Mass fraction of a substance is the ratio of the mass of a certain substance to the mass of a mixture or solution in which this substance is located. Expressed in fractions of a unit or as a percentage.

Instructions

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

2. If the value of the mass is not given in the condition of the problem, then it is allowed to calculate it with the support of several formulas, the values ​​given in the condition will help to prefer the necessary one. The first formula for finding mass: m = V * p, where m is mass, V is volume, p is density. The further formula looks like this: m = n * M, where m is the mass, n is the number of the substance, M is the molar mass. The molar mass, in turn, is made up of the nuclear masses of the elements that make up the substance.

3. For a better understanding of this material, we will solve the problem. A mixture of copper and magnesium sawdust weighing 1.5 g was treated with an excess of sulfuric acid. As a result of the reaction, 0.56 L of hydrogen was released (typical data). Calculate the mass fraction of copper in the mixture. In this problem, a reaction takes place, we write down its equation. Of the 2 substances, only magnesium interacts with an excess of hydrochloric acid: Mg + 2HCl = MgCl2 + H2. In order 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). Given the mass of the mixture, we find the mass of copper: m (Cu) = m (cm) - m (Mg). We are looking for the mass of magnesium: m (Mg) = n (Mg) * M (Mg). The equation of the reaction will help to find the number of magnesium substance. We find the number 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 mass of magnesium 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 It remains to calculate the mass fraction: w (Cu) = 0.9 / 1.5 = 0.6 or 60%.

Mass fraction shows in percent or in fractions the table of contents of a substance in a solution or an element in the composition of a substance. Knowing to calculate the mass fraction is beneficial not only in chemistry lessons, but also when you want to prepare a solution or mixture, say, for culinary purposes. Or change the percentage in the composition you have.

Instructions

1. The mass fraction is calculated as the ratio of the mass of a given component to the total mass of the solution. To acquire the total in percent, you need to multiply the resulting quotient by 100. The formula looks like this:? = M (solute) / m (solution) ?,% =? * 100

2. Consider, for example, the direct and inverse problems: Let's say you dissolved 5 grams of table salt in 100 grams of water. What percentage of the solution did you receive? The solution is hefty primitive. You know the mass of the substance (table salt), the mass of the solution will be equal to the sum of the masses of water and salt. Thus, you should divide 5 g by 105 g and multiply the result of division by 100 - this will be the result: you will get a 4.7% solution. Now the reverse problem. You want to prepare 200 g of a 10% aqueous solution of which is desirable. How much substance to take for dissolution? We act in the reverse order, divide the mass fraction, expressed as a percentage (10%) by 100. We get 0.1. Now let's draw up a simple equation, where we denote the required number of substances by x and, consequently, the mass of the solution as 200 g + x. Our equation will look like this: 0.1 = x / 200g + x. When we solve it, we get that x equals approximately 22.2 g. The result is checked by solving the direct problem.

3. It is more difficult to find out what numbers of solutions of a certain percentage must be taken to acquire a certain number of solutions with new specified qualities. Here it is required to compose and solve more closely a system of equations. In this system, the first equation is the expression of the famous mass of the resulting mixture, in terms of two unknown masses of the initial solutions. Say, if our goal is to get 150 g of a solution, the equation will have the form x + y = 150 g. The second equation is the mass of a solute equal to the sum of the same substance, in the composition of 2 mixed solutions. Say, if you want to have a 30% solution, and the solutions that you mix are 100%, that is, a pure substance, and 15%, then the second equation will look like: x + 0.15y = 45 g. for small, solve the equation system and find out how much substance you need to add to a 15% solution in order to get a 30% solution. Try it.

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To calculate number substances, find out its mass with the help of weights, express it in grams and divide by the molar mass that can be detected with the support of the periodic table. To determine the number substances gas under typical conditions, apply Avogadro's law. If the gas is in other conditions, measure the pressure, volume and temperature of the gas, and then calculate number substances in him.

You will need

• You will need a scale, thermometer, pressure gauge, ruler or tape measure, periodic table.

Instructions

1. Determining the number substances in a solid or liquid. Find the mass of the investigated body using scales, express it in grams. Determine which substances the body consists, then with the support of the periodic table, find the molar mass substances... To do this, find the elements that make up the molecule substances of which the body is made. Determine their nuclear masses from the table; if a fractional number is indicated in the table, round it to the nearest whole. Find the sum of the masses of all atoms in a molecule substances, get the molecular weight, which is numerically equal to the molar weight substances in grams per mole. Later, divide the previously measured mass by the molar mass. As a result, you will get number substances in moles (? = m / M).

2. Number substances gas under typical conditions. If the gas is in typical conditions (0 degrees Celsius and 760 mmHg), detect its volume. To do this, measure the volume of the room, cylinder or vessel where it is located, from the fact that the gas occupies each volume provided to it. In order to get its value, measure the geometric dimensions of the vessel, where it is located with the support of a tape measure and with the support of mathematical formulas, find its volume. A particularly classic case is a parallelepiped room. Measure its length, width and height in meters, then multiply them and get the volume of gas, which is in it in cubic meters. To discover number substances gas, divide the resulting volume by 0.0224 - the molar volume of gas under typical conditions.

3. Number substances gas with arbitrary parameters. Measure the gas pressure with a pressure gauge in pascals, its temperature in Kelvin, for which add 273 to the degrees Celsius in which the thermometer measures. Determine also the volume of gas in cubic meters. To discover number substances Divide the product of pressure and volume by the temperature and the number 8.31 (universal gas continuous),? = PV / (RT).

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Many liquids are solutions. These are, in particular, human blood, tea, coffee, sea water. The solution is based on a solute. There are tasks to find the mass fraction of this substance.

Instructions

1. Solutions are called homogeneous homogeneous systems that consist of 2 or more components. They are divided into three categories: - liquid solutions; - solid solutions; - gaseous solutions. Liquid solutions include, say, dilute sulfuric acid, solid - an alloy of iron and copper, and gaseous - all kinds of mixtures of gases. Regardless of the state of aggregation of the solution, it consists of a solvent and a solute. The most common solvent is water, which is used to dilute the substance. The composition of solutions is expressed in different ways, especially the value of the mass fraction of the solute is often used for this. The mass fraction is a dimensionless quantity, and it is equal to the ratio of the mass of the solute to the total mass of each solution:? In = mw / m The mass fraction is expressed as a percentage or decimal fractions. In order to calculate this parameter as a percentage, use the following formula: w (substance) = mw / m (solution) · 100%. To find the same parameter in the form of a decimal fraction, do not multiply by 100%.

2. The mass of each solution is the sum of the masses of water and solute. Consequently, occasionally the formula indicated above is written in a slightly different way:? In = mw / (mw + m (H2O)), where m (solution) = mw + m (H2O) Let's say that dilute nitric acid consists of a solvent - water, and solute-acid. From this it follows that the mass of the solute is calculated in the following way:? In = mHNO3 / mHNO3 + mH2O

3. If the mass of a substance is unknown, but only the mass of water is given, then in this case the mass fraction is found according to a slightly different formula. When the volume of a dissolved substance is famous, its mass is found by the further formula: mw = V *? It follows from this that the mass fraction of a substance is calculated in the following way:? In = V *? / V *? + M (H2O)

4. Finding the mass fraction of a substance is repeatedly carried out for utilitarian purposes. For example, when bleaching a material, you need to know the concentration of perhydrol in a peroxide solution. In addition, an accurate calculation of the mass fraction is occasionally required in medical practice. In addition to formulas and an approximate calculation of the mass fraction, in medicine, experimental verification with the help of devices is also used, which makes it possible to reduce the likelihood of errors.

5. There are several physical processes during which the mass fraction of a substance and the composition of a solution change. The first of them, called evaporation, is the reverse process of dissolution of a substance in water. In this case, the solute remains, and the water is completely evaporated. In this case, the mass fraction cannot be measured - there is no solution. The opposite process is the dilution of a concentrated solution. The more it is diluted, the more strongly the mass fraction of the substance dissolved in it decreases. Concentration is a partial evaporation in which not every water evaporates, but only a part of it. At the same time, the mass fraction of the substance in the solution increases.

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What is mass fraction element? From the name itself, it is allowed to realize that this is a value indicating the ratio of the mass element, which is part of the substance, and the total mass of this substance. It is expressed in fractions of a unit: percent (hundredths), ppm (thousandths), etc. How is it allowed to calculate the mass of some element ?

Instructions

1. For clarity, consider the carbon that is well-known to everyone, without which there would be no organic matter. If carbon is a pure substance (say, diamond), then its mass share can be bravely taken as a unit or 100%. Of course, diamond also contains impurities of other elements, but in most cases, in such small numbers that they can be neglected. But in such modifications of carbon as coal or graphite, the content of impurities is quite high, and such ignoring is unacceptable.

2. If carbon is part of a difficult substance, you need to do it in a further way: write down the exact formula of the substance, after that, knowing the molar masses of each element included in its composition, calculate the exact molar mass of this substance (of course, taking into account the "index" of any element). Later this determine the mass share by dividing the total molar mass element per molar mass of the substance.

3. Let's say it is necessary to detect a mass share carbon in acetic acid. Write the formula for acetic acid: CH3COOH. To simplify calculations, convert it to the form: С2Н4О2. The molar mass of this substance consists of the molar masses of the elements: 24 + 4 + 32 = 60. Accordingly, the mass fraction of carbon in this substance is calculated as follows: 24/60 = 0.4.

4. If you need to calculate it as a percentage, respectively, 0.4 * 100 = 40%. That is, every kilogram of acetic acid contains (approximately) 400 grams of carbon.

5. Of course, in absolutely the same way it is allowed to detect the mass fractions of all other elements. Let's say the mass fraction of oxygen in the same acetic acid is calculated as follows: 32/60 = 0.533 or approximately 53.3%; and the mass fraction of hydrogen is 4/60 = 0.666 or approximately 6.7%.

6. To check the accuracy of the calculations, add the percentages of all elements: 40% (carbon) + 53.3% (oxygen) + 6.7% (hydrogen) = 100%. The account came together.

You have a two-hundred-liter barrel. You plan to fill it entirely with diesel fuel, which you use to heat your mini-boiler room. And how much will it weigh, filled with solarium? Now let's calculate.

You will need

• - table of specific gravity of substances;
• - knowledge to make the simplest mathematical calculations.

Instructions

1. In order to find the mass of a substance by its volume, use the formula for the specific density of the substance. P = m / v here p is the specific density of the substance; m is its mass; v is the occupied volume. We will consider the mass in grams, kilograms and tons. Volumes in cubic centimeters, decimeters and measures. And the specific density, respectively, in g / cm3, kg / dm3, kg / m3, t / m3.

2. It turns out, according to the terms of the problem, you have a two-hundred-liter barrel. This means: a barrel with a capacity of 2 m3. It is called two-hundred-liter, because water, with its specific gravity equal to one, contains 200 liters in such a barrel. You are worried about the mass. Consequently, bring it to the first place in the presented formula m = p * v On the right side of the formula, the value of p is unknown - the specific gravity of diesel fuel. Find it in the directory. It is even easier to enter a search query on the Internet “specific gravity of diesel fuel”.

3. Found: the density of summer diesel fuel at t = +200 C - 860 kg / m3. Substitute the values ​​in the formula: m = 860 * 2 = 1720 (kg) 1 ton and 720 kg - this is how much 200 liters of summer diesel fuel weigh. Having hung the barrel in advance, it is allowed to calculate the total weight and estimate the capacity of the rack under the barrel with solarium.

4. In rural areas, it can be useful to first calculate the mass of firewood required by cubic capacity in order to determine the carrying capacity of the transport on which this firewood will be delivered. For example, you need at least 15 cubic meters for the winter. meters of birch firewood. Look in the reference books for the density of birch firewood. This is: 650 kg / m3. Calculate the mass by substituting the values ​​in the same formula for specific gravity. M = 650 * 15 = 9750 (kg) Now, based on the carrying capacity and capacity of the body, you can determine the type of vehicle and the number of trips.

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Note!
Older people are more familiar with the concept of specific gravity. Specific gravity of a substance is the same as specific gravity.

The mass fraction of a substance shows its contents in a more difficult structure, say, in an alloy or mixture. If the total mass of a mixture or alloy is famous, then knowing the mass fractions of the constituent substances it is possible to detect their masses. To find the mass fraction of a substance, it is permissible to know its mass and the mass of each mixture. This value can be expressed in fractions or percentages.

You will need

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

Instructions

1. Determine the mass fraction of the substance that is in the mixture through the mass of the mixture and the substance itself. To do this, with the support of weights, determine the masses of the substances that make up the mixture or alloy. Then fold them up. Take the resulting mass as 100%. In order 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 total by 100% (?% = (M / M)? 100%). Let's say that 20 g of sodium chloride is dissolved in 140 g of water. In order to find the mass fraction of salt, add the masses of these 2 substances M = 140 + 20 = 160 g. After that, find the mass fraction of the substance?% = (20/160)? 100% = 12.5%.

2. If you need to find the table of contents or the mass fraction of an element in a substance with a known formula, use the periodic table of chemical elements. On it, find the nuclear masses of the elements that make up the substance. If one element occurs several times in the formula, multiply its nuclear mass by this number and add up the results. This is the molecular weight of the substance. In order 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 mass of a given substance M. Multiply the total by 100% (?% = (M0 / M)? 100%).

3. Let's say, determine the mass fraction of chemical elements in copper sulfate. Copper sulfate (copper II sulfate), has the chemical formula CuSO4. The nuclear masses of the 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 oxygen atoms. Calculate the molecular weight of the substance, it is equal to the sum of the mass numbers of the substances making up the molecule 64 + 32 + 64 = 160. Determine the mass fraction of copper (Cu) in the composition of copper sulfate (?% = (64/160)? 100%) = 40%. According to the same thesis, it is allowed to determine the mass fractions of all elements in this substance. Mass fraction of sulfur (S)?% = (32/160)? 100% = 20%, oxygen (O)?% = (64/160)? 100% = 40%. Please note that the sum of all mass fractions of the substance must be 100%.

Mass fraction is the percentage of a component in a mixture or an element in a substance. It is not only schoolchildren and students who face the problems of calculating the mass fraction. The knowledge to calculate the percentage concentration of a substance finds absolutely utilitarian use in real life - where it is required to draw up solutions - from construction to cooking.

You will need

• - Mendeleev table;
• - formulas for calculating the mass fraction.

Instructions

1. Calculate the mass share a-priory. Because the mass of a substance is composed of the masses of the elements that make it up, then on share any constituent element is brought to some part of the mass of the substance. The mass fraction of the solution is equal to the ratio of the mass of the solute to the mass of each solution.

2. The mass of the solution is equal to the sum of the masses of the solvent (traditionally water) and the substance. The mass fraction of the mixture is equal to the ratio of the mass of the substance to the mass of the mixture containing the substance. Multiply the resulting total by 100%.

3. Detect massive share output with the support of the formula? = md / mp, where mp and md are the values ​​of the assumed and actual obtained yield of the substance (mass), respectively. Calculate the assumed mass from the reaction equation using the formula m = nM, where n is the chemical number of the substance, M is the molar mass of the substance (the sum of the nuclear masses of all the elements included in the substance), or by the formula m = V?, Where V is the volume of the substance, ? - its density. The number of the substance, in turn, if necessary, replace with the formula n = V / Vm, or also find from the reaction equation.

4. Massive share calculate the element of difficult substance with the help of the periodic table. Add up the nuclear masses of all the elements that make up the substance, multiplying by indices if necessary. This will give you the molar mass of the substance. Find the molar mass of an element from the periodic table. Calculate the mass share by dividing the molar mass of the element by the molar mass of the substance. Multiply by 100%.

Helpful advice
Pay attention to the physical process, the one that takes place. When evaporating, do not calculate the mass fraction, because there is no solution (water or any other liquid). Do not forget that during concentration, on the contrary, called partial evaporation, the mass fraction of the substance increases. If you dilute a concentrated solution, the mass fraction decreases.

The mass fraction of any component in a substance shows which part of the total mass is brought into the atoms of this particular element. Applying the chemical formula of a substance and the periodic table of Mendeleev, it is allowed to determine the mass fraction of all of the elements included in the formula. The resulting value is expressed as a regular fraction or as a percentage.

Instructions

1. If you want to determine the mass fraction of each element that composes it by a chemical formula, start by calculating the number of atoms, which is brought to all of the elements. Let's say the chemical formula of ethanol is written as follows: CH? -CH? -OH. And the chemical formula of dimethyl ether is CH? -O-CH ?. The number of oxygen (O) atoms in any of the formulas is equal to one, carbon (C) - two, hydrogen (H) - six. Please note that these are different substances, because the identical number of atoms of the entire element in their molecules is located differently. Nevertheless, the mass fractions of the whole element in dimethyl ether and ethanol will be identical.

2. Using the periodic table, determine the nuclear mass of each element in the chemical formula. Multiply this number by the number of atoms of each element calculated in the previous step. In the example used above, the formula each contains one oxygen atom, and its atomic mass from the table is 15.9994. There are two carbon atoms in the formula, its atomic mass is 12.0108, which means that the total weight of the atoms will be 12.0108 * 2 = 24.0216. For hydrogen, these numbers are 6, 1.00795 and 1.00795 * 6 = 6.0477, respectively.

3. Determine the total atomic mass of the entire molecule of the substance - add the numbers obtained in the previous step. For dimethyl ether and ethanol, this value should be equal to 15.9994 + 24.0216 + 6.0477 = 46.0687.

4. If the total is required to be obtained in fractions of one, make up an individual fraction for each element in the formula. Its numerator should contain the value calculated for this element in the second step, and put the number from the third step in the denominator of the entire fraction. The resulting ordinary fraction can be rounded to the required degree of accuracy. In the example used above, the mass fraction of oxygen is 15.9994 / 46.0687 × 16/46 = 8/23, carbon - 24.0216 / 46.0687 × 24/46 = 12/23, hydrogen - 6.0477 / 46, 0687? 6/46 = 3/23.

5. To obtain the total in percentage, convert the resulting ordinary fractions into decimal format and increase it by a factor of one hundred. In the example used, the mass fraction of oxygen in percent is expressed by the number 8/23 * 100 × 34.8%, carbon - 12/23 * 100 × 52.2%, hydrogen - 3/23 * 100 × 13.0%.

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Note!
The mass fraction cannot be more than one or, if it is expressed as a percentage, more than 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% / 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 a substance A x B y in fractions of a unit:

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 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.

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%.

At the moment, about 120 different chemical elements are known, of which no more than 90 can be found in nature. The variety of different chemical substances around us is incommensurably greater than this number.
This is due to the fact that very rarely chemical substances consist of separate, unconnected atoms of chemical elements. Under normal conditions, such a structure is possessed by only a small number of gases called noble gases - helium, neon, argon, krypton, xenon and radon. More often than not, chemical substances do not consist of scattered atoms, but of their combinations into various groupings.
That is, the atoms of most chemical elements are able to bond with each other. Most often, this results in molecules - particles, which are groups of two or more atoms. For example, the chemical hydrogen is made up of hydrogen molecules, which are formed from atoms as follows:

Figure 3. Formation of a hydrogen molecule

Atoms of different chemical elements can also form bonds with each other, for example, when an oxygen atom interacts with two hydrogen atoms, a water molecule is formed:

Figure 4. Formation of a water molecule

Since it is inconvenient to draw atoms of chemical elements every time and sign them, chemical formulas were invented to reflect the composition of the molecules. For example, the formula for molecular hydrogen is written as H2, where the number 2, written in subscript to the right of the hydrogen atom symbol, denotes the number of atoms of this type in a molecule. Thus, the formula of water can be written as H 2 O. The unit, which should show the number of oxygen atoms in a molecule, according to the rules adopted in chemistry, is not written. The numbers denoting the number of atoms in one molecule are called indices.
Let's consider a few more examples of chemical formulas of substances. So, the ammonia formula is written as NH 3, which means that each ammonia molecule consists of one nitrogen atom and three hydrogen atoms.
Often there are molecules in which you can count several identical groups of atoms. For example, from the formula of aluminum sulfate Al 2 (SO 4) 3, it can be concluded that the molecule of this substance contains two groups of SO 4 atoms.
Thus, the chemical formulas of substances unambiguously characterize both their qualitative and quantitative composition.
From all of the above, the law of the constancy of the composition of a substance, established back in 1808 by the French scientist Joseph Louis Proust, logically follows, and it sounds like this:

Any pure chemical substance has a constant qualitative and quantitative composition, regardless of the method of obtaining this substance.

Since any chemical substance is a collection of molecules of the same composition, this leads to the fact that the proportions between the atoms of chemical elements in any portion of the substance are the same as in one molecule of this substance. All differences in the chemical properties of substances depend on the quantitative and qualitative composition of the molecules and, in addition, on the order of the bonds between atoms, if possible.
Thus, the following definition of the term molecule can be given:

A molecule is the smallest particle of any chemical that has its chemical properties.

Similar to the relative atomic mass, there is also such a concept as the relative molecular weight M r:

The relative molecular weight (M r) of a substance is the ratio of the mass of one molecule of this substance to one twelfth of the mass of one carbon atom (1 atomic mass unit).

Thus, it is obvious that the relative molecular weight is the sum of the relative atomic masses of the elements, each of which is multiplied by the number of atoms of a given specific type in one molecule. So, for example, the relative molecular weight of the nitric acid molecule HNO 3 is the sum of the relative atomic weight of hydrogen, the relative atomic weight of nitrogen, and three relative atomic masses of oxygen:

To describe the qualitative and quantitative composition of a substance, such a concept as the mass fraction of a chemical element is used w (X).

What is mass fraction? For example, the 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 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 in this. 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, there are rather coarse meanings, 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 the calculations !!

Solution refers to a homogeneous mixture of two or more components.

The substances, by mixing which the solution is obtained, call it components.

Among the components of the solution are distinguished solute which may not be one, and solvent... For example, in the case of a solution of sugar in water, sugar is a solute and water is a solvent.

Sometimes the concept of a solvent can be applied equally to any of the components. For example, this applies to those solutions that are obtained by mixing two or more liquids, ideally soluble in each other. So, in particular, in a solution consisting of alcohol and water, both alcohol and water can be called a solvent. However, most often in relation to aqueous solutions, it is customary to call water a solvent, and a second component as a dissolved substance.

As a quantitative characteristic of the composition of the solution, the most often used concept is mass fraction substances in solution. The mass fraction of a substance is the ratio of the mass of this substance to the mass of the solution in which it is contained:

where ω (in-va) - mass fraction of the substance contained in the solution (g), m(in-va) - the mass of the substance contained in the solution (g), m (solution) - the mass of the solution (g).

From formula (1) it follows that the mass fraction can take values ​​from 0 to 1, that is, it is a fraction of a unit. In this regard, the mass fraction can also be expressed as a percentage (%), and it is in this format that it appears in almost all problems. The mass fraction, expressed as a percentage, is calculated using a formula similar to formula (1) with the only difference that the ratio of the mass of the solute to the mass of the entire solution is multiplied by 100%:

For a solution consisting of only two components, the mass fraction of the solute ω (r.v.) and the mass fraction of the solvent ω (solvent) can be calculated accordingly.

The mass fraction of the solute is also called concentration of solution.

For a two-component solution, its mass consists of the masses of the solute and the solvent:

Also, in the case of a two-component solution, the sum of the mass fractions of the solute and the solvent is always 100%:

Obviously, in addition to the formulas written above, you should know all those formulas that are mathematically derived directly from them. For example:

It is also necessary to remember the formula that relates the mass, volume and density of a substance:

m = ρ ∙ V

and you also need to know that the density of water is 1 g / ml. For this reason, the volume of water in milliliters is numerically equal to the mass of water in grams. For example, 10 ml of water has a mass of 10 g, 200 ml - 200 g, etc.

In order to successfully solve problems, in addition to knowing the above formulas, it is extremely important to bring the skills of their application to automatism. This can be achieved only by solving a large number of different problems. Problems from real examinations of the Unified State Exam on the topic "Calculations using the concept of" mass fraction of a substance in a solution "" can be solved.

Examples of problems for solutions

Example 1

Calculate the mass fraction of potassium nitrate in a solution obtained by mixing 5 g of salt and 20 g of water.

Solution:

The dissolved substance in our case is potassium nitrate, and the solvent is water. Therefore, formulas (2) and (3) can be written respectively as:

From the condition m (KNO 3) = 5 g, and m (H 2 O) = 20 g, therefore:

Example 2

What mass of water must be added to 20 g of glucose to obtain a 10% glucose solution.

Solution:

From the conditions of the problem it follows that the solute is glucose, and the solvent is water. Then formula (4) can be written in our case as follows:

From the condition we know the mass fraction (concentration) of glucose and the mass of glucose itself. Denoting the mass of water as x g, we can write down the following equivalent equation based on the formula above:

Solving this equation, we find x:

those. m (H 2 O) = x g = 180 g

Answer: m (H 2 O) = 180 g

Example 3

150 g of a 15% sodium chloride solution was mixed with 100 g of a 20% solution of the same salt. What is the mass fraction of salt in the resulting solution? Indicate your answer to the nearest whole.

Solution:

To solve problems for the preparation of solutions, it is convenient to use the following table:

where m r.v. , m solution and ω r.v. - the values ​​of the mass of the solute, the mass of the solution and the mass fraction of the solute, respectively, individual for each of the solutions.

From the condition we know that:

m (1) solution = 150 g,

ω (1) r.v. = 15%,

m (2) solution = 100 g,

ω (1) r.v. = 20%,

Let's insert all these values ​​into the table, we get:

We should remember the following formulas required for calculations:

ω r.v. = 100% ∙ m r.v. / m solution, m r.v. = m solution ∙ ω r.v. / 100%, m solution = 100% ∙ m r.v. / ω r.v.

We begin to fill in the table.

If only one value is missing in a row or column, then it can be calculated. An exception is a line with ω r.v., knowing the values ​​in two of its cells, the value in the third cannot be calculated.

The first column is missing a value in only one cell. So we can calculate it:

m (1) r.v. = m (1) r-ra ∙ ω (1) r.v. / 100% = 150 g ∙ 15% / 100% = 22.5 g

Similarly, we know the values ​​in two cells of the second column, which means:

m (2) r.v. = m (2) r-ra ∙ ω (2) r.v. / 100% = 100 g ∙ 20% / 100% = 20 g

Let's enter the calculated values ​​into the table:

Now we know two values ​​in the first line and two values ​​in the second line. So we can calculate the missing values ​​(m (3) r.v. and m (3) r-ra):

m (3) r.v. = m (1) r.v. + m (2) r.v. = 22.5 g + 20 g = 42.5 g

m (3) solution = m (1) solution + m (2) solution = 150 g + 100 g = 250 g.

Let's enter the calculated values ​​into the table, we get:

Now we have come close to calculating the required value of ω (3) r.v. ... In the column where it is located, the contents of the other two cells are known, which means we can calculate it:

ω (3) r.v. = 100% ∙ m (3) r.v. / m (3) solution = 100% ∙ 42.5 g / 250 g = 17%

Example 4

To 200 g of a 15% sodium chloride solution was added 50 ml of water. What is the mass fraction of salt in the resulting solution. Indicate your answer to the nearest hundredth _______%

Solution:

First of all, you should pay attention to the fact that instead of the mass of added water, we are given its volume. Let's calculate its mass, knowing that the density of water is 1 g / ml:

m ext. (H 2 O) = V ext. (H 2 O) ∙ ρ (H 2 O) = 50 ml ∙ 1 g / ml = 50 g

If we consider water as a 0% sodium chloride solution containing, respectively, 0 g of sodium chloride, the problem can be solved using the same table as in the example above. Let's draw such a table and insert the values ​​we know into it:

In the first column, two values ​​are known, which means we can calculate the third:

m (1) r.v. = m (1) r-ra ∙ ω (1) r.v. / 100% = 200 g ∙ 15% / 100% = 30 g,

In the second line, two values ​​are also known, which means we can calculate the third:

m (3) solution = m (1) solution + m (2) solution = 200 g + 50 g = 250 g,

Let's enter the calculated values ​​into the corresponding cells:

Now two values ​​in the first line have become known, which means we can calculate the value of m (3) r.v. in the third cell:

m (3) r.v. = m (1) r.v. + m (2) r.v. = 30 g + 0 g = 30 g

ω (3) r.v. = 30/250 ∙ 100% = 12%.