How to find the mass fraction of a substance using the formula. Mass fraction of a substance in solution

In chemistry lessons, quite often it is necessary to solve problems that use mathematical methods and techniques that cause difficulties for students, and the chemistry teacher has to take on the functions of a mathematics teacher and, at the same time, problems with a chemical content, using special terms, are difficult to explain without special training for mathematics teachers. Thus, the idea was born to prepare and conduct a series of optional classes jointly by a teacher of chemistry and mathematics to solve problems on a mixture with students of grade 9.

TOPIC: SOLVING PROBLEMS USING THE CONCEPT “MASS FRACTION OF DISSOLVED SUBSTANCE. DILUTION AND CONCENTRATION OF SOLUTIONS” (INTEGRATION OF CHEMISTRY AND ALGEBRA)

GOALS :

Significantly expand the range of algebraic problems with chemical content;

Show the possibility of solving a chemical problem in an algebraic way;

To teach to make a conscious choice of the method and method of solving problems in a chemistry lesson;

Show the presence of interdisciplinary connections in the field of chemistry and mathematics.

EQUIPMENT: COMPUTER, MULTIMEDIA BOX, SCREEN, PRESENTATION.

DURING THE CLASSES.

Chemistry teacher: The quantitative composition of a solution is expressed by its concentration, which has different forms expressions. Most often, mass concentration or mass fraction of a solute is used. Recall the mathematical formula for expressing the mass fraction of a dissolved substance.

The mass fraction of the dissolved substance is denoted by - W r.v.
The mass fraction of a solute is the ratio of the mass of the solute to the mass of the solution: W (r.v.) \u003d m (r.v.) / m (p-ra) x 100%.
The mass of the solution is the sum of the mass of the solute and the mass of the solvent: m (r-ra) \u003d m (r.v.) + m (r-la)
The formula for the mass fraction of a dissolved substance will look like this: W (r.v.) \u003d m (r.v.) / m (r.v.) + m (p-la) x 100%
Let's transform this formula and express the mass of the dissolved substance and the mass of the solution: m (r.v.) \u003d w (r.v.) x m (p-ra) / 100%, m (p-ra) \u003d m (r.v. )/w(r.h.) x 100%

Chemistry teacher: I propose to solve the problem using the proposed formulas.

A task. How many grams of iodine and alcohol should be taken to prepare 500 grams of 5% iodine tincture?

GIVEN:	SOLUTION:
M (r-ra) = 500 g.	W (r.v.) \u003d m (r.v.) / m (p-ra)
W (r.v.)=5%=0.05	W (r.v.) \u003d m (I2) / m (real)
FIND:	m (I2)=W(r.v.)x m(real)
m(I2)=?	m(I2)=0.05 x 500 g.=25 g.
m(alcohol)=?	m (p-ra) \u003d m (I2) + m (alcohol)
	m (alcohol) \u003d m (solution) -m (I2)
	m (alcohol) \u003d 500 g.-25 g. \u003d 475 g.

ANSWER: m (I2) \u003d 25 g, m (alcohol) \u003d 475 g.

Chemistry teacher: Very often in the work of chemical laboratories it is necessary to prepare solutions with a certain mass fraction th solute by mixing two solutions or diluting a strong solution with water. Before preparing the solution, certain arithmetic calculations must be carried out.

A task. 100 grams of a solution with a mass fraction of a certain substance of 20% and 50 grams of a solution with a mass fraction of this substance of 32% are mixed. Calculate mass fraction solute in the newly obtained solution.

Chemistry teacher: Let's solve this problem using the mixing rule.

Let's write the condition of the problem in the table:

Let's solve the problem using the mixing rule:

m 1 w 1 + m 2 w 2 \u003d m 3 w 3
m 1 w 1 + m 2 w 2 \u003d (m 1 + m 2) w 3
m 1 w 1 + m 2 w 2 \u003d m 1 w 3 + m 2 w 3
m 1 w 1 -m 1 w 3 \u003d m 2 w 2 -m 2 w 2
m 1 (w 1 -w 3) \u003d m 2 (w 3 -w 2)
m 1 /m 2 \u003d (w 3 -w 2) / (w 1 -w 3)

The ratio of the mass of the first solution to the mass of the second is equal to the ratio of the difference in the mass fractions of the mixture and the second solution to the difference in the mass fractions of the first solution and the mixture:

1 /m 2 \u003d (w 3 -w 2) / (w 1 -w 3)

100:50 \u003d (w 3 -0.32): (0.2-w 3)

100 (0.2-w 3) \u003d 50 (w 3 -0.32)

20-100w3=50w3-16

20+16=50w3 +100w3

36=150w3

W 3 \u003d 0.24

ANSWER: the mass fraction of the dissolved substance in the newly obtained solution is 24%.

Math teacher: This problem can be solved using algebraic transformations:

1. Find the mass of the dissolved substance in each of the solutions:

20% of 100 g 32% of 50 g

0.2x100=20(g) 0.32x50=16(g)

2. Find the mass of the dissolved substance in the mixture:

3. Find the mass of the solution:

4. Let the concentration of the resulting solution be x%, then the mass of the dissolved substance in the mixture:

0.01Xx150=1.5X

5. Let's make an equation and solve it:

ANSWER: the concentration of the resulting solution is 24%.

Chemistry teacher: In the course of chemistry there are problems that can be solved only by the method of systems of equations

Task: A 30% solution of hydrochloric acid was mixed with a 10% solution of the same acid and 600 grams of a 15% solution were obtained. How many grams of each solution was taken?

W 1 \u003d 30% \u003d 0.3
W 2 \u003d 10% \u003d 0.1
W 3 \u003d 15% \u003d 0.15
m 3 (r-ra) \u003d 600 g.

m1(r-ra)=?
m2(r-ra)=?

Mathematic teacher: Let's introduce the notation:

let m 1 (r-ra) -X g., and m 2 (r-ra) -Y g., then:

m 3 (r-ra) \u003d m 1 (r-ra) + m 1 (r-ra) \u003d X + Y.

Calculate the masses of dissolved substances:

m 1 \u003d 0.3X,
m 2 \u003d 0.1Y,
m 3 \u003d 600 g. x 0.15 \u003d 90 g.

Let's make a system of equations:

Solve the underlined equation:

180-0.3Y+0.1Y=90

if Y=450 g., then X=600 g.-450 g.=150 g.

weight of 1 solution = 150 g.
weight 2 r-ra = 450g.

Chemistry teacher. Let's solve the same problem by the mixing method. What answer did you get? (Answers converge).

HOMEWORK.

In what mass should 20% and 5% solutions of the same substance be mixed in order to obtain a 10% solution?

SOLUTION ALGORITHM:

1.Enter letter designations for mass solutions.
2. Calculate the masses of dissolved substances in the first, second solution and mixture.
3. Compose a system of equations and solve it.
4. Write down the answer.

This lesson is devoted to the study of the topic "Mass fraction of a substance in a solution." Using the lesson materials, you will learn how to quantify the content of a solute in a solution, as well as determine the composition of a solution from data on the mass fraction of a solute.

Topic: Classes of inorganic substances

Lesson: Mass fraction of a substance in solution

The mass of the solution is the sum of the masses of the solvent and the solute:

m (p) \u003d m (c) + m (r-la)

The mass fraction of a substance in a solution is equal to the ratio of the mass of the solute to the mass of the entire solution:

We will solve several problems using the above formulas.

Calculate the mass fraction (in%) of sucrose in a solution containing 250 g of water and 50 g of sucrose.

The mass fraction of sucrose in solution can be calculated using the well-known formula:

We substitute the numerical values and find the mass fraction of sucrose in the solution. Received 16.7% in response.

By transforming the formula for calculating the mass fraction of a substance in a solution, you can find the values of the mass of a solute from the known mass of the solution and the mass fraction of the substance in the solution; or the mass of the solvent by the mass of the solute and the mass fraction of the substance in solution.

Consider the solution of a problem in which the mass fraction of a solute changes when the solution is diluted.

To 120 g of a solution with a mass fraction of salt of 7% was added 30 g of water. Determine the mass fraction of salt in the resulting solution.

Let's analyze the condition of the problem. In the process of diluting the solution, the mass of the solute does not change, but the mass of the solvent increases, which means that the mass of the solution increases and, conversely, the mass fraction of the substance in the solution decreases.

First, we determine the mass of the solute, knowing the mass of the initial solution and the mass fraction of salt in this solution. The mass of a solute is equal to the product of the mass of the solution and the mass fraction of the substance in the solution.

We have already found out that the mass of a solute does not change when a solution is diluted. This means that by calculating the mass of the resulting solution, you can find the mass fraction of salt in the resulting solution.

The mass of the resulting solution is equal to the sum of the masses of the initial solution and the added water. The mass fraction of salt in the resulting solution is equal to the ratio of the mass of the solute and the mass of the resulting solution. Thus, a mass fraction of salt in the resulting solution was obtained equal to 5.6%.

1. Collection of tasks and exercises in chemistry: 8th grade: to textbook. P.A. Orzhekovsky and others. “Chemistry. Grade 8 / P.A. Orzhekovsky, N.A. Titov, F.F. Hegel. - M .: AST: Astrel, 2006. (p. 111-116)

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; ed. prof. P.A. Orzhekovsky - M .: AST: Astrel: Profizdat, 2006. (p. 111-115)

3. Chemistry. 8th grade. Textbook for general education institutions / P.A. Orzhekovsky, L.M. Meshcheryakova, M.M. Shalashova. – M.: Astrel, 2013. (§35)

4. Chemistry: 8th grade: textbook for general education. institutions / P.A. Orzhekovsky, L.M. Meshcheryakova, L.S. Pontak. M.: AST: Astrel, 2005. (§41)

5. Chemistry: inorg. chemistry: textbook for 8 cells. general education institutions / G.E. Rudzitis, F.G. Feldman. - M .: Education, JSC "Moscow textbooks", 2009. (§ 28)

6. Encyclopedia for children. Volume 17. Chemistry / Editor-in-Chief. V.A. Volodin, leading. scientific ed. I. Leenson. – M.: Avanta+, 2003.

Additional web resources

3. Interaction of substances with water ().

Homework

1. p. 113-114 №№ 9,10 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; ed. prof. P.A. Orzhekovsky - M.: AST: Astrel: Profizdat, 2006.

2. p.197 №№ 1,2 from the textbook P.A. Orzhekovsky, L.M. Meshcheryakova, M.M. Shalashova "Chemistry: 8th grade", 2013

Instruction

Mass fraction is the ratio of the mass of a solute to the mass solution. Moreover, it can be measured or, then for this the result must be multiplied by 100% or in mass fractions (in this case it has no units).
Any solution consists of (water is the most common solvent) and a solute. For example, in any salt solution, water will be the solvent, and the salt itself will act as the solute.
For calculations, it is necessary to know at least two parameters - the mass of water and the mass of salt. This will make it possible to calculate the mass share substance which is w (omega).

Example 1 Mass solution hydroxide (KOH) 150 g, mass of solute (KOH) 20 g. Find the mass share(KOH) in the resulting solution.
m (KOH) = 20 g
m (KOH) = 100 g
w (KOH) - ? share substances.
w(KOH) = m(KOH) / m( solution(KOH) x 100% Now calculate the mass share solute potassium hydroxide (KOH):
w (KOH) = 20 g / 120 g x 100% = 16.6%

Example 2. The mass of water is 100 g, the mass of salt is 20 g. Find the mass share chloride in solution.
m(NaCl) = 20 g
m (water) = 100 g
w (NaCl) - ? There is a formula by which you can determine the mass share substances.
w(NaCl) = m(NaCl) / m( solution NaCl) x 100% Before using this formula, find the mass solution, which consists of the mass of the solute and the mass of water. Therefore: m ( solution NaCl) = m (NaCl solute) + m (water) Plug in specific values
m ( solution NaCl) = 100 g + 20 g = 120 g Now calculate the mass share solute:
w (NaCl) = 20 g / 120 g x 100% = 16.7%

Useful advice

When calculating, do not confuse such concepts as the mass of a solute and the mass fraction of a solute

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

You will need

scales;
periodic table of chemical elements;
calculator.

Instruction

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 balance to determine the masses that make up the mixture or . Then fold them up. 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, in 140 g of water dissolve 20 g table salt. To find the mass fraction of salt, add the masses of these two substances М=140+20=160 g. Then find the mass fraction of the substance ω%=(20/160)∙100%=12.5%.