How to find the mass fraction of an element in a substance. How to find the mass fraction of a substance using the formula
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Mass fraction of an element in complex substance
The paragraph will help you:
> find out what the mass fraction of an element in a compound is and determine its value;
> calculate the mass of the element in a certain mass of the compound, based on the mass fraction of the element;
> correctly formulate the solution of chemical problems.
Every difficult substance(chemical compound) is formed by several elements. To know the content of the elements in the compound is necessary for its effective use. For example, the best nitrogen fertilizer is considered to be the one that contains the largest amount of Nitrogen (this element is necessary for plants). Similarly, the quality of metal ore is assessed, determining how much it " rich» on a metal element.
Content element in the compound characterize its mass fraction. This value is denoted by the Latin letter w (“double-ve”).
Let us derive a formula for calculating the mass fraction of an element in a compound from the known masses of the compound and the element. We denote the mass fraction of the element by the letter x. Taking into account that the mass of the compound is a whole, and the mass of an element is a part of the whole, we make up the proportion:
Note that the masses of the element and the compound must be taken in the same units of measurement (for example, in grams).
This is interesting
In two Sulfur compounds - SO 2 and MoS 3 - the mass fractions of the elements are the same and amount to 0.5 (or 50%) each.
The mass fraction has no dimension. It is often expressed as a percentage. In this case formula takes this form:
It is obvious that the sum of the mass fractions of all elements in the compound is 1 (or 100%).
Let us give several examples of solving computational problems. The condition of the problem and its solution are drawn up in this way. A sheet of notebook or blackboard is divided by a vertical line into two unequal parts. In the left, smaller part, the condition of the problem is abbreviated, a horizontal line is drawn and under it they indicate what needs to be found or calculated. Mathematical formulas, explanation, calculations and answer are written on the right side.
80 g of the compound contains 32 g oxygena. Calculate the mass fraction of oxygen in the compound.
The mass fraction of an element in a compound is also calculated using the chemical formula of the compound. Since the masses of atoms and molecules are proportional to the relative atomic and molecular masses, then
where N(E) is the number of element atoms in the compound formula.
From the known mass fraction of the element, it is possible to calculate the mass of the element contained in a certain mass of the compound. From the mathematical formula for the mass fraction of an element follows:
m(E) = w(E) m(compounds).
What mass of Nitrogen is contained in ammonium nitrate (nitrogen fertilizer) weighing 1 kg, if the mass fraction of this element in the compound is 0.35?
The concept of "mass fraction" is used to characterize the quantitative composition of mixtures of substances. The corresponding mathematical formula looks like this:
conclusions
The mass fraction of an element in a compound is the ratio of the mass of the element to the corresponding mass of the compound.
The mass fraction of an element in a compound is calculated from the known masses of the element and the compound or from its chemical formula.
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92. How to calculate the mass fraction of an element in a compound if: a) the mass of the element and the corresponding mass of the compound are known; b) the chemical formula of the compound?
93. 20 g of a substance contains 16 g of Bromine. Find the mass fraction of this element in the substance, expressing it ordinary fraction, decimal and in percentage.
94. Calculate (preferably orally) the mass fractions of elements in compounds with the following formulas: SO 2 , LiH, CrO 3 .
95. Comparing the formulas of substances, as well as the values of relative atomic masses, determine in which of the substances of each pair the mass fraction of the first element in the formula is greater:
a) N 2 O, NO; b) CO, CO 2 ; c) B 2 O 3, B 2 S 3.
96. Perform the necessary calculations for acetic acid CH 3 COOH and glycerol C 3 H 5 (OH) 3 and fill in the table:
| C x H y O z | M r (C x H y O z) | w(C) | W(H) | W(O) |
97. The mass fraction of Nitrogen in a certain compound is 28%. What mass of the compound contains 56 g of Nitrogen?
98. The mass fraction of Calcium in its combination with Hydrogen is 0.952. Determine the mass of hydrogen contained in 20 g of the compound.
99. Mixed 100 g of cement and 150 g of sand. What is the mass fraction of cement in the prepared mixture?
Popel P. P., Kriklya L. S., Chemistry: Pdruch. for 7 cells. zahalnosvit. navch. zakl. - K .: Exhibition Center "Academy", 2008. - 136 p.: il.
Lesson content lesson summary and support frame lesson presentation interactive technologies accelerating teaching methods Practice quizzes, testing online tasks and exercises homework workshops and trainings questions for class discussions Illustrations video and audio materials photos, pictures graphics, tables, schemes comics, parables, sayings, crossword puzzles, anecdotes, jokes, quotes Add-ons abstracts cheat sheets chips for inquisitive articles (MAN) literature main and additional glossary of terms Improving textbooks and lessons correcting errors in the textbook replacing obsolete knowledge with new ones Only for teachers calendar plans learning programs guidelinesSince the 17th century Chemistry is no longer a descriptive science. Chemical scientists began to widely use the measurement of matter. The design of balances, which make it possible to determine the masses of samples, has been improved more and more. For gaseous substances, in addition to mass, volume and pressure were also measured. The use of quantitative measurements made it possible to understand the essence of chemical transformations, to determine the composition of complex substances.
As you already know, the composition of a complex substance includes two or more chemical elements. Obviously, the mass of all matter is composed of the masses of its constituent elements. This means that each element accounts for a certain part of the mass of matter.
The mass fraction of an element is the ratio of the mass of this element in a complex substance to the mass of the entire substance, expressed in fractions of a unit (or in percent):
The mass fraction of an element in a compound is denoted by a Latin lowercase letter w(“double-ve”) and shows the share (part of the mass) attributable to this element in total mass substances. This value can be expressed in fractions of a unit or as a percentage. 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 less than the whole, just as a slice of an orange is less than an orange.
For example, mercury oxide contains two elements, mercury and oxygen. When 50 g of this substance is heated, 46.3 g of mercury and 3.7 g of oxygen are obtained (Fig. 57). 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 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 by the difference:
w(O) \u003d 1 - 0.926 \u003d 0.074,
w(O) = 100% - 92.6% = 7.4%.
In order to find the mass fractions of elements by the proposed method, it is necessary to conduct a complex and time-consuming chemical experiment to determine the mass of each element. If the formula of a complex substance is known, the same problem is solved much easier.
To calculate the mass fraction of an element, multiply its relative atomic mass by the number of atoms ( n) of a given element in the formula and divided by the relative molecular weight substances:
For example, for water (Fig. 58):
M r(H 2 O) \u003d 1 2 + 16 \u003d 18,
Task 1.Calculate the mass fractions of elements in ammonia, the formula of which is NH3 .
Given:
substance ammonia NH 3.
Find:
w(N) w(H).
Solution
1) Calculate the relative molecular weight of ammonia:
M r(NH3) = A r(N) + 3 A r(H) = 14 + 3 1 = 17.
2) Find the mass fraction of nitrogen in the substance:
3) Calculate the mass fraction of hydrogen in ammonia:
w(H) = 1 - w(N) = 1 - 0.8235 = 0.1765, or 17.65%.
Answer. w(N) = 82.35%, w(H) = 17.65%.
Task 2.Calculate the mass fractions of elements in sulfuric acid, which has the formula H2SO4 .
Given:
sulfuric acid H2SO4.
Find:
w(H) w(S) w(O).
Solution
1) Calculate the relative molecular weight of sulfuric acid:
M r(H 2 SO 4) \u003d 2 A r(H)+ A r(S)+4 A r(O) = 2 1 + 32 + 4 16 = 98.
2) Find the mass fraction of hydrogen in the substance:
3) Calculate the mass fraction of sulfur in sulfuric acid:
4. Calculate the mass fraction of oxygen in the substance:
w(O) = 1 – ( w(H)+ w(S)) = 1 - (0.0204 + 0.3265) = 0.6531, or 65.31%.
Answer. w(H) = 2.04%, w(S) = 32.65%, w(O) = 65.31%.
More often, chemists have to solve the inverse problem: to determine the formula of a complex substance by mass fractions of elements. How such problems are solved, we will illustrate with one historical example.
From natural minerals - tenorite and cuprite - two compounds of copper with oxygen (oxides) were isolated. They differed from each other in color and mass fractions of elements. In black oxide, the mass fraction of copper was 80%, and the mass fraction of oxygen was 20%. In red copper oxide, the mass fractions of elements were 88.9% and 11.1%, respectively. What are the formulas for these complex substances? Let's do some simple math.
Example 1 Calculation of the chemical formula of black copper oxide ( w(Cu) = 0.8 and w(O) = 0.2).
x, y- by the number of atoms of chemical elements in its composition: Cu x O y.
2) The ratio of the indices is equal to the ratio of the quotients from dividing the mass fraction of the element in the compound by the relative atomic mass of the element:
3) The resulting ratio must be reduced to the ratio of integers: the indices in the formula showing the number of atoms cannot be fractional. To do this, we divide the resulting numbers by the smaller (i.e. any) of them:
The formula is CuO.
Example 2 Calculation of the formula for red copper oxide from known mass fractions w(Cu) = 88.9% and w(O) = 11.1%.
Given:
w(Cu) = 88.9%, or 0.889,
w(O) = 11.1%, or 0.111.
Find:
Solution
1) Denote the formula of oxide Cu x O y.
2) Find the ratio of indices x And y:
3) We give the ratio of indices to the ratio of integers:
Answer. The compound formula is Cu 2 O.
And now let's complicate the task a little.
Task 3.According to elemental analysis, the composition of calcined bitter salt, which was used by alchemists as a laxative, is as follows: the mass fraction of magnesium is 20.0%, the mass fraction of sulfur is 26.7%, the mass fraction of oxygen is 53.3%.
Given:
w(Mg) = 20.0%, or 0.2,
w(S) = 26.7%, or 0.267,
w(O) = 53.3%, or 0.533.
Find:
Solution
1) Denote the formula of a substance using indices x, y, z: Mg x S y O z.
2) Find the ratio of indices:
3) Determine the value of the indices x, y, z:
Answer. The formula of the substance is MgSO 4.
1. What is the mass fraction of an element in a compound called? How is this value calculated?
2.
Calculate the mass fractions of elements in substances: a) carbon dioxide CO 2;
b) calcium sulfide CaS; c) sodium nitrate NaNO 3; d) aluminum oxide Al 2 O 3.
3. In which of the nitrogen fertilizers is the mass fraction of the nitrogen nutrient the largest: a) ammonium chloride NH 4 Cl; b) ammonium sulfate (NH 4) 2 SO 4; c) urea (NH 2) 2 CO?
4. In the mineral pyrite, 7 g of iron accounts for 8 g of sulfur. 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 extracted from the ashes of a fire and was used to make soap. Mass fractions of elements in this substance: potassium - 56.6%, carbon - 8.7%, oxygen - 34.7%. Determine the formula for potash.
Knowing the chemical formula, you can calculate the mass fraction of chemical elements in a substance. element in substances is denoted by the Greek. the letter "omega" - ω E / V and is calculated by the formula:
where k is the number of atoms of this element in the molecule.
What is the mass fraction of hydrogen and oxygen in water (H 2 O)?
Solution:
M r (H 2 O) \u003d 2 * A r (H) + 1 * A r (O) \u003d 2 * 1 + 1 * 16 \u003d 18
2) Calculate the mass fraction of hydrogen in water:
3) Calculate the mass fraction of oxygen in water. Since the composition of water includes atoms of only two chemical elements, the mass fraction of oxygen will be equal to:
Rice. 1. Formulation of the solution of problem 1
Calculate the mass fraction of elements in the substance H 3 PO 4.
1) Calculate the relative molecular weight of the substance:
M r (H 3 RO 4) \u003d 3 * A r (H) + 1 * A r (P) + 4 * A r (O) \u003d 3 * 1 + 1 * 31 + 4 * 16 \u003d 98
2) We calculate the mass fraction of hydrogen in the substance:
3) Calculate the mass fraction of phosphorus in the substance:
4) Calculate the mass fraction of oxygen in the substance:
1. Collection of tasks and exercises in chemistry: 8th grade: to the textbook by P.A. Orzhekovsky and others. "Chemistry, Grade 8" / P.A. Orzhekovsky, N.A. Titov, F.F. Hegel. - M.: AST: Astrel, 2006.
2. Ushakova O.V. Chemistry workbook: 8th grade: to the textbook by P.A. Orzhekovsky and others. “Chemistry. Grade 8” / O.V. Ushakova, P.I. Bespalov, P.A. Orzhekovsky; under. ed. prof. P.A. Orzhekovsky - M .: AST: Astrel: Profizdat, 2006. (p. 34-36)
3. Chemistry: 8th grade: textbook. for general institutions / P.A. Orzhekovsky, L.M. Meshcheryakova, L.S. Pontak. M.: AST: Astrel, 2005.(§15)
4. Encyclopedia for children. Volume 17. Chemistry / Chapter. edited by V.A. Volodin, leading. scientific ed. I. Leenson. - M.: Avanta +, 2003.
1. A single collection of digital educational resources ().
2. Electronic version journal "Chemistry and Life" ().
4. Video lesson on the topic “Mass fraction chemical element in matter" ().
1. p.78 No. 2 from the textbook "Chemistry: 8th grade" (P.A. Orzhekovsky, L.M. Meshcheryakova, L.S. Pontak. M .: AST: Astrel, 2005).
2. With. 34-36 №№ 3.5 from Workbook in chemistry: 8th grade: to the textbook by P.A. Orzhekovsky and others. “Chemistry. Grade 8” / O.V. Ushakova, P.I. Bespalov, P.A. Orzhekovsky; under. ed. prof. P.A. Orzhekovsky - M.: AST: Astrel: Profizdat, 2006.
The concept of "share" is probably already familiar to you.
For example, the piece of watermelon shown in the figure is one quarter of the whole watermelon, that is, its share is 1/4 or 25%.
To better understand what a mass fraction is, imagine a kilogram of sweets (1000g) that a mother bought for her three children. From this kilogram younger child got half of all the sweets (unfair of course!). The eldest - only 200g, and the average - 300g.
This means that the mass fraction of sweets in the youngest child will be half, or 1/2 or 50%. The middle child will have 30% and the older child will have 20%. It should be emphasized that the mass fraction can be a dimensionless value (quarter, half, third, 1/5, 1/6, etc.), and can be measured as a percentage (%). When solving computational problems, it is better to convert the mass fraction into a dimensionless quantity.
Mass fraction of a substance in solution
Any solution consists of a solvent and a solute. Water is the most common inorganic solvent. Alcohol, acetone, diethyl ether, etc. can be organic solvents. If a solvent is not specified in the problem statement, the solution is considered to be aqueous.
The mass fraction of a solute is calculated by the formula:
$\omega_\text(v-v)=\dfrac(m_\text(v-v))(m_\text(p-ra))(\cdot 100\%)$
Consider examples of problem solving.
How many grams of sugar and water should be taken to prepare 150 g of a 10% sugar solution?
Solution
m(r-ra)=150g
$\omega$(sugar)=10%=0.1
m(sugar)=?
m(sugar) = $\omega\textrm((sugar)) \cdot m(p-pa) = 0.1 \cdot 150 \textrm(r) = 15 \textrm(r)$
m (water) \u003d m (solution) - m (sugar) \u003d 150g - 15g \u003d 135g.
ANSWER: you need to take 15g of sugar and 135g of water.
Solution with a volume of 350 ml. and a density of 1.142 g/ml contains 28 g of sodium chloride. Find the mass fraction of salt in the solution.
Solution
V(solution)=350 ml.
$\rho$(solution)=1.142 g/ml
$\omega(NaCl)$=?
m(r-ra) =V(r-ra) $\cdot \rho$(r-ra)=350 ml $\cdot$ 1.142 g/ml=400g
$\omega(NaCl)=\dfrac(m(NaCl))(m\textrm((p-ra)))=\dfrac(28\textrm(r)) (400\textrm(r)) = 0.07 $=7%
ANSWER: mass fraction of sodium chloride $\omega(NaCl)$=7%
MASS FRACTION OF AN ELEMENT IN A MOLECULE
Formula chemical, for example $H_2SO_4$, carries a lot important information. It denotes either a single molecule of a substance, which is characterized by a relative atomic mass, or 1 mole of a substance, which is characterized by a molar mass. The formula shows the quality (consists of hydrogen, sulfur and oxygen) and quantitative composition(consists of two hydrogen atoms, a sulfur atom and four oxygen atoms). Using the chemical formula, you can find the mass of the molecule as a whole (molecular weight), as well as calculate the ratio of the masses of the elements in the molecule: m(H) : m(S) : m(O) = 2: 32: 64 = 1: 16: 32. When calculating the ratios of the masses of elements, one must take into account their atomic mass and the number of corresponding atoms: $m(H_2)=1*2=2$, $m(S)=32*1=32$, $m(O_4)=16*4 =64$
The principle of calculating the mass fraction of an element is similar to the principle of calculating the mass fraction of a substance in solution and is found using a similar formula:
$\omega_\text(element)=\dfrac(Ar_(\text(element))\cdot n_(\textrm(atoms)))(m_\text(molecules))(\cdot 100\%) $
Find the mass fraction of elements in sulfuric acid.
Solution
Method 1 (proportion):
Find the molar mass of sulfuric acid:
$M(H_2SO_4) = 1\cdot 2 + 32 + 16 \cdot 4=98\hspace(2pt)\textrm(g/mol)$
One sulfuric acid molecule contains one sulfur atom, so the mass of sulfur in sulfuric acid will be: $m(S) = Ar(S) \cdot n(S) = 32\textrm(g/mol) \cdot 1$= 32g/mol
We take the mass of the entire molecule as 100%, and the mass of sulfur as X% and make up the proportion:
$M(H_2SO_4)$=98 g/mol - 100%
m(S) = 32g/mol - X%
Whence $X=\dfrac(32\textrm(g/mol) \cdot 100\%)(98\textrm(g/mol)) =32, 65\% =32\%$
Method 2 (formula):
$\omega(S)=\dfrac(Ar_(\text(element))\cdot n_(\textrm(atoms)))(m_\text(molecules))(\cdot 100\%)=\dfrac( Ar(S)\cdot 1)(M(H_2SO_4))(\cdot 100\%)=\dfrac(32\textrm(g/mol)\cdot 1)(98\textrm(g/mol))(\cdot 100\%) \approx32, 7\%$
Similarly, using the formula, we calculate the mass fractions of hydrogen and oxygen:
$\omega(H)=\dfrac(Ar(H)\cdot 2)(M(H_2SO_4))(\cdot 100\%)=\dfrac(1\textrm(g/mol)\cdot 2)(98\ textrm(g/mol))(\cdot 100\%)\approx2\%$
$\omega(O)=\dfrac(Ar(O)\cdot 4)(M(H_2SO_4))(\cdot 100\%)=\dfrac(16\textrm(g/mol)\cdot 4)(98\ textrm(g/mol))(\cdot 100\%)\approx65, 3\%$
TOPIC OF THE LESSON: Mass fraction of a chemical element in a compound.
THE PURPOSE OF THE LESSON: To teach how to calculate the mass fraction of elements in a compound according to the formula of the compound and establish the chemical formula of a complex substance from known mass fractions of chemical elements.
Basic concepts. Mass fraction of a chemical element.
Planned learning outcomes
Subject. To be able to calculate the mass fraction of an element in a compound according to its formula and establish the chemical formula of a complex substance from known mass fractions of chemical elements.
Metasubject . To form the ability to establish analogies, use algorithms to solve educational and cognitive problems.
The main activities of students. Calculate the mass fraction of an element in a compound using its formula. Establish the chemical formula of a complex substance according to known mass fractions of chemical elements.
Lesson structure
I. Organizational stage
II. Update basic knowledge
III. Learning new material
IV. Consolidation. Summing up the lesson
V. Homework
During the classes
Organizing time.
Checking homework.
Updating of basic knowledge.
Give definitions: relative atomic mass, relative molecular weight.
In what units can relative atomic mass be measured?
In what units can relative molecular weight be measured?
Learning new material.
Work with the textbook. Workbook.
Guys, let's say we have a substance - sulfuric acidH 2 SO 4,
Can we find out which atoms are part of the compound.
What about their number?
And in what mass ratio do they combine?
Calculation of chemical mass ratios
elements in complex matter. (page 51)
And how can you find out in what mass ratios the elements are connected in a compound whose formula isH 2 SO 4 ?
m(H): m(S): m(O)= 2*2 + 32 + 16*4= 2:32:64 = 1:16:32.
1 + 16 + 32 \u003d 49, that is, 49 mass parts of sulfuric acid, contains 1 mass part of hydrogen, 16 mass parts of sulfur, 32 mass parts of oxygen.
Guys, what do you think, can we calculate the proportion of each element in the compound?
Today we will get acquainted with the new concept of the mass fraction of an element in a compound.
W- mass fraction of the element in the compound.
nis the number of atoms of the element.
Mr- relative molecular weight.
Calculation of mass fractions of chemical elements
in complex matter. (RT)
1. Study the algorithm for calculating the mass fraction of an element in a compound.
Task #1 (RT)
Conclusion chemical formulas if mass fractions of chemical elements are known,
included in this substance. (RT)
2. Study the algorithm for calculating the mass fraction of an element in a compound.
Task #5 (RT)
Consolidation of the studied material.
RT p. 25 No. 2.
RT p. 27 No. 6.
Summing up the lesson.
What new concepts did you learn in class today?
Independent work.
Homework:
study §15 pp. 51 - 53;
answer questions No. 3,4,7 pp. 53-54 (in writing).
P list of used literature.
Textbook. Chemistry grade 8. ed. G.E. Rudzitis, F.G. Feldman. Publishing house "Enlightenment", 2014.
Chemistry workbook. ed. Borovskikh T.A.
