How to solve the mass fraction of elements. Mass fraction of an element in a complex substance - Knowledge Hypermarket
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 one or as a percentage:
ω (E) = m (E) / Mr (in-va) (1)
ω% (E) = m (E) 100% / Мr (in-va)
The sum of the mass fractions of all elements of a substance is 1 or 100%.
As a rule, to calculate the mass fraction of an element, a portion of a substance is taken equal to the molar mass of a 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 a molecule.
So, for substance A x B y in fractions of one:
ω (A) = Ar (E) X / Mr (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 the formula (2), we get:
ω (A) / ω (B) = X Ar (A) / Y Ar (B) (4)
The design 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 you know the number of atoms in a molecule of a substance for one of the elements and its mass fraction, you can determine the molar mass of the substance:
Mr (in-va) = Ar (E) X / W (A)
Examples of solving problems for calculating the mass fractions of chemical elements in a complex substance
Calculation of the 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 a percentage.
Solution
1. Calculate the relative molecular weight of sulfuric acid:
Mr (H 2 SO 4) = 1 2 + 32 + 16 4 = 98
2. We calculate the mass fractions of elements.
For 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 the element with the letter ω, the calculations of the 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 a percentage.
Solution
1. Calculate the relative molecular weight of aluminum oxide:
Mr (Al 2 O 3) = 27 2 + 16 3 = 102
2. We 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 the 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 is the mass of the entire system
Mass fraction is a dimensionless quantity. It is expressed in fractions of one 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 of H 2 O. Hence, the mass of water contained in BaCl 2 2H 2 O can be determined:
m (H2O) = 2 18 = 36 g.
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 a rock sample weighing 25 g, containing the mineral argentite Ag 2 S, silver was isolated weighing 5.4 g. Determine the mass fraction of argentite in the sample.
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Determine the amount of silver substance 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 two times less than 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%. |
What is mass fraction? For example, mass fraction of a chemical element is the ratio of the mass of an element to the mass of the whole substance... Mass fraction can be expressed as a percentage or a fraction.
Where can the mass fraction be applied?
Here are some of the directions:
Determination of the elemental composition of a complex chemical
Finding the mass of an element by the mass of a complex substance
For calculations, the Molar Mass of a Substance calculator is used online with extended data that can be seen if you use an XMPP request.
The calculation of similar tasks, which are indicated above, when using this page, becomes even easier, more convenient and more accurate. By the way, about the accuracy. In school textbooks, for some reason, the molar masses of the elements are rounded to whole values, which is quite useful for solving school problems, although in fact the molar masses of each chemical element are periodically adjusted.
Our calculator does not strive to show high accuracy (above 5 decimal places), although there is nothing difficult about it. For the most part, those atomic masses of elements that use the calculator are sufficient to solve the tasks set for determining the mass fractions of elements
But for those pedants :) who value accuracy, I would like to recommend the link Atomic Weights and Isotopic Compositions for All Element s which displays all chemical elements, their relative atomic masses, as well as the masses of all isotopes of each element.
That's all I would like to say. Now we will consider specific tasks and how to solve them. Note that despite the fact that they are all dissimilar, they inherently rely on the molar mass of the substance and the mass fractions of the elements in this substance.
At the beginning of autumn 2017, I added another calculator Mole fractions of a substance and the number of atoms, which will help solve problems on the mass of a pure substance in a complex substance, the number of moles in a substance and in each element, as well as the number of atoms / molecules in a substance.
Examples of
Calculate the mass fraction of elements in copper sulfate CuSO 4
The request is very simple, just write the formula and get the result, which will be our answer.
As already mentioned in school textbooks, the values \ u200b \ u200bare coarse enough, so do not be surprised if in the answers of paper books you see Cu = 40%, O = 40%, S = 20%. These are, let's say, "side effects" of simplifying school material for students. For real problems, our answer (the bot's answer) is naturally more accurate.
If we were talking about what to express in fractions and not percentages, then we divide the percentages of each of the elements by 100 and get the answer in fractions.
How much sodium is there in 10 tons of Na3 cryoline?
Let's introduce the cryoline formula and get the following data
From the data obtained, we see that the 209.9412 amount of the substance contains 68.96931 amount of sodium.
Whether we measure it in grams, or in kilograms or tons for the ratio, it does not change anything.
Now it remains to build another correspondence where we have 10 tons of the original substance and an unknown amount of sodium
This is a typical proportion. You can of course use the bot Calculation of proportions and ratios, but this proportion is so simple that we will do it with pens.
209.9412 refers to 10 (tons) as 68.96391 to an unknown number.
Thus, the amount of sodium (in tons) in cryoline will be 68.96391 * 10 / 209.9412 = 3.2849154906231 tons of sodium.
Again, for the school, sometimes it will be necessary to round up to an integer the mass content of elements in a substance, but the answer actually does not differ much from the previous one.
69*10/210=3.285714
Accuracy to hundredths is the same.
Calculate how much oxygen is contained in 50 tons of calcium phosphate Ca3 (PO4) 2?
The mass fractions of a given substance are as follows
The same proportion as in the previous problem 310.18272 refers to 50 (tons) as well as 127.9952 to an unknown value
The answer is 20.63 tons of oxygen is in a given mass of matter.
If we add an exclamation mark to the formula, which tells us that the problem is a school one (rough rounding of atomic masses to integers is used), then we get the following answer.
What is mass fraction? For example, mass fraction of a chemical element is the ratio of the mass of an element to the mass of the whole substance... Mass fraction can be expressed as a percentage or a fraction.
Where can the mass fraction be applied?
Here are some of the directions:
Determination of the elemental composition of a complex chemical
Finding the mass of an element by the mass of a complex substance
For calculations, the Molar Mass of a Substance calculator is used online with extended data that can be seen if you use an XMPP request.
The calculation of similar tasks, which are indicated above, when using this page, becomes even easier, more convenient and more accurate. By the way, about the accuracy. In school textbooks, for some reason, the molar masses of the elements are rounded to whole values, which is quite useful for solving school problems, although in fact the molar masses of each chemical element are periodically adjusted.
Our calculator does not strive to show high accuracy (above 5 decimal places), although there is nothing difficult about it. For the most part, those atomic masses of elements that use the calculator are sufficient to solve the tasks set for determining the mass fractions of elements
But for those pedants :) who value accuracy, I would like to recommend the link Atomic Weights and Isotopic Compositions for All Element s which displays all chemical elements, their relative atomic masses, as well as the masses of all isotopes of each element.
That's all I would like to say. Now we will consider specific tasks and how to solve them. Note that despite the fact that they are all dissimilar, they inherently rely on the molar mass of the substance and the mass fractions of the elements in this substance.
At the beginning of autumn 2017, I added another calculator Mole fractions of a substance and the number of atoms, which will help solve problems on the mass of a pure substance in a complex substance, the number of moles in a substance and in each element, as well as the number of atoms / molecules in a substance.
Examples of
Calculate the mass fraction of elements in copper sulfate CuSO 4
The request is very simple, just write the formula and get the result, which will be our answer.
As already mentioned in school textbooks, the values \ u200b \ u200bare coarse enough, so do not be surprised if in the answers of paper books you see Cu = 40%, O = 40%, S = 20%. These are, let's say, "side effects" of simplifying school material for students. For real problems, our answer (the bot's answer) is naturally more accurate.
If we were talking about what to express in fractions and not percentages, then we divide the percentages of each of the elements by 100 and get the answer in fractions.
How much sodium is there in 10 tons of Na3 cryoline?
Let's introduce the cryoline formula and get the following data
From the data obtained, we see that the 209.9412 amount of the substance contains 68.96931 amount of sodium.
Whether we measure it in grams, or in kilograms or tons for the ratio, it does not change anything.
Now it remains to build another correspondence where we have 10 tons of the original substance and an unknown amount of sodium
This is a typical proportion. You can of course use the bot Calculation of proportions and ratios, but this proportion is so simple that we will do it with pens.
209.9412 refers to 10 (tons) as 68.96391 to an unknown number.
Thus, the amount of sodium (in tons) in cryoline will be 68.96391 * 10 / 209.9412 = 3.2849154906231 tons of sodium.
Again, for the school, sometimes it will be necessary to round up to an integer the mass content of elements in a substance, but the answer actually does not differ much from the previous one.
69*10/210=3.285714
Accuracy to hundredths is the same.
Calculate how much oxygen is contained in 50 tons of calcium phosphate Ca3 (PO4) 2?
The mass fractions of a given substance are as follows
The same proportion as in the previous problem 310.18272 refers to 50 (tons) as well as 127.9952 to an unknown value
The answer is 20.63 tons of oxygen is in a given mass of matter.
If we add an exclamation mark to the formula, which tells us that the problem is a school one (rough rounding of atomic masses to integers is used), then we get the following answer:
The proportion will already be like this
310 refers to 50 (tons) as well as 128 to an unknown value. And the answer
20.64 tons
Something like this:)
Good luck with your calculations !!
1. Fill in the blanks in the sentences.
a) In mathematics, "share" is the relationship of a part to a whole. To calculate the mass fraction of an element, its relative atomic mass must be multiplied by the number of atoms of a given element in the formula and divided by the relative molecular weight of the substance.
b) The sum of the mass fractions of all the elements that make up the substance is 1 or 100%.
2. Write down mathematical formulas for finding the mass fractions of elements if:
a) the formula of the substance is P 2 O 5, M r = 2 * 31 + 5 * 16 = 142
w (P) = 2 * 31/132 * 100% = 44%
w (O) = 5 * 16/142 * 100% = 56% or w (O) = 100-44 = 56.
b) the substance formula - A x B y
w (A) = Ar (A) * x / Mr (AxBy) * 100%
w (B) = Ar (B) * y / Mr (AxBy) * 100%
3. Calculate the mass fraction of elements:
a) in methane (CH 4)
b) in sodium carbonate (Na 2 CO 3)
4. Compare the mass fractions of the indicated elements in substances and put a sign<, >or =:
5. In the combination of silicon with hydrogen, the mass fraction of silicon is 87.5%, hydrogen is 12.5%. The relative molecular weight of the substance is 32. Determine the formula of this compound.
6. Mass fractions of elements in the compound are shown in the diagram:
Determine the formula for this substance if it is known that its relative molecular weight is 100.
7. Ethylene is a natural stimulator of fruit ripening: its accumulation in fruits accelerates their ripening. The earlier the accumulation of ethylene begins, the earlier the fruits ripen. Therefore, ethylene is used to artificially accelerate the ripening of fruits. Derive the formula of ethylene if it is known that the mass fraction of carbon is 85.7%, and the mass fraction of hydrogen is 14.3%. The relative molecular weight of this substance is 28.
8. Derive the chemical formula of a substance if it is known that
a) w (Ca) = 36%, w (Cl) = 64%
b) w (Na) 29.1%, w (S) = 40.5%, w (O) = 30.4%.
9. Lapis has antimicrobial properties. Previously, it was used to cauterize warts. In small concentrations, it acts as an anti-inflammatory and astringent, but can cause burns. Derive the formula for lapis if it is known that it contains 63.53% silver, 8.24% nitrogen, 28.23% oxygen.
What is the essence of the concept of "mass fraction"?
Mass fraction is measured in percent or just tenths. A little higher, we talked about the classic definition, which can be found in reference books, encyclopedias or school chemistry textbooks. But it is not so easy to understand the essence of what has been said. So, suppose we have 500 g of some complex substance. Complex in this case means that it is not homogeneous in its composition. By and large, any substances that we use are complex, even simple table salt, the formula of which is NaCl, that is, it consists of sodium and chlorine molecules. If we continue the reasoning using the example of table salt, then we can assume that 500 grams of salt contains 400 g of sodium. Then its mass fraction will be 80% or 0.8.
Why does a summer resident need this?
I think you already know the answer to this question. The preparation of all kinds of solutions, mixtures, etc. is an integral part of the economic activity of any gardener. In the form of solutions, fertilizers, various nutritional mixtures, as well as other drugs are used, for example, growth stimulants "Epin", "Kornevin", etc. In addition, it is often necessary to mix dry substances such as cement, sand and other components, or ordinary garden soil with the purchased substrate. At the same time, the recommended concentration of these agents and preparations in prepared solutions or mixtures in most instructions is given precisely in mass fractions.
Thus, knowing how to calculate the mass fraction of an element in a substance will help the summer resident to properly prepare the necessary fertilizer solution or nutrient mixture, and this, in turn, will certainly affect the future harvest.
Calculation algorithm
So, the mass fraction of an individual component is the ratio of its mass to the total mass of a solution or substance. If the result obtained needs to be converted into percentages, then it must be multiplied by 100. Thus, the formula for calculating the mass fraction can be written as follows:
W = Mass of substance / Mass of solution
W = (Mass of substance / Mass of solution) x 100%.
An example of determining the mass fraction
Suppose we have a solution, for the preparation of which 5 g of NaCl was added to 100 ml of water, and now it is necessary to calculate the concentration of sodium chloride, that is, its mass fraction. We know the mass of the substance, and the mass of the resulting solution is the sum of two masses - salt and water and is equal to 105 g. Thus, we divide 5 g by 105 g, multiply the result by 100 and get the desired value of 4.7%. This is the concentration that the saline solution will have.
A more practical task
In practice, the summer resident often has to face tasks of a different kind. For example, it is necessary to prepare an aqueous solution of any fertilizer, the concentration of which by weight should be 10%. In order to accurately observe the recommended proportions, you need to determine how much of the substance is needed and in what volume of water it will need to be dissolved.
The solution to the problem begins in the reverse order. First, the mass fraction expressed as a percentage should be divided by 100. As a result, we get W = 0.1 - this is the mass fraction of the substance in units. Now let us designate the amount of substance as x, and the final mass of the solution - M. In this case, the last value is made up of two terms - the mass of water and the mass of fertilizer. That is, M = MV + x. Thus, we get a simple equation:
W = x / (Mw + x)
Solving it with respect to x, we get:
x = W x MV / (1 - W)
Substituting the available data, we get the following dependence:
x = 0.1 x MV / 0.9
Thus, if for the preparation of the solution we take 1 liter (that is, 1000 g) of water, then to prepare the solution of the required concentration, approximately 111-112 g of fertilizer will be needed.
Solving problems with dilution or addition
Suppose we have 10 liters (10,000 g) of a ready-made aqueous solution with a concentration of a certain substance in it W1 = 30% or 0.3. How much water will you need to add to it in order for the concentration to decrease to W2 = 15% or 0.15? In this case, the formula will help:
Мв = (W1х М1 / W2) - М1
Substituting the initial data, we get that the amount of added water should be:
MV = (0.3 x 10,000 / 0.15) - 10,000 = 10,000 g
That is, you need to add the same 10 liters.
Now imagine the inverse problem - there is 10 liters of an aqueous solution (M1 = 10,000 g) with a concentration of W1 = 10% or 0.1. It is necessary to obtain a solution with a mass fraction of fertilizer W2 = 20% or 0.2. How much starting material will you need to add? To do this, you need to use the formula:
x = M1 x (W2 - W1) / (1 - W2)
Substituting the original values, we get x = 1 125 g.
Thus, knowledge of the simplest basics of school chemistry will help the gardener to properly prepare fertilizer solutions, nutrient substrates from several elements or mixtures for construction work.