl 2 2H 2 O.


ω(H 2 O) = m(H 2 O)/m(BaCl 2 2H 2 O) = 36 / 244 = 0.1475 = 14.75%.


Example 2. From the sample rock weighing 25 g, containing the mineral argentite Ag 2 S, silver weighing 5.4 g was isolated. Determine the mass fraction of argentite in the sample.

We determine the amount of silver substance found in argentite:


n(Ag) = m(Ag) / M(Ag) = 5.4 / 108 = 0.05 mol.


From the formula Ag 2 S it follows that the amount of argentite substance is half as much as the amount of silver substance.


Determine the amount of argentite substance:


n(Ag 2 S) = 0.5 n(Ag) = 0.5 0.05 = 0.025 mol


We calculate the mass of argentite:


m(Ag 2 S) = n(Ag 2 S) M(Ag2S) = 0.025 248 = 6.2 g.


Now we determine the mass fraction of argentite in a rock sample weighing 25 g.


ω(Ag 2 S) = m(Ag 2 S) / m = 6.2/25 = 0.248 = 24.8%.